Schoolwork

narangkar and painting

I peevishly plodded into the Philadelphia Museum of Art on a brisk Saturday afternoon, hung-over, not necessarily in the mood to be analyzing artwork. I had not been to a museum in ages, so I was not exactly sure what to expect. As I dragged my disheveled and tentative self throughout the building, it became apparent that I was going to have a difficult time finding a work of art that struck me enough to be able to write a three to four page paper on it. Many paintings and sculptures, while expertly crafted to the utmost detail, simply bored me (sorry Manet and Monet). Even the Picasso’s which I found to be pure eye candy, did not stir up enough emotion for me to be able to discuss them in depth.

Feeling nearly defeated and heading towards the exit, I lost my way into a room containing nothing but two solid colors (if they are even considered that); black and white. This hit me, as no other room in the entire museum was like this. After being exposed to a wide range of tones and tints for the previous hour or more, it felt like I had just stepped into a Twilight Zone of some sorts, depraved of all color. The extreme contrast of the room had truly taken me back. Unsurprisingly, these paintings were all constructed by the same artist, Ellsworth Kelly. As I examined each piece, they all seemed to exhume this sense of unity, form, and excessive calculation. Each work appeared to be precisely concocted in order to stretch the colors of black and white to the apex of their potential. Each piece showed this perfectionist character, save one.

“Tennis Court” in my opinion stood out in a room that stood out from the rest of the museum. Though it appears to be something a caveman may have doodled millions of years ago, it evoked a certain je ne sais pas within me. In passing, it looks like the most primitive piece of art in the building, something that I am sure in many minds should not even be construed as artwork. I however felt that “Tennis Court” evolves to become a surprisingly complex painting when you sit down and absorb it for an hour within its surroundings. (Fair warning: you may receive some odd glances from passers-by and museum attendants for being locked on such a “simple” painting for such a long time.)

Kelly is obviously an incredibly deliberate artist. Every other one of his works, though not detailed per say, is formulated very carefully. I can imagine him painstakingly deliberating on where to place each line and how to orient every angle on the canvas in order to get the most out of his two color palette, like some kind of mad scientist mixing chemicals to create a powerful potion. “Tennis Court” appears to be painted at a time when he may have been delusional, drunk, or on drugs; a moment when he lost his sense of extreme order.

The painting is about two feet high by one foot wide, give or take a handful of inches either way. His other paintings in the room are all bigger than this one by a relatively noticeable margin; they are all around at least two to three feet wide and high. This may suggest that “Tennis Court” was not a work Kelly necessarily wanted to be shown off, that it was more of a painting he did to experiment against his natural inclinations and was not sure how it would turn out.

To further accentuate the postulate that “Tennis Court” may not be his favorite creation, it is actually somewhat dirty and uncared for; the edges of this oil on canvas work are soiled and unfinished. It appears that Kelly probably carried this painting around town after eating lunch and his dirty fingertips tarnished the pure white color he used as the background. The texture around the edges also makes it apparent that it was not handled with the greatest of care. There appears to be some chipped paint, possibly from Kelly dropping or scraping the painting, and the grime from his unwashed hands creates somewhat of a sheen or gloss in areas, which is not visible on the meat of the painting. It’s actually a little gross thinking back on it.

Kelly could have simply put a frame around the piece to hide these blemishes, but he chose not to. He left the piece in its most bare form, which I suppose is fitting as the way the subject matter is presented is as innate as it gets. Appropriately, a pieced called “Tennis Court” portrays just that; a tennis court. However, it is not drawn the right way. I am a huge tennis aficionado, so I know exactly what a tennis court looks like, and Kelly did not paint one. I am not exactly sure what he was looking at. It appears that he drew a bird’s eye view of the court, but the way he orients the lines bothers me. I can’t tell if the middle box he drew is supposed to be the two service courts, or if it is supposed to be representative of one service court and the net. The reason that I am not able to tell is because the boxes are not the same size. One is more appropriately sized to be a service box, but the other is more rectangular, which makes me question what is supposed to be. Kelly does not give any hints by employing only two flat colors.

I am also annoyed that the shapes are placed off center. The box creating the border of the court is shifted to the right, which the service box within that box is shifted to the left. This does create a sense of balance as a whole, but the individual parts are not aligned correctly. However, when I squinted my eyes and looked at the painting from a distance, I saw nearly perfect symmetry; everything looks perfectly placed. I was surprised that it comes off as being so uniform when viewing it in this manner. The painting actually exudes the calculated characteristics of Kelly’s other works. Whether or not this is intended be would make an interesting question for debate.

Viewing “Tennis Court” in this fashion also eliminates the shoddy brushwork he employed in the painting. Squinting your eyes makes the white and black paint seem as solid and piercing as they are in his other works. When looking at the piece without a funny face, it is a totally different story. Kelly appears to use one thick brush for the entire work. He paints in what appears to be an uninterested and uncaring manner, using paint squeezed straight from the tube onto his brush. You can visibly see that he starts by drawing the outline of the court in black paint, then paints over it with white deciding that he doesn’t like how it looks, but does not even put enough effort to completely hide this “mistake” as he only uses enough white to mask the black a small degree. It looks like he then paints with wide but loose horizontal strokes of white paint to fill in the blank canvas, but does not seem to mind if the paint is of a uniform thickness throughout. He then paints the remaining outline of the tennis court in black with the same distracted brushstrokes. For whatever reason, possibly inebriation, he is not able to connect all the lines properly and leaves stay marks. Kelly again somewhat conceals these blunders with scant amounts of white paint.

If this piece was not entitled “Tennis Court,” I am not entirely certain that I would have recognized that as the subject matter. Kelly could have easily named it “Box Enclosed in Another Box” and I would have totally bought that. The painting uses only two colors and a total of eleven lines, but is able to evoke a myriad of questions and interpretations. If you look closely, Kelly does give us a hint that it is indeed a tennis court he is attempting to portray. Along the top edge of the canvas, among the smudges, you will see a tiny splotch of pale green paint. This could be construed as a stray marking, but seeing how calculated Kelly’s other works are, I have no doubt that it is part of the design. This almost microscopic green dot brings the piece together, showing that yes, this is a tennis court, no matter how rudimentary the resemblance. This technique is akin to what David does with “Death of Marat.”

I would love to know more about the background of “Tennis Court,” but I am not even able to find a picture of it online. The tag at the museum said it was painted in Paris, but other than that I know nothing about it. I would like to know exactly in what context Kelly painted it and what he was trying to achieve. None of his other paintings or works are at all similar to it in technique and outward expression. Only when viewed with squinted eyes does one see the essence of Kelly’s expression within this piece. It is quite unique that Kelly is not able to escape his style, no matter how dissimilar it appears to be from the rest of his works.

Abstract

Vaska’s complex, Ir(Cl)[P(C₆H₅)₃]₂(CO), reacts with O₂ at room temperature to form Ir(Cl)[P(C₆H₅)₃]₂(CO)(O₂) at a ratio of 3.11:1 reactant to product and with HCl to form Ir(Cl)₂[P(C₆H₅)₃]₂(CO)H at 47.7% yield. The CO stretch on the IR spectra of these compounds is found at a lower frequency than that of the CO stretch from Vaska’s complex because the additional ligands lead to increased π back-bonding. In comparison to the ³¹P NMR spectrum of Ir(Cl)[P(C₆H₅)₃]₂(CO), the signal given by the ³¹P NMR spectrum of Ir(Cl)₂[P(C₆H₅)₃]₂(CO)H is shifted upfield because of additional electronegative ligands added to the metal, which draw in electron density and deshield the phosphorus molecules. Finally, the ¹H NMR spectra of Ir(Cl)[P(C₆H₅)₃]₂(CO) and Ir(Cl)₂[P(C₆H₅)₃]₂(CO)H are nearly identical aside from a signal given off by Ir(Cl)₂[P(C₆H₅)₃]₂(CO)H at δ -15.36 representative of the Ir-H addition. This signal is seen as a triplet of quartets due to coupling with Ir and P.

Introduction

Vaska’s complex, Ir(Cl)[P(C₆H₅)₃]₂(CO), is a versatile complex because of its ability to bind other additional ligands.¹ Whereas most complexes contain 18 electrons and are considered to be saturated, Vaska’s complex contains only 16 electrons and is thus able to add certain two-electron donors to reach 18 valence electrons. It can also undergo oxidative addition in which the Ir¹ center inserts into the σ bond of certain molecules, and the oxidation state of Ir is increased while reaching 18 electrons. Oxygenation and hydrochlorination of Ir(Cl)[P(C₆H₅)₃]₂(CO) proceed in the following manners:

Scheme 1

Scheme 2

These oxidative additions are of interest because the relative ease of identifying their products. The additional ligands will both increase π back-bonding to the metal and draw in electron density. The effects of these two characteristics are apparent through IR and ³¹P NMR spectroscopy, as a weakened CO bond will cause a lowering of CO stretch frequency in an IR spectrum, and deshielded phosphorus will be shifted upfield in a ³¹P NMR spectrum.

Experimental

All syntheses were carried out in air and the reagents and solvents were purchased from commercial sources and used as received unless otherwise noted. The synthesis of Ir(Cl)[P(C₆H₅)₃]₂(CO)(O₂) (2) and Ir(Cl)₂[P(C₆H₅)₃]₂(CO)H (3) were based on reports published previously.¹

Ir(Cl)[P(C₆H₅)₃]₂(CO) (1). The ¹H NMR, ³¹P NMR, and IR spectra of (1) were taken by Dr. Graham. This compound was not synthesized but purchased commercially. ¹H NMR (CDCl₃): δ 7.25-7.97 (3 H, series of signals, -C₆H₅). ³¹P NMR (CDCl₃): δ 24.5 (s, -P(C₆H₅)₃). FTIR (ATR) ν_(CO) 1951 cm^-1 (s, C-O linkage).

Ir(Cl)[P(C₆H₅)]₂(CO)(O₂) (2). A stir bar, 1 (0.010 g, 1.28 x 10^-5 mol), and toluene (10 mL) were subsequently added to a 25 mL single neck round bottom flask. The flask was covered with a septum and the vessel was degassed with O₂ for 3 minutes. The solution was then stirred at room temperature at moderate speed for 1 h. The septum was taken of the flask and the solvent was removed via rotary evaporation so that only a few mL of solution remained. One drop of this solution was placed onto the ATR and allowed to dry before taking the IR spectrum of the complex. FTIR (ATR) ν_(CO) 1952 cm^-1 (m, C-O linkage), ν_(CO) 2000 cm^-1 (m, C-O linkage).

Ir(Cl)₂[P(C₆H₅)₃]₂(CO)H (3). 1 (0.032 g, 4.10 x 10^-5 mol), THF (10 mL), HCl (concentrated, 5 drops), and Et₂O (50 mL) were subsequently added to a 250 mL Erlenmeyer flask. The solution was swirled around for about 5 minutes to allow a whitish precipitate to form. The solution was filtered using a small frit and the precipitate was vacuum dried. The product was determined to be 3 (0.016 g, 1.96 x 10^-5 mol, 47.7% yield based on the amount of 1 used). An extension of the ¹H NMR spectra of this substance was given out by Dr. Graham. ¹H NMR (CDCl₃): δ -15.36 (tq, J_Ir, J_P, Ir-H), δ 7.24-7.91 (3 H, series of signals, -C₆H₅). ³¹P NMR (CDCl₃): δ -1.74 (s, -P(C₆H₅)₃). FTIR (ATR) ν_(CO) 1951 cm^-1 (s, C-O linkage), ν_(CO) 2021 cm^-1 (s, C-O linkage).

Results

The reaction of 1 with O₂ was not directly measured for percent yield, but could indirectly be measured via the IR spectrum of the product 2. The stretch at 1952 cm^-1 was telling of 1 and the stretch at 2000 cm^-1 was indicative of 2. The ratio of the area of these peaks was 3.11:1, reactant to product. The reaction of 2 with HCl resulted 0.016 g of product, which was determined to be 3. This translated to 1.96 x 10^-5 mol and a 47.7% yield based on the amount of 1 used. The reactants and products reacted in 1:1 ratios in both instances. The IR spectrum of 1 was used to differentiate the two stretches in the 1950 to 2000 cm^-1 region on the IR spectra of 2 and 3. The stretch around 1950 cm^-1 could be identified as the CO stretch from 1, and the stretches around 2000 cm^-1 were from the CO stretches of 2 and 3.

The ¹H NMR spectrum of 1 showed a series of signals from δ 7.25-7.97 which was representative of protons attached to the phenyl rings. The ¹H NMR spectrum of 3 had these same phenyl signals, but additionally contained a signal from the hydride at δ -15.36 that was coupled with Ir and P into a triplet of quartets. The ³¹P NMR spectrum of 1 gave a singlet peak at δ 24.5 representative of the two identical phosphorus molecules on the compound. The ³¹P NMR spectrum of 3 displayed its singlet peak shifted upfield to δ -1.74.

Discussion

The ratio of formation of 2 seems reasonable, but it is unable to be determined whether or not that is a high or low ratio given the reaction time. If the solution was given more time to react, perhaps more product would have formed. If the flask was degassed with O₂ for a longer amount of time, it is likely that would also favor the formation of more product, as additional oxygen would increase the interactions with 1 to form 2. In retrospect, the solution could have been stirred at more rigorous speed, as that would also likely increase the interactions between 1 and O₂. The percent yield of 3 was close to 50%, which seems fairly good, though not all of the product that was weighed out actually was 3. It can be seen on the IR spectrum of the product that a significant amount of 1 remained, due to the stretch visible around 1950 cm^-1.

The IR spectra for 1, 2, and 3 are all very similar. The IR spectrum of 1 shows a single CO stretch at 1951 cm^-1. The IR spectra of 2 and 3 also show stretches around 1950 cm^-1, which suggests that those products obtained contained unreacted 1. The IR spectra of 2 and 3 also contain a second CO stretch around 2000 cm^-1. These stretches are representative of desired product. The lowered frequency is due to increased π back-bonding from the addition of O₂ and HCl to the Ir in 1 in each case. This strengthens the Ir-C bond and weakens the C-O bond causing the shifts in frequency.¹

The ¹H NMR spectra of 1 and 3 are nearly identical save for the signal given off by the Ir-H bond by 3 at δ -15.36. This signal is first coupled with phosphorus, which has a spin of 1/2.¹ There are two phosphorus, so using the equation 2nI + 1, the value of 3 is obtained. Because the spin is 1/2, this means that 3 peaks will be observed in a 1:2:1 ratio. The hydrogen is then coupled to iridium, which has a spin of 3/2.² There is only one iridium, so using the equation 2nI + 1, the value of 4 is obtained. Because the spin is 3/2, this means that the 4 peaks will be observed in a 1:1:1:1 ratio.³ This explains the appearance of the hydride signal.

The ³¹P NMR spectrum of 3 has a singlet peak shifted upfield from that of the ³¹P NMR spectrum of 1. This is due to the electronegativity of the hydrogen and chlorine added to the metal, which draw electron density away from the phosphorus molecules leaving them less shielded. The oxidation state of Ir in complex 1 is +1 while being +3 in complexes 2 and 3. Its electron count in 1 is 16 electrons, while its electron count in 2 and 3 is 18 electrons.

Conclusion

The main purposes of the experiments were to synthesize 2 and 3, confirm their structures by comparing their various spectra to those of 1, and to determine their percent yields or reactant to product ratios. The ratio of reactant to product for 2 was 3.11:1 which was obtained from the ratio of the areas of the two CO stretches on its IR spectrum representative of reactant and product. The percent yield of 3 was calculated to 47.7%, but was in reality lower because of CO stretches on its IR spectrum representative of 1. The visibility of this stretch means the reaction did not go to completion.

The structures of 2 and 3 were somewhat validated by their IR spectra, which gave CO stretches around 2000 cm^-1. It was expected to see CO stretches for those compounds in this area because the additional ligands would cause increased π back-bonding, making the C-O bond weaker and thus lowering the frequency.¹ A series of peaks seen on both the ¹H NMR spectra of 1 and 3 around δ 7.24-7.91 is suggestive of phenyl groups. The only notable difference between the ¹H NMR spectra of 1 and 3 is the addition of a triplet of quartets at δ -15.36 for compound 3. The splitting of the peaks is due to coupling of the proton from the Ir-H bond to Ir and to the two P. The P split the signal into triplets of 1:2:1 ratio and the Ir split those signals into quartets of 1:1:1:1 ratio. Finally, the comparison of the 1 and 3 ³¹P NMR spectra seem to confirm the identity of 3 as the singlet seen in the spectrum of 1 is shifted upfield in the spectrum of 3. This is due to the addition of H and Cl to the compound, which are electronegative and draw electron density away from the P, leaving it deshielded.

References

(1) Angelici, R. J.; Girolami, G. S.; Rachufuss T. B. Synthesis and Technique in Inorganic Chemistry: A Laboratory Manual; University Science Books: Sausilito, CA, 1999; pp 189-195, 259.

(2) http://www.webelements.com/iridium/nmr.html

(3) http://en.wikipedia.org/wiki/NMR_spectroscopy

Purpose

To develop an understanding of how light is refracted, to apply the concept of refraction to the study of how thin lenses form images, to learn to draw ray diagrams to assist in the predicting the locations of images formed by spherical thin lenses, and to determine the focal length of a converging lens using three different methods.

Hypothesis

When light hits the convex lens, it will refract and converge at a point in front of lens that will be construed from the rays diverged behind the lens. The distance between this point of convergence and the lens is the focal length, which should be similar in value to an indirect measurement of the focal length of the converging lens by varying the distance between the lens and an object. Using the distance between the lens and object and the lens and projected image, the focal length will be able to be determined using the thin lens equation 1/p + 1/q = 1/f. As the object is moved further past the curvature, the image will become smaller. The closer the object is moved to the lens between the curvature and focal length, the image will become larger. While the object is beyond the focal length, the image will be real and inverted. Once the object is placed between the focal length and lens, the image will become virtual and upright. Finally, the focal length interpreted using the conjugate method should also be similar to the previous focal length measurements.

Labeled Diagrams

See attached sheet.

Data

Part 1:

Part 2A:

f = 7.70 cm

Part 2B:

f_average = 7.40 cm

Part 2C:

f = 7.41 cm

Questions

1. What is the measured value of the focal length and how does it compare with the given value of focal length for the length for the lens?

The measured focal length is 7.70 cm which is fairly close to the given value of the focal length, 7.50 cm. The percent difference is 2.63%.

2. For each p and q in your data table above, calculate f. Record in your data table.

See data table.

3. Calculate and record the average value of your f’s.

The average value of the focal lengths is 7.40 cm.

4. How does the average focal length compare with the focal length printed on the lens? What is the percent difference?

The average focal length calculated is slightly less than the focal length printed on the lens. The percent difference is 1.34%.

5. Calculate the focal length of the lens using f = (D² – d²) / 4D where D is the distance between the object light and the image screen and d is the distance between the two conjugate positions.

D = 51.1 cm and d = 33.1 cm, so f = 7.41 cm.

6. How does this value for the focal length compare to the given value of the focal length for the lens? What is the percent difference?

This value for the focal length is again slightly less than the given focal length of the lens. The percent difference is 1.21%.

7. How do your focal lengths calculated from Parts 2A, 2B, and 2C compare? What is the percent difference between f from 2A to 2B? 2A to 2C? 2B and 2C?

The focal lengths from part 2B and 2C are nearly identical, while 2A is a tad larger than each of them. The percent difference between f from 2A to 2B is 3.97%, from 2A to 2C is 3.84%, and from 2B and 2C is 0.135%.

Conclusion

During part 1 of the experiment, ray diagrams of thin lenses were constructed for the following scenarios: an object beyond the curvature, an object at the curvature, an object between the curvature and focal length, an object at the focal length, and an object between the focal length and lens itself. The image size, orientation, location, and realness were predicted and recorded for each scenario. These predictions were used to aid with part 2B of the experiment.

During the half of the experiment, the focal length of a positive lens was measured in three different manners. The first of these methods, part 2A, used the application of a direct measurement to find the focal length. Equipment was set up on the optics bench so that light shone through a parallel ray lens, slit plate, and 75 mm convex lens onto a ray table. The parallel ray lens was first adjusted in order to align the light rays in a parallel manner before placing the 75 mm convex lens in front of the ray table. The light rays refracted through the lens and diverged onto the ray table. The outermost rays were traced on a piece of paper and were extended to meet at a focal point. The distance between this focal point and the lens was measured as 7.70 cm and recorded as the focal length. This was 2.63% difference from the given value of 7.50 cm as the focal length of the lens. This error can be attributed in part to difficulty keeping the tracing paper in place. It undoubtedly shifted some during tracing of the light rays. It was also difficult decipher the exact distance from that drawn point to the lens, as they were not on the same plane; the ray table was elevated and at an angle in relation to the lens. These attributions are most likely what led to that slight error.

During part 2B, the thin lens equation, 1/p + 1/q = 1/f, was used to measure the focal length. The crossed arrow target was placed at five positions beyond the measured focal length from of the lens part 2A. The distance from the lens to object (crossed arrow target) and from the lens to focused image were recorded for each instance. As the object was moved further away from the lens, the image became smaller, and as it was moved closer to the lens, the image became larger. The image was real and inverted in all cases. The average focal length from these recordings was calculated to be 7.40 cm, which was 1.34% different than the given focal length of the lens. The minor error could be attributed to difficulty locating the exact position where the image was truly focused; there was not definitive way to tell if the image was focused or not. There was likely some error in the interpretation of the positioning of the instruments as well, due to their thickness. Each measurement may have been misread by a couple tenths of a centimeter.

During part 2C, the conjugate method was used to measure the focal length. The method called for the crossed arrow target to be placed directly in front of the light source with the viewing screen at the opposite end of the optics bench, as far away as possible. The 75 mm convex lens was positioned between the object and viewing screen, adjacent to the crossed arrow target. The lens was slowly moved towards the viewing screen until a large focused image came into picture on the viewing screen. This positioning was noted and recorded as the first conjugate position. The lens was then moved towards the viewing screen until a minute focused image came into picture. This positioning was noted and recorded as the second conjugate position. The distance between these two positions was recorded as d and the distance between the crossed arrow target and viewing screen was recorded as D. These values were subbed into the equation f = (D² – d²) / 4D to find the focal length. It was calculated to be 7.41 cm using this method, which is 1.21% different than the given focal length. Error from this part of the experiment could again be attributed to possibly not getting the image in perfect focus, which would through off the positioning. Moreover, it was also difficult to read the exact positioning of the lens, object, and image as these apparatuses all had a thickness to them. As in part 2B, there may have been a couple tenths of a centimeter error in each reading. The measured and calculated focal lengths from all three methods were fairly consistent. The focal lengths from part 2B and 2C were nearly identical, while 2A was a small amount larger than each of them. The percent difference between f from 2A to 2B was 3.97%, from 2A to 2C was 3.84%, and from 2B and 2C was only 0.135%.

Equations

C = 2f

1/p + 1/q = 1/f

f = (D² – d²) / 4D

Percent Difference = |x₁ – x₂| / (x₁ + x₂)/2 x 100%

Abstract

Self-enhancement is the desire to maintain and cultivate positive feelings of the self. It is the driving force behind the search for self-knowledge, and is thus the focal point of much clinical research. While several researchers suggest that self-enhancement is integral to an individual’s well-being, emerging research has shown convincing evidence that self-enhancement can be detrimental to one’s mental health, social standing, and physical well-being. The conflicting findings call for analytic measures of the experimental procedures used in these cases to decipher which theories can be withheld.

The Mental, Physical, and Social Implications of Self Enhancement

Self-enhancement is thought to be the foremost motive in the perpetual search for self-knowledge (Sedikides, 1993). It is defined as a desire to magnify positive aspects of self-conceptions while distancing oneself from negative feedback and information. The motive is driven by a fundamental need to maximize feelings of self-worth; to feel good about oneself (Brown, 1998). This pursuit of a positive self construct is an active undertaking, as individuals are quite selective in their interpretations of their surroundings (Brown; Sedikides & Gregg, 2007). These biased views of the self are maintained by several tendencies exhibited by individuals in moments of self-enhancement.

A number of these positivist strategies have been detailed in the literature. Self-serving bias helps to maintain and develop positive views of the self by attributing positive outcomes as being internally based, but the negative consequences of actions as being externally caused (Sedikides & Gregg, 2007). In other words, individuals are inclined to credit successes to their disposition and shortcomings to their environment. In the cases of others, individuals tend to apply the opposite labeling, meaning that they accredit the character of others to their faults and the environment to their fortunes (Brown, 1998). Mnemic neglect is a strategy in which the individual self-enhances via a selective memory; they are more likely to remember instances of praise rather than criticism (Brown; Sedikides & Gregg). Strategic construal is also used as a method of self-enhancement by creating a concept of the world based on the individual’s strengths and weaknesses. They diagnose abilities they hold as being more telling of their selves than skills they lack. Sedikides and Gregg go on to discuss several more of the self-enhancing tendencies individuals exhibit.

While knowledge of the self construed from self-enhancement motives is often inaccurate, these illusionary interpretations are believed to be essential for well-being (Taylor & Brown, 1988). Holding accurate views of the self is not indicative of the typical individual, who holds of overly positive self-evaluations, exaggerated perceptions of control, and unrealistic optimism. More people see themselves as being above average than being below average, which is not statistically possible. Individuals who gamble perceive to have control over the outcomes of games of chance, and most test subjects see their future as being brighter than that others’. Despite the irrationality of such individuals, Taylor and Brown suggest that these applications of self-enhancement are actually beneficial to mental health.

Individuals who hold illusionist views are reported to be more happy that individuals who do not carry these views of themselves (Taylor & Brown, 1988). There is a correlation between self-enhancement and self-esteem, thus those individuals that self-enhance tend to be more content. Overly positive views are also correlated with better acuity in social settings (Taylor & Brown). Again, self-enhancement leads to higher levels of self-esteem, and thus individuals displaying those characteristics fare better in settings of social interaction. Positive illusions are also believed to promote productivity. Taylor and Brown say of overly positive views “First, these illusions may facilitate intellectually creative functioning itself; second, they enhance motivation, persistence, and performance” (pp. 198). It is thought that self-enhancement can facilitate the organizational storage of memory, and that increased levels of optimism foster elevated work ethic.

Further bolstering the belief that self-enhancement is advantageous, there have been studies showing that self-enhancement is beneficial to one’s health (Taylor, Lerner, Sherman, Sage, & McDowell, 2003). AIDS patients holding overly positive views of their situation have been found to have a less rapid course of illness and live longer than patients who do not carry excessively optimistic views of their state. High self-enhancers are also found to be physiologically less effected by stress. They tend to have lower cardiovascular responses, quicker cardiovascular recovery, and lower cortisol levels when exposed to stressful stimuli than low self-enhancers. The use of self-enhancement seems to aid not only in their mental well-being, but physical well-being as well.

If these findings seem to suggest that self-enhancement is a key to health and happiness, then one could postulate that self-enhancement is the panacea for all of life’s problems. The more one builds themselves up and the more farfetched positive illusions they hold, the more prosperous they will be. However, in contrast to the aforementioned research, there are numerous findings that suggest that the exact opposite; that self-enhancement can be detrimental to one’s well-being. Attempts to improve feelings of self-worth and merit through self-enhancement can lead to poor mental health, negative peer evaluations, and increased risks of bodily harm.

Mental Health

Colvin, Block, and Funder challenge the discoveries that Taylor and Brown lay out in their article (1988), finding in their own research that self-enhancement is not correlated with well-being, but rather poor social skills and psychological maladjustment (1995). They argue that Taylor and Brown did not employ adequate criteria of self-enhancement in their research; that their means of measuring self-enhancement were too broad. Instead of using generalizations in measurements of self-enhancement, a comparison between an individual’s self-description and some external criteria would yield far more accurate and valid measures of the characteristic. When using unspecific measures, individuals may self-enhance in defining areas of their self-concept, that is to say self-relevant areas, which may not be representative of what the experimenter was trying to elicit in their experiment.

Using more specific criteria for measuring self-enhancement, research shows that self-enhancers are described as being “guileful and deceitful, distrustful of people, and as having a brittle ego-defense system” (Colvin et al., 1995, pp. 1154). Individuals less apt to self-enhancement are seen as being more respected, intelligent, and consistent people. A negative correlation between self-enhancement and ego-resiliency is also noted. Overall, it is found that negative views observers hold of self-enhancers suggest they are maladjusted individuals, which runs contrary to the theses of Taylor and Brown (1988). While self-enhancement may boost one’s self-esteem in the short run, in the long run this boosting of one’s moral can cause one to alienate themselves from their peers (Colvin et al., 1995).

Other studies have further explored the short-term and long-term mental implications of self-enhancement (Robins & Beer, 2001). Again, the proposition in this research is that Taylor and Brown (1988) inadequately measured positive illusions in their studies, and thus their conclusions should not be considered valid. These more recent findings seem to suggest that self-enhancement is linked to disinterest in academic contexts, lowered levels of self-esteem, and decreased well-being (Robins & Beer). Narcissism also appears to be linked to overly positive views of the self. In addition, Robins and Beer find that self-enhancers do not necessarily perform better academically than non-self-enhancers, and that self-enhancers are no more likely to graduate from college than non-self-enhancers, which seems to disprove the theory that positive illusions are motivational. In conclusion, it is found that self-enhancement may be beneficial to mental health and well being in the short-run, but in the long-run there appear possible negative implications for the self.

Social Well-Being

Self-enhancement, especially in group situations, can be costly to one’s ulterior motives (Anderson, Ames, & Gosling, 2008). Individuals who exhibit this type of behavior are seen as disruptive to group processes and thus suffer a few implications. These individuals are said to be less accepted by other group member and are paid less for their work. Having positive illusions about one’s status in a group seems to be generally frowned upon by group members and is seen as a form of aggrandizement. Prior studies have suggested that self-enhancement can be used as a motivational tool, so while it can increase work ethic, there must be a fine line between the types of self-enhancement methods used in group and work settings (Anderson et al., 2008; Taylor & Brown, 1988).

In the context of relationships, self-enhancement appears to be detrimental to the quality and outcome of the courtship (Busby, Holman, & Niehuis, 2009). There is evidence to show that couples who rate themselves individually as the more affable partner suffer poorer relationship outcomes. The tendency to attribute a positive characteristic to themselves, rather than their partner, is detrimental to the health of the relationship. On the contrary, couples who each see their partner as the more affable of the pair experience more positive relationship outcomes. Other-enhancement, rather than self-enhancement, is more beneficial to the success of romantic relations, and thus in most cases an individual’s mental well-being.

Excessive self-enhancement in the context of interpersonal relationships can also result in negative outcomes (Joiner, Vohs, Katz, Kwon, & Kline, 2003). Undergraduate roommates were subject of a study aiming to determine the affect of self-enhancement among roommates. It was found that males that were excessive self-enhancers received unfavorable evaluations from their roommates. Excessively self-enhancing females on the other hand received positive evaluations from their roommates. It is thought that self-enhancing women received favorable evaluations because of the thought that women are more oriented towards interdependence than men. Thus, the self-enhancement style of women will display an inclination and motive to be held in high-esteem by their peers, while men self-enhance in ways that promote independence and alienate themselves from fellow man.

Physical Health

Efforts of self-presentation, a form of self-enhancement, can lead to risk taking and unhealthy behavior (Leary, Tchividijian, & Kraxberger, 1994). Self-presentation is little more than public self-enhancement; individuals make attempts to influence how they are perceived by other people, hoping for reinforcement of their positive self-views. However, the lengths at which individuals strive to uphold their desired self-presentation can carry some serious health risks. For example, individuals often feel embarrassment over purchasing condoms, and to uphold self-presentational ideals, do not purchase them. Even in cases where the individual does purchase a condom, self-presentational concerns may deter them from using it. They may not want to appear as though they anticipated sex or had intentionally tried to seduce their partner. This leaves them at risk for sexually transmitted diseases, which are well documented to be stigmatized conditions, and would cause far worse self-presentational concerns in the future than simply buying contraception in the present moment.

Another example of risk taking behavior in regards to self-presentational and self-enhancing behavior is sunbathing (Leary et al., 1994). In order to achieve their desired glow, individuals will expose themselves to dangerous amounts of sunlight which can potentially cause melanoma. Individuals know that they putting their health at risk, but motives to self-present and self-enhance outweigh logic. Eating disorders are also a crux of self-presentation. Individuals go to far lengths to achieve and maintain a certain look. This can be gone about in a healthy way, but many people try to achieve their desired body type by through disordered eating habits, which leads to the deterioration of one’s health. Leary et al. discuss several more damaging characteristics self-presentation, such as alcohol, tobacco, and drug use, steroid use, failure to exercise, and cosmetic surgery. All these activities have negative implications for one’s physical health and are motivated in large part by a drive for self-enhancement.

Efforts to self-enhance also cause individuals to misremember negative information about themselves (Croyle et al., 2006). This can be unfavorable to one’s health in certain situations. For example, participants were screen for cholesterol levels. The subjects who had the worst cholesterol levels remembered their scores as being lower than they actually were when tested a few months later. This could be considered a form of mnemic neglect (Brown, 1998). While this type of self-enhancement may not directly cause harm one’s body, in the long run it could expose an individual to increased risk of health problems such as heart attack or stroke if they were to think that they were in better shape then they actually were. They may dissuade themselves from taking precautions and changing their lifestyle. Self-enhancing biases of self-relevant health information can be nearly as dangerous as the self-presentational risks described earlier (Leary et al., 1994).

Discussion

With strong evidence both supporting and eschewing claims that self-enhancement is beneficial to an individual’s well-being, it is difficult to discern which side presents the soundest argument. Taylor and Brown were groundbreaking with their study and seem to draw fairly conclusive evidence to support their claim that self-enhancement is normal and that because most people display tendencies towards it, there must be positive correlations associated with it (1988). Their finding that low self-esteem and depressed individuals do not self-enhance as much as the majority people is strong evidence to show that it is a vital key of a person’s success and happiness.

The central argument against their findings is that they used inadequate means for measuring self-enhancement (Colvin et al., 1995; Robins & Beer, 2001). It appears to be somewhat difficult to obtain accurate measures of self-enhancement, thus there may be no conclusive evidence to support either case. Without universal means to gauge an individual’s positive illusions, there will always be room for argument, as the postulates in this field of research are based upon measuring self-enhancement. It may be the case that specific types of self-enhancement need to be measured during future research, rather than self-enhancement in general. For example, in the Colvin et at. article, they set out to use external and valid criteria for measuring self-enhancement. This seems logical, but perhaps they should have taken their research a step further and honed in on the specific self-enhancing tendencies such as strategic construal, mnemic neglect, and self-serving bias and measured these traits individually, rather than an overall blueprint of self-enhancement.

With that being said, there are some very convincing arguments that self-enhancement is detrimental to one’s well-being, especially in regards to negative affect of the body. The evidence that Leary et al. provide concerning risks individuals take in order to self-present in particular seems sound (1994). The only issue in regards to self-enhancement is that they do not directly measure levels of self-enhancement in their study, but it is commonly recognized that self-presentation is merely a public form of self-enhancement. Further research in this field would require some means to measure individual’s levels of self-presentation and self-enhancement in these health risking situations, as there is some evidence that self-enhancement can be beneficial to the body (Taylor et al., 2003).

In regards to the social implications of self-enhancement, it seems that some studies do show evidence supporting claims that it is detrimental to social interactions, but it appears to only be a specific type of self-enhancement that causes these issues (Anderson et al., 2008). Namely, status self-enhancement is what elicits negative evaluations by peers. The paper does not delve into other types of self-enhancement and how they may or may not be perceived by a group. It seems as only public self-enhancement is viewed downwardly. Privately held notions of self-enhancement would not be acknowledged by anyone but the individual, and may increase their resolve and self-esteem, enabling them to function better within the group.

Finally, in terms of the affects of self-enhancement on mental health, it appears that research is inconclusive. Taylor and Brown are steadfast in their belief that holding overly positive illusions is advantageous for one’s well-being (1988), while Colvin et al. correlate self-enhancement with maladjustment (1995). With such contrasting findings in this area, one must question whether the experimental procedures employed by each research group influenced the outcome of their tests to support their hypotheses. Colvin et al. even explicitly mention the shortcomings of Taylor and Brown’s assessment of individuals’ self-enhancement, which means they may have unintentionally have overextended in efforts to avoid those mistakes, and thus forced measurements of self-enhancement to swing in negative correlation with well being.

The research in this field is intriguing because of the conflicting findings. In the future there may be more adequate and specific guidelines from measuring self-enhancement and more conclusive results will be able to be formed. As of now, it seems that in specific situations and in specific types of self-enhancement, some valid conclusions have been drawn in regard to the benefits and costs of these self-enhancing tendencies. It appears to be a complex topic that may never be fully understood, but having some knowledge of potential implications of it can help to give psychologists a better grasp on what makes people act in the days that they do.

References

Anderson, C., Ames, D., & Gosling, S. (2008). Punishing hubris: The perils of overestimating one’s status in a group. Personality and Social Psychology Bulletin, 34(1), 90-101. doi:10.1177/0146167207307489.

Brown, J.D. (1998). The search for self knowledge. The Self (pp. 49-81). New York, NY: Taylor & Francis Group.

Busby, D., Holman, T., & Niehuis, S. (2009). The association between partner enhancement and self-enhancement and relationship quality outcomes. Journal of Marriage & the Family, 71(3), 449-464. doi:10.1111/j.1741-3737.2009.00612.x.

Colvin, C., Block, J., & Funder, D. (1995). Overly positive self-evaluations and personality: Negative implications for mental health. Journal of Personality and Social Psychology, 68(6), 1152-1162. doi:10.1037/0022-3514.68.6.1152.

Croyle, R., Loftus, E., Barger, S., Sun, Y., Hart, M., & Gettig, J. (2006). How well do people recall risk factor test results? Accuracy and bias among cholesterol screening participants. Health Psychology, 25(3), 425-432. doi:10.1037/0278-6133.25.3.425.

Joiner, T., Vohs, K., Katz, J., Kwon, P., & Kline, J. (2003). Excessive self-enhancement and interpersonal functioning in roommate relationships: Her virtue is his vice?. Self and Identity, 2(1), 21-30. doi:10.1080/15298860309020.

Leary, M., Tchividijian, L., & Kraxberger, B. (1994). Self-presentation can be hazardous to your health: Impression management and health risk. Health Psychology, 13(6), 461-470. doi:10.1037/0278-6133.13.6.461.

Robins, R., & Beer, J. (2001). Positive illusions about the self: Short-term benefits and long-term costs. Journal of Personality and Social Psychology, 80(2), 340-352. doi:10.1037/0022-3514.80.2.340.

Sedikides, C. (1993). Assessment, enhancement, and verification determinants of the self-evaluation process. Journal of Personality and Social Psychology, 65(2), 317-338. doi:10.1037/0022-3514.65.2.317.

Sedikides, C., & Gregg, A.P. (2007). Portraits of the self. In: M.A. Hogg & J. Cooper (Eds.) The Sage Handbook of Social Psychology (pp. 92-122). Thousand Oaks, CA: Sage Publications Ltd.

Taylor, S., & Brown, J. (1988). Illusion and well-being: A social psychological perspective on mental health. Psychological Bulletin, 103(2), 193-210. doi:10.1037/0033-2909.103.2.193.

Taylor, S., Lerner, J., Sherman, D., Sage, R., & McDowell, N. (2003). Are self-enhancing cognitions associated with healthy or unhealthy biological profiles?. Journal of Personality and Social Psychology, 85(4), 605-615. doi:10.1037/0022-3514.85.4.605.

Purpose

To develop an understanding of the Law of Reflection, to apply the Law of Reflection to finding images formed by plane and spherical mirrors, and to learn to draw ray diagrams to assist in predicting the locations of images formed by spherical concave mirrors.

Hypothesis

According to the Law of Reflection, the angle of incidence will equal the angle of reflection when light is shone off a flat reflecting surface. When light is shone off a spherical mirror, it will converge at a focal point. Light will converge at a real focal point in front the concave mirror, and light will converge at a virtual focal point somewhere behind the convex mirror. An object placed beyond the curvature of a mirror will cast an inverted, shrunken, real image. An object placed at the curvature of a mirror will project and inverted, true to size, real image. Finally, an object placed between the curvature and focal point will project an inverted, magnified, real image.

Labeled Diagrams

See attached sheet.

Data

Part 1

Part 2

Part 3

Focal length of mirror f = 5.5 cm

Case 1

Case 2

Case 3

Graphs

Part 3

Questions

Part 1

1. What statement can you make regarding the relative positioning of the normal, the incident ray and the reflected ray?

The angle between the incident ray and the normal is equal to the angle between the reflected ray and the normal.

2. Do your observations validate the Law of Reflection?

Yes, the observations validate the Law of Reflection as θ_i = θ_r or the values are extremely close in all trials.

Part 3

3. Using your data above, create a graph in Graphical Analysis of pq vs. p + q. Your graph should appear linear. Perform a linear fit on the graph.

See graphs section.

4. There is an equation in geometrical optics called the mirror equation. It relates the object distance p and the image distance q to the focal length of the mirror f: 1/p + 1/q = 1/f. The mirror equation can be used to determine a mirror’s focal length. Solve the above equation algebraically for f.

In the instance of case 1, for trial 1 f = 4.0 cm, for trial 2 f = 4.1 cm, and for trial 3 f = 3.8 cm. In the instance of case 2, for trial 1 f = 4.1 cm. In the instance of case 3, for trial 1 f = 4.0 cm, for trial 2 f = 4.2 cm, and for trial 3 f = 4.3 cm. The average value for f is 4.1 cm.

5. How is your answer to Question 4 related to the slope of your graph from Question 3?

The slope of the graph from Question 3 is 4.0 cm, so these values are strikingly similar.

6. What is the percent difference between your slope and the focal length of the mirror that you measured?

The percent difference between the slope, 4.0 cm, and the focal length of the mirror that was measured, 5.5 cm, is 32%.

7. The magnification of the image of an object from a spherical mirror can also be expressed as the ratio –q/p. Calculate this ratio for each of your object and image distances and record in your data table.

See data table.

8. How does the ratio of –q/p compare to your calculated magnifications h_i/h_o for each entry? What is the percent difference?

In regards to case 1, the values for both h_i/h_o and –q/p are negative, but the values for h_i/h_oare more negative than that of –q/p. The percent difference for trial 1 is 126%, for trial 2 is 132%, and for trial 3 is 153%.

Case 2 shares the same characteristics of case 1. The percent difference is 112%.

In regards to case 3, the values are quite dissimilar because all h_i/h_ovalues are positive while all –q/p values are negative. The percent difference for trial 1 is 1200%, trial 2 is 700%, and trial 3 is 569%. It is thought that the images were recorded as upright when they were really inverted, which caused this error, but it cannot be validated by repeating the laboratory procedure at this time.

9. Do your data verify the prediction from your ray diagrams?

In regards to case 1, the values for –q/p verify the predictions made from the ray diagram, as when the object was moved further away from the mirror, the images became smaller. The values for h_i/h_o dot not support this claim however, as they say that the image way magnified, but in reality the projected image was smaller. The images were also inverted as told by the negative sign.

In regards to case 2, neither the value for –q/p nor h_i/h_o verifies the prediction made from the ray diagram. The magnification should have been 0.

In regards to case 3, the values for –q/p do verify the predictions made from the ray diagram, as when the object was moved closer to f, the images became more magnified. The images were recorded as being upright, but in reality were probably inverted as suggested by theory and the negative sign the –q/p value carries.

Conclusion

For part 1 of the experiment, the reflection of light from a plane mirror was measured. Equipment was set up on the optics bench so that light shone through a slit plate and slit mask onto a plane mirror. A ray table was used to measure the angle at which the line hit and reflected off the mirror. The ray table was rotated from 0^o to 90^o at 10^o intervals. The angle of incidence and angle of reflection were measured for each trial. The measured angles were identical or nearly identical in all trials, which seem to confirm the Law of Reflection. Any discrepancy in the measurements may be attributed to the ray optics mirror not being perfectly aligned on the ray table; without any way to secure it in place, it may have shifted slightly during some of the trials. This would have caused a difference in the angles of incidence and reflection.

For part 2 of the experiment, the focal points of a concave and convex mirror were measured. Equipment was set up on the optics bench so that light shone through a parallel ray lens and then through a slit plate and then onto the concave or convex mirror situated on a ray table. The parallel ray lens had to be adjusted to make the light rays project in a parallel fashion onto the mirror. Once parallel, the mirror was situated so that the centermost light ray would hit the center of the mirror perpendicularly. The light rays converged at a focal point which was measured and recorded. In the case of the convex mirror, a piece of paper was place underneath the mirror and the projected light rays were draw onto the piece of paper. The paper was then removed and the lines were extended to find the focal point which was located behind the mirror. In the case of the concave mirror, the focal point was in front of the mirror. The focal length of the concave mirror was 0.060 m and the focal point of the convex mirror was 0.058 m. This slight discrepancy could be attributed to difficulty tracing the lines projected by the convex mirror, but these values are rather close in value, which is expected.

For part 3 of the experiment, the cases of 3 ray diagrams were tested. Equipment was set up on the optics bench so that light shone through a crossed arrow target onto an angled spherical mirror which then reflected an image onto a viewing holder. The focal length of the mirror was first determined by placing the mirror as far away from the crossed arrow as target as possible. The viewing screen was moved to locate the point where the image of the target was focused, and that was designated as the focal point. In the case of this experiment, the focal length was 5.5 cm. The target was then placed at three positions beyond the curvature, directly on the curvature, and then at three positions between the curvature and the focal length. The viewing screen was situated in each trial to find the point where the projected image was focused. The distance from object to mirror, distance from image to mirror, height of the object, and height of the image were measured in each trial.

The results from this part of the experiment are not very consistent. In case 1, the values for both h_i/h_o and –q/p were both negative, but the values for h_i/h_owere more negative than that of –q/p. The percent difference for trial 1 was 126%, for trial 2 was 132%, and for trial 3 was 153%. The values for –q/p seems most reasonable as they predict that the image was shrunken and inverted, which was actually the case. The values for h_i/h_o suggest that the images were magnified and inverted, which was not what was observed. Case 2 shares the same characteristics of case 1, in that the value for both h_i/h_o and –q/p was negative, but the value for h_i/h_owas more negative than that of –q/p. The percent difference was 112%. During this case, it was predicted that the image would be inverted, but would be life size; not magnified or shrunken. In regards to case 3, the values were quite dissimilar because all h_i/h_ovalues were positive while all –q/p values were negative. The percent difference for trial 1 was 1200%, trial 2 was 700%, and trial 3 was 569%. It is thought that the images were recorded as upright when they were really inverted, which caused this discrepancy, but it cannot be validated by repeating the laboratory procedure at this time. The values for –q/p are most logical, as they suggest that the image was inverted and magnify, which is also what theory suggests.

The error from this part of the experiment came from the inability to distinguish when the image on the viewing screen was focused. Many times it was thought that the image was focused, but may not have truly been focused; there was not way to tell with certainty if it was focused or not. The viewing screen could be moved a few centimeters in either direction and the image would look about the same. All measurements for the height of the image are in question as well. The spherical mirror was placed at an angle in order to view the image, but this angle was never taken into consideration in any of the equations. The undoubtedly is what caused all the h_i/h_ovalues have such a stark difference from the –q/p values. It was not stated in the lab manual how to take that angle into consideration, and thus those values should most likely be thrown out. The –q/p values are most representative of the projected image, though the values for –q/p and h_i/h_o should have been equal.

Equations

θ_i = θ_r

C = 2f

1/p + 1/q = 1/f

Magnification = -q/p = h_i/h_o

Percent Difference = |x₁ – x₂| / (x₁ + x₂)/2 x 100%

Abstract

The reaction of RuCl₂(PPh₃)₂, THF, and diphenylpropargyl alcohol under reflux yields C₅₁H₄₀P₂Cl₂Ru in 46% yield. ¹H NMR spectroscopy of C₅₁H₄₀P₂Cl₂Ru shows a series of overlapping peaks at δ 7.3-7.8. C₅₁H₄₀P₂Cl₂Ru can then react with dichloromethane and tricyclohexylphosphine to form C₅₁H₇₆Cl₂P₂Ru. ¹H NMR spectroscopy of C₅₁H₇₆Cl₂P₂Ru yields the same series of peaks found around δ 7.3-7.8 that C₅₁H₄₀P₂Cl₂Ru exhibits, along with a faint series of peaks at δ 1.8-2.1. ³¹P NMR spectroscopy of both products shows a single peak around δ 29.5. This suggests what was believed to be C₅₁H₇₆Cl₂P₂Ru was actually mostly C₅₁H₄₀P₂Cl₂Ru. Catalytic measures of the two synthesized products were inconclusive due to their similar natures, however, it is expected that C₅₁H₇₆Cl₂P₂Ru is the better catalyst as it has bulkier, more readily dissociating substituents.

Introduction

The reaction of RuCl₂(PPh₃)₂ with THF and diphenylpropargyl alcohol under reflux yields C₅₁H₄₀P₂Cl₂Ru.¹ The reaction specifically takes place in the following manner:

Scheme 1

C₅₁H₄₀P₂Cl₂Ru can then react with dichloromethane and tricyclohexylphosphine to form C₅₁H₇₆Cl₂P₂Ru. The reaction occurs in the following manner:

Scheme 2

These products be distinguished via ¹H and ³¹ NMR spectroscopy. The ¹H NMR spectrum of the C₅₁H₇₆Cl₂P₂Ru will yield peaks representative of the newly added cyclo groups, which are missing in C₅₁H₄₀P₂Cl₂Ru. The ³¹P NMR spectra of each product should theoretically each show 1 peak, with the peak of C₅₁H₇₆Cl₂P₂Ru being downfield from C₅₁H₄₀P₂Cl₂Ru because of the lower electron density around the phosphorus.

The products from these two reaction are of interest because they are ruthenium alkidene complexes, which are alternatives to Grubbs’ catalysts and are much less difficult to prepare in the laboratory.¹ These two ruthenium indenylidene complexes can be used as catalysts in ring closing metathesis. Show below are the balanced reaction and mechanism in which diethyl diallylmalonate undergoes this process with the aid of a ruthenium catalyst:

Scheme 3

Scheme 4

The relative catalytic rates of the two ruthenium indenylidene complexes can be monitored via GC/MS. Determination of the starting material and product from this technique can show the relative percentages of each material within a solution. By comparing the ratio of reagent to product for each of the ruthenium complexes, it can be determined which is a better catalyst, as the more efficient catalyst will sport the lower ratio of reagent to product.

Experimental

All syntheses were carried out in nitrogen and the reagents and solvents were purchased from commercial sources and used as received unless otherwise noted. The synthesis of C₅₁H₄₀P₂Cl₂Ru (1A), C₅₁H₇₆Cl₂P₂Ru (1B), and C₁₁H₁₆O₄ (2) were based on reports published previously.¹

C₅₁H₄₀P₂Cl₂Ru (1A). A hot, dry 100 mL 3 neck round bottom flask was obtained from an oven and connected to it were a cold water condenser, septum, and sidearm stopcock. A gas inlet was connected to the condenser and a bubbler was connected to the gas inlet. All joints were greased. A stir bar was placed in the round bottom flask and the apparatus was connected to a nitrogen source. The condenser was connected to a cold water source. The round bottom flask was degassed with N₂ until cool, at which time RuCl₂(PPh₃)₂ (0.179 g, 1.87 x 10^-4 mol), THF (10 mL), and diphenylpropargyl alcohol (0.080 g, 3.84 x 10^-4 mol) were subsequently added to the reaction vessel. A sand bath was constructed and was used to heat the solution. The sand bath was set to 80% power and the mixture began to reflux a while later, but THF began to evaporate over time so the sand bath was turned down to around 40% power and an additional 30 mL of THF had to be added to the solution during the 2.5 h reflux period. The stir bar was spun at a moderate speed during this time.

After the reflux period had been completed, the reaction mixture was allowed to cool to room temperature. The solution was then transferred to a single neck 50 mL round bottom flask at which time the solution was taken off the N₂ supply and was exposed to air for the remainder of the synthesis. The solvent was removed via rotary evaporation leaving a thick, dark, brownish, reddish liquor. 1.5 mL dichloromethane was added to the liquor along with 9 mL hexane, which was slowly pipeted in. A dark red solid was precipitated and filtered using a small fritted funnel and was washed 3 times with about 2 mL hexane during each rinsing. The solid was vacuum dried and placed into a pre-weighed vial (9.698 g). The vial was stored in a dessicator for 1 week. The final weight of the vial was 9.767 g. The product was determined to be 1A (0.069g, 7.78 x 10^-5 mol, 41.6% yield based on the amount of RuCl₂(PPh₃)₂ used). ¹H NMR (CDCl₃): δ 7.3-7.8 (6 H, overlapping signal, Phand indenylidene). ³¹P NMR (CDCl₃): δ 29.5 (s, Ru-P). FTIR (ATR) ν 1928 cm^-1 (m).

C₅₁H₇₆Cl₂P₂Ru (1B). A hot, dry 100 mL 3 neck round bottom flask was obtained from an oven and connected to it were a cold water condenser, septum, and sidearm stopcock. A gas inlet was connected to the condenser and a bubbler was connected to the gas inlet. A stir bar was placed in the round bottom flask and the apparatus was connected to a nitrogen source. The condenser was connected to a cold water source. The round bottom flask was degassed with N₂ until cool, at which time 1A (0.050 g, 5.64 x 10^-5 mol), dichloromethane (7 mL), and tricyclohexylphosphine (0.055 g, 1.96 x 10^-4 mol) were subsequently added to the reaction vessel. The mixture was stirred at a moderate speed at room temperature for 1.5 h. 2 mL of additional dichloromethane was added to the solution during this time as some had evaporated off.

The solution was then transferred to a 50 mL single neck round bottom flask at which time the solution was taken off the N₂ supply and was exposed to air for the remainder of the synthesis. The solvent was removed via rotary evaporation. The remaining solid was suspended with 5 mL of hexane. This new solution was stirred at a moderate speed at ambient temperature for 0.5 h. The resulting solid was filtered using a small fritted funnel and was washed 3 times with about 2 mL hexane during each rinsing. The solid was vacuum dried and placed into a pre-weighed vial (9.737 g). This vial was stored in a dessicator for 1 week. The final weight of the vial was 9.824 g. The product was determined to be 1B (0.087g, 9.42 x 10^-5 mol, 167% yield based on the amount of 1A used). ¹H NMR (CDCl₃): δ 1.8-2.1 (5 H, overlapping signal, PCy₃), δ 7.1-7.9 (6 H, overlapping signal, Ph and indenylidene). ³¹P NMR (CDCl₃): δ 29.8 (s, Ru-P). FTIR (ATR) ν 1921 cm^-1 (m).

C₁₁H₁₆O₄ (2). A hot, dry 100 mL 3 neck round bottom flask was obtained from an oven and connected to it were a cold water condenser, septum, and sidearm stopcock. A gas inlet was connected to the condenser and a bubbler was connected to the gas inlet. A stir bar was placed in the round bottom flask and the apparatus was connected to a nitrogen source. The condenser was connected to a cold water source. The round bottom flask was degassed with N₂ until cool, at which time 1B (0.010 g, 1.08 x 10^-5 mol), anhydrous dichloromethane (6 mL), and diethyl diallylmalonate (0.100 g, 4.16 x 10^-4 mol) were subsequently added to the reaction vessel. The mixture was stirred at a moderate speed at room temperature for just over 1 h. The solution was then transferred to a 25 mL single neck round bottom flask at which time the solution was taken off the N₂ supply and was exposed to air for the remainder of the synthesis. The solvent was removed via rotary evaporation. ¹H NMR (CDCl₃): δ 1.2 (t, -CH₃), δ 2.6 (d, -CH₂), δ 4.1 (q, O-CH₂), δ 5.1 (m, =CH₂), δ 5.6 (tt, C-H), δ 6.8-7.7 (6 H, overlapping signal, Ph and indenylidene). GC-MS (CH₂Cl₂): 212 (2.5%, (2)), 241 (82.2%, (3)).

The process described above was repeated by a laboratory partner using 1A in lieu of 1B. ¹H NMR (CDCl₃): δ 0.9 (t), δ 1.25 (s), δ 1.55 (s), δ 1.84 (t), δ 3.74 (t), δ 6.8-7.7 (6 H, overlapping signal, Ph and indenylidene). GC-MS (CH₂Cl₂): 212 (0.12%, (2)), 241 (59.1%, (3)).

C₁₃H₂₀O₄ (3). The ¹H NMR spectrum of (3) was obtained from Sigma Aldrich.^{2 1}H NMR (CHCl₃): δ 1.25 (t, -CH₃), δ 2.6 (d, -CH₂), δ 4.2 (q, O-CH₂), δ 5.1 (m, =CH₂), δ 5.7 (tt, C-H).

Results

The reaction of RuCl₂(PPh₃)₂ with diphenylpropargyl alcohol yielded 0.069g of product, which was determined to be 1A. This translated to 7.78 x 10^-5 mol and thus a 41.6% yield based on the amount of RuCl₂(PPh₃)₂ used, which was the limiting reagent in the reaction. Proton NMR spectroscopy of 1A yielded one series of peaks of interest. From δ 7.3-7.8 there was a sequence of peaks representing the 6 different aromatic hydrogens from the phenyl and indenylidene groups. ³¹P NMR spectroscopy elicited one peak at δ 29.5 which can be attributed to phosphorus coordinated with the metal, Ru. The IR spectrum of the substance gave one notable peak at 1928 cm^-1, but the identity of this peak was unable to be determined.

The reaction of 1A with dichloromethane and tricyclohexylphosphine yielded 0.087g of product, which was determined to be 1B. This translated to 9.42 x 10^-5 mol and thus a 167% yield based on the amount of 1A used, which was the limiting reagent in the reaction. Proton NMR spectroscopy of 1B yielded two series of peaks of interest. From δ 1.8-2.1 were noted a faint sequence of overlapping signals, which were thought to be due to the 5 different hydrogens from the PCy₃ groups. From δ 7.1-7.9 there was a string of peaks representing the 6 different aromatic hydrogens from the phenyl and indenylidene groups. ³¹P NMR spectroscopy elicited one peak at δ 29.8 which can be attributed to phosphorus coordinated with the metal, Ru. The IR spectrum of the substance gave one notable peak at 1921 cm^-1, but again the identity of this peak was unable to be determined.

The reaction using 1B as a catalyst to perform ring closing metathesis on diethyl diallylmalonate produced a product with a ¹H NMR spectrum containing several peaks of interest. The triplet δ 1.2 was thought to be due to the methyl group, the doublet at δ 2.6 was thought to be due to –CH₂ groups, the quartet at δ 4.1 was thought to be due to the O-CH₂ groups, the multiple peaks at δ 5.1 were thought to be from =CH₂, the triplet of triplets at δ 5.6 was thought to be from C-H, and lastly the extremely weak overlapping signals at δ 6.8-7.7 were thought to be from phenyl and indenylidene groups. These assumptions are made taking into consideration that the ¹H NMR spectrum of diethyl diallylmalonate was identical, save for the almost negligible peaks from δ 6.8-7.7.² The GC/MS of 1B gave what were thought to be signals of interest at times 6.648 min and 6.945 min. The reading at 6.648 min accounted for 2.5% of the scan and was thought to be C₁₁H₁₆O₄ because its m/z of 212 appeared as a peak. The reading at 6.945 min accounted for 82.2% of the scan and was thought to be diethyl diallylmalonate because its m/z of 241 appeared as a peak, albeit very small. This gave a proposed ratio of 33:1, reactant to product.

When using 1A as the catalyst in lieu of 1B in this reaction, proton NMR spectroscopy of the product elicited several peaks, most of which were not able to be identified. The sequence of overlapping peaks from δ 6.8-7.7 was attributed to the 6 different hydrogens from phenyl and indenylidene groups, but the triplet at δ 0.9, the singlet at δ 1.25, the singlet at δ 1.55, the triplet at δ 1.84, and the triplet at δ 3.74 could not be determined. A standard ¹H NMR spectrum of the desired product C₁₁H₁₆O₄ was unobtainable for comparison. The GC/MS of 1A gave what were thought to be signals of interest at times 6.648 min and 6.974 min. The reading at 6.648 min accounted for 0.12% of the scan and was thought to be C₁₁H₁₆O₄ because its m/z of 212 appeared as a peak. The reading at 6.974 min accounted for 59% of the scan and was thought to be diethyl diallylmalonate because its m/z of 241 appeared as a peak, again albeit very small. This gave a proposed ratio of 491:1, reactant to product.

Discussion

The results of this experiment are inconclusive. The first reaction seemed to give a decent percent yield of 1A and it was identifiable through ¹H and ³¹P NMR spectroscopy, however there were a few erroneous peaks noted on the ¹H NMR spectrum and the peaks of interest were somewhat weak. The ³¹P NMR spectrum of 1A was inconclusive at first, so a new scan was done at a later time with a different sample. These facts seem to suggest that the original 1A obtained was not very pure. During the procedure, the sand bath was not adequately controlled, and this is most likely what caused the impure product. Because the reaction was overheated, side products may have formed or the original reagents did not react to completion, and in turn, the percent yield was in reality not as high as it appeared. This also attributes to the extra peaks that showed up on the ¹H NMR spectrum. The oxidation state of 1A is +4 and its electron count is 16.

The second reaction resulted in a percent yield of 167% of what was thought to be 1B, which again suggests some error. The ³¹P of this product gave a peak in nearly the exact same position as 1A, so this seems to confirm that the product obtained from the second reaction was not 1B, but mostly 1A. The peak should have shifted downfield to about δ 41, which is what colleagues have reported. The proton NMR spectrum does show faint peaks from δ 1.8-2.1 which is where one would expect hydrogens attached to non-aromatic cyclo groups to be found. This means that some of the -PPh₃ groups did convert to -PCy₃ groups, but a significant amount on the whole. The IR spectra of the products after reactions one and two are also quite similar, again hinting that nothing really transpired during reaction two. The procedure during reaction two went as detailed by the laboratory manual, so this means the starting material was probably impure and thus could not react to completion.¹ The oxidation state of 1B would also be +4 with an electron count of 16.

Because reaction one and reaction two seemed to yield the same product, the ring closing reactions cannot accurately be compared for catalytic activity. Theoretically 1B is the better catalyst, as it has PCy₃ ligands opposed to the PPh₃ ligands characteristic of 1A. PPh₃ ligands have a cone angle of 145^o while PCy₃ ligands have a cone angle of 170^o.³ The larger the cone angle, the bulkier the ligand and the faster it dissociates, allowing for expedited ring closing metathesis.³ The mechanism in which this takes place can be seen in Scheme 4. The reaction of diethyl diallylmalonate with 1B did not seem to elicit the ring closing mechanism. The ¹H NMR spectra of the product looks identical to that of the starting material, diethyl diallylmalonate, save for one area around δ 6.8-7.7 where traces of what looks like aromatic structures, namely phenyl and indenylidene groups can be found. It looks like there was such a minute amount of catalyst available that it never interacted with diethyl diallylmalonate to close the ring.

GC/MS of 1B shows two signals which may account for diethyl diallylmalonate and the closed ring. At time 6.648, a peak accounting for 2.5% all that was picked up by the scan contains a signal of 212 can be seen which corresponds with the m/z of C₁₁H₁₆O₄. At time 6.945 min, a peak accounting for 82.2% of the scan contains a signal of 241 can be seen which corresponds with the m/z of diethyl diallylmalonate. This gives a ratio of 33:1, reactant to product, which means the yield was rather poor. It does seem to suggest that some product may have been formed, however product was not visible on the ¹H NMR spectrum, so this interpretation may be inaccurate.

The reaction of diethyl diallylmalonte with 1A yielded a different ¹H NMR than the reaction with 1B did. It also shows overlapping peaks at δ 6.8-7.7 indicative of phenyl and indenylidene groups, but these peaks are much more noteworthy, meaning there was an abundance of catalyst available, where in the other reaction there was almost no catalyst available. Hence, upfield peaks are seen and are believed to be product, but these peaks are unable to be confirmed. A standard ¹H NMR spectrum of C₁₁H₁₆O₄ is unobtainable for comparison. The peaks reminiscent of the starting material seen in the ¹H NMR spectrum for the reaction with 1B are not visible, which means there was some sort of change in the starting material.

GC/MS analysis however does not seem to confirm the presence of a closed ring product. At time 6.648, a peak accounting for 0.12% all that was picked up by the scan contains a signal of 212 can be seen which corresponds with the m/z of C₁₁H₁₆O₄. At time 6.974 min, a peak accounting for 59% of the scan contains a signal of 241 can be seen which corresponds with the m/z of diethyl diallylmalonate. This gives a ratio of 491:1, reactant to product, which means the almost no product formed at all despite the presence of what seems to be a copious amount of catalyst. The reaction with 1B has a ratio of 33:1 and had almost no visible catalyst in its ¹H spectrum, so it could be possible that the GC/MS was analyzed improperly.

The sources of error are difficult to pinpoint, but one issue may have been the flow of nitrogen through the system. If the flow was too great, solvent would have been lost and it would have hindered the reactions. If the hot 100 mL three neck round bottom flask was not allowed to cool completely, that may have also caused a side reaction to occur due to the unwarranted heat. Also, as noted earlier during the synthesis of 1A, the reaction was overheated, which could have caused side products to form and thus inhibit the results of the following syntheses.

Conclusion

The main purposes of the experiments were to synthesize 1A and 1B, confirm their structures via ¹H, ³¹P, and IR spectroscopy, and to determine their relative catalytic rates during ring closing metathesis of diethyl diallylmalonate. 1A was identifiable by a series of overlapping peaks at δ 7.3-7.8 representative six different hydrogens attached to phenyl and indenylidene groups. This material was collected in a 46% yield, but in reality the yield was likely lower due to contaminants. 1B was synthesized with 167% yield, which suggests error. It was vaguely identifiable through its ¹H NMR spectrum by a series of peaks found at δ 1.8-2.1 representative of protons attached to cyclo groups, namely the PCy₃ substituents. This spectrum also contained the same series of overlapping peaks found around δ 7.3-7.8 for 1A. The ³¹P NMR and IR spectra for 1A and 1B are nearly identical, suggesting that almost no change in structure took place during the synthesis of 1B from 1A.

Because 1B did not properly synthesize, or did in an extremely low proportion, it was not feasible to measure 1A and 1B in comparison of their catalytic properties. It would be expected that 1B would be a better catalyst, as it contains bulkier groups which in theory dissociate faster.³ The 1A and 1B synthesized were both used as catalysts for ring closing metathesis of diethyl diallylmalonate. The product from the synthesis with 1B gave a ¹H spectrum nearly identical to that of the starting material, diethyl diallylmalonate, which says that there was too low of a concentration of catalyst for the reaction to occur in the time allotted. The product from the synthesis with 1A gave a different ¹H with peaks that are thought to be the desired product, but no standard ¹H NMR spectrum of the product is obtainable. The results from the GC/MS of both products runs contrary to the belief that any significant amount of C₁₁H₁₆O₄ was synthesized at all, and thus the results from this laboratory experiment are inconclusive.

References

(1) Pappenfus et al. Synthesis and Catalytic Performance of Ruthenium Carbene Complexes for Olefin Metathesis: A Microscale Organometallic Experiment. Journal of Chemical Education. 2007, 84, 1998-2000.

(2) http://www.sigmaaldrich.com/spectra/fnmr/FNMR005436.PDF

(3) Miessler, G. L.; Tarr, D. A. Inorganic Chemistry: Third Edition. Pearson Prentice Hall: Upper Saddle River, 2004; pp 523-546.

Purpose

To understand the magnetic field generated by a long, straight, current-carrying conductor, the behavior of a conductor carrying a constant current in a magnetic field, and to verify the relationship associated with the force between two current-carrying conductors and the current in the wires.

Hypothesis

According to the theory that F = mg = μ_oLI² / 2πd_o, as the weight on the upper wire the increased, the current needed to return it to its original position will also increase as long as the length of the upper conductor and center-to-separation between the wires are kept constant. In addition, with the theory that d = rs / 2D and that d_o = d + r_upper + r_lower, iff the distance between the mirror and whiteboard were to increase, then less current would be needed to return the upper wire to its original position when a weight force is applied to it. Furthermore, the larger the value of s_o, the more current will be needed to for the upper wire to reach its original position when a weight force is applied to it. Finally, because the wires run in opposite directions, they will experience a force of repulsion when a current is run through them.

Labeled Diagrams

See attached sheet.

Data

First Separation

Second Separation

Graphs

Part 1

Part 2

Questions

Part 1

1. Plot a graph in Graphical Analysis of F vs. I (F is the weight force of the mass in the pan). What type of graph is it? What appears to be the relationships between force and current? Does your graph verify what is expected from theory?

It is a quadratic graph. The relationship between force and current appears to be that F is proportional to I² multiplied by some constants (μ_oL / 2πd_o). Yes, the graph verifies what is expected from theory.

2. Linearize your graph. To do this, you will need to perform some operation on the x-axis variable. Include both your graph of F vs. I and your linearized graph in your lab report.

See graphs section above.

3. What is the slope of your linearized graph?

For part one, the slope of the linearized graph is 1.19 x 10^-5 N/I². For part two, the slope of the linearized graph is 7.65 x 10^-6 N/I².

4. How does the slope of your linearized graph compare to μ_oL / 2πd_o? What is the percent difference?

For part one, μ_oL / 2πd_o = 5.99 x 10^-6 Tm / A, so the percent difference is 66.1%. For part two, μ_oL / 2πd_o = 9.65 x 10^-6 Tm / A, so the percent difference is 23.1%.

5. Assuming your linearized graph is a fairly good straight line and the slope is about right (see previous question), what physical relationships have you confirmed in this experiment?

The physical relationships that should have been confirmed are that F = mg = μ_oLI² / 2πd_o.

Conclusion

To begin the experiment, a current was connected to two parallel wires in a manner so that it would run in opposite directions. No current was actually run through the wires at this point. The length of the upper wire was measured, along with the radius of both the upper and lower wires, the distance from the mirror to the end of the upper conductor, and the distance from the mirror to the whiteboard. A He/Ne laser was turned on and reflected off the mirror onto a whiteboard, making sure that the upper and lower wires were touching. The initial position of the laser was marked on the board, and then the wires were allowed to repel to a distance of about 2 mm apart, using a counterweight to achieve this separation. The new position of the laser on the whiteboard was marked, and the distance between the two noted points was measured and recorded.

Masses were then added in increments of about 20 mg to the pan on the upper wire. At each weight, current was run through the wires to return the laser to its secondary position. After reaching the secondary position, the current was recorded and the next trial was performed, until six trials were completed. This whole process was repeated after using the counterweight to achieve an initial separation between the wires of about 4 to 5 mm.

Talk about results calculation number from questions in comparison to slope (percent difference).

Sources of error (elaborate on these a little bit and add any more you can think of): Inaccurate s_o measurement (dots marked were not extremely precise). The laser was pointed at an angle at the mirror, not head on. This would cause the calculation of d to be slightly thrown off. Hard to match laser perfection with marking because fluctuation in reaching equilibrium. Any other inaccuracies in measurements. Overall the perfect differences are probably not too bad considering all the possible sources of error.

Equations

B = μ_oI’ / 2πd_o

F = ILB = IL μ_oI’ / 2πd_o = μ_oLI² / 2πd_o

F = mg = μ_oLI² / 2πd_o

d = rs / 2D

d_o = d + r_upper + r_lower

Percent Difference = |x₁ – x₂| / (x₁ + x₂)/2 x 100%

I. Introduction

The word perfection is thrown around quite often, but what exactly does perfection mean and is it humanly possible to fathom such an idea? The New Oxford American Dictionary defines perfection as “the condition, state, or quality of being free or as free as possible from all flaws or defects.” This interpretation in my opinion dances around the meaning of the word, as it defines it in terms of what is lacks, rather than what it encompasses. Other dictionaries define perfection similarly, declaring that it is a state of flawlessness. This in itself hints that perhaps perfection is unknowable if a tangible definition is unable to be construed. How is one to know whether or not something is free from all faults? Who is the authority on such matters?

In subjective terms, the individual can make claims to experiencing or knowing perfection, but these assertions can in no case be made with complete assurance. There are no objective examples of perfection, thus the individual has no basis for making claims of perfection; there are simply no known ideal objects or concepts for comparison. Without any concrete notion of perfection, it is impossible to know such an idea. It may be possible to understand representations or derivations of perfection, but where certainty is concerned, it is beyond human comprehension.

II. Analysis

I feel the philosopher John Locke would contend that certainty of perfection is well within the reaches of human comprehension. He argues that we come to know things through perception, reason and inference, memory, and testimony. While he does concede that each of these attributes are flawed, he states that when used in tandem they can yield certainty. Locke ranks perception as the most important of these factors leading to knowledge, followed by reason and memory which carry equal importance, and finally testimony. He conveniently chooses perception to be the foremost factor in this process as his theories are predominantly based upon empiricism.

Locke believes that the mind is a tabula rasa which organizes raw sense data by a “simple operation of the mind.” The aforementioned raw sense data is information derived from the senses. This organization of perceptions leads to ideas, which are in a sense written onto the tabula rasa and are available for access by one’s memory. Locke strengthens his claim to empiricism by denouncing Socrates’ idea of innatism, the idea that all knowledge has been with us since birth, through the examples of universal assent, children and idiots, and noble savages. In short, he asserts that what we know must be environmental; knowledge is a spatial experience.

With those principles in mind, I believe Locke would approach the idea of perfection in the following manner: certainty of perfection can be achieved through the application of the four ways in which we come to know things. To demonstrate Locke’s method, let’s take for example the perfect pizza. First and foremost, Locke would pose the questions “How do you perceive this pizza?” and “What are your senses telling you?” The subject would first look at the pizza and declare that in their mind, the pizza looks perfect; it is without any flaws. The subject would then take a bite of the pizza and feel as if the pizza could not possibly taste any better than it does. The crust is just the right texture, the cheese is cooked to a golden finish, and the sauce is spiced exquisitely; this is truly the food of the Gods.

With perception of perfection fulfilled, the subject would then be asked to use reason and inference to test their thoughts. The individual may then be exposed to another pizza that is not as appetizing. Maybe this pizza is too cold and the crust is burnt. With this lesser pizza available for comparison, the subject would then be able to infer that if the second pizza is not perfect, then the first pizza has the potential to be perfect. The individual could then strengthen their claim to knowledge by thinking back to past experiences. They may try to think if there has been a time when they were exposed to a better pizza. If they cannot, then their claim to perfection is warranted. The final way to solidify their claim would be to ask for outside testimony. They may offer a slice of their perfect pizza to a passer-by. If that person also agrees that the pizza is perfect, then the individual has a solid claim for certainty of perfection.

Immanuel Kant on the other hand I believe would be not as apt to allow for claims of certainty in regards to perfection. Kant is an advocate of the ding-an-sich, or the thing in itself. It is the idea that any object or idea is unknowable; only representations of it can be known. This philosophy is borrowed in part from Plato who coined the notions of the realms of being and of becoming, which Kant refers to as the noumenal and phenomenal realms. The phenomenal realm refers to that which is knowable and contains all that is perceivable by human senses, namely subjective representations of truth. The noumenal realm on the other hand is far more objective and is inclusive of ideals and certainty beyond human comprehension. Kant’s ding-an-sich resides in the noumenal realm, which is beyond human experience.

Kant philosophizes that these noumenal ideas vary in degrees of perfection and that the categories of understanding are what allow us to obtain knowledge about the world around us; to apprehend some semblance of the thing in itself. Knowledge of the world begins with the senses, but reason is what allows us to gain a fuller understanding of things than other people. The categories of understanding which allow for reasoning include quantity, quality, relation, and modality. These a priori aspects of knowledge can then be used to make a posteriori judgments, and thus form some order of representations.

Kant also acknowledges another way in which one can further their understanding of reality and that is through aesthetic experience. He says that by way of mediums such as art, good food, and music, that the individual is able to transcend empirical experience and gain an even further understanding of reality. It is a state of knowledge acquisition which is difficult to explain, as the individual uses an instrument above senses and reason to secure understanding. However, even with the combination of aesthetic experience and the categories of understanding, Kant claims that one can never know the ding-an-sich.

Once again using the example of the perfect pizza, I feel as though Kant may argue that the idea of pizza itself is an entity of perfection which resides in the noumenal realm. He seems to think that all ideas and objects that one perceives are merely representations of the idealness which an item posses. We may perceive a pizza to possess the quality of perfection, but because we can never know the ding-an-sich of a perfect pizza, this means we will never be certain in making such an assumption. What we consider to be a perfect pizza may actually be bad pizza in comparison to the idea of pizza that resides in the noumenal realm. Unfortunately, the thing in itself can never be known, therefore we will never know how close we are to experiencing perfection.

Aesthetic experience can give rise to an even greater understanding of perfection in the case of pizza, however. Food, along with art and music, is one of the few means which allow for a higher comprehension of reality. Beyond the use of categories of understanding for making judgments on what one may think to be the perfect pizza, the aesthetic event of consuming the pie yields knowledge surpassing that which could have been construed through senses and reason. This combination of apparatuses of the mind still falls short according to Kant, in reaching any certainty about idea of perfection; the most perfect form of an idea, the ding-an-sich, is unknowable.

III. Critique

I believe that perfection is an idea beyond human comprehension. My view is that without any objective notion of perfection, no claims of the concept can be undeniably withheld. As far as I know, there is no idea, concept, or object that is universally agreed upon as being perfect. Without any basis with which to make claims of perfection, any assertions of perfection are made with uncertainty. I acknowledge subjective claims of perfection to simply be derivations from the idea.

For example, in baseball when a pitcher throws a complete game without giving up a hit or walk, it is considered a perfect game. I feel that there are different levels of perfection that can be construed from this scenario. Let’s say three different pitchers all throw a perfect game; pitcher one throws the most strikeouts, pitcher two throws the least total pitches, and pitcher three receives a generous call from the umpire that preserves his perfect game. Even though by definition all three pitchers achieved the same perfection, the question could then be asked “did one player pitch a more perfect game than another?” The argument could be made that because pitcher three received a gratuitous call that his perfect game was not as perfect as pitcher one’s or two’s. There could also be debate or whether is it a more difficult task to throw more strikeouts or less total pitches in a game, which would question whether pitcher one or pitcher two pitched a more perfect game. There is no clear model to base perfection off of; there is only evidence that these pitchers reached some degree of perfection, as in relation to the normal pitching outing, they performed exceptionally well.

In this sense I am in agreement with the philosophy of Kant. I believe that we can only know representations of ideals. The ding-an-sich is something that can never quite be apparent to us, though we can get close to knowing it. We may be able to state that we eaten an incredibly good pizza, but we can never claim with certainty that we have eaten the perfect pizza; objects and ideas can only approach perfection. I also agree with him in that we use our senses for the basis of knowledge, but that reason plays a major part in giving credulity to what we constitute as fact, maybe even more-so than the senses. Without reason, we succumb to the fallacies associated with the senses. Because of how easily we can be deceived by the senses, I disagree with Locke on most of him assertions.

Locke bases his philosophy predominantly on something that is subjective and varies within each of us from time to time. If our senses could adequately be used to justify certainty, then there would be no need for math, science, or any type of research. I know Locke states that reason, memory, and testimony need to be used in conjunction with perception in order to obtain certainty, but he places much of his emphasis on the empirical portion of his postulate. Just because you may perceive of something as being perfect, that does not constitute validity.

I am also bothered by the fact that he considers perception to be a completely spatial experience and fails to acknowledge the aspect of time. Ideas of perfection undoubtedly change over time. If you were to declare a pizza perfect using Locke’s four criteria, but then try a different pizza a week later that surpasses the previous pizza in every way possible, what label do you now give each pizza? According the Locke, the original pizza would still be considered perfect; if it was once perfect, it is always perfect. If the second pizza is even better however, would it not also be considered perfect? You are now left with two perfect pizzas, one of which is superior to the other. This is an illogical dilemma that Locke’s philosophy fails to prevent. In conclusion, the objective and undefinable nature of the idea of perfection is what prevents it from being known with certainty.

Purpose

To measure and determine the relationship between a magnetic field generated by a line of current and a radial distance from a conductor, and to measure and determine the relationship between a magnetic field at the center of a coil and the number of turns in a coil.

Hypothesis

As the distance from the center of the conductor increases, the magnetic field strength will decrease in accordance with the equation B = μ_oI / 2πR. As the number of turns in the coil increases, the magnetic field strength will increase, in accordance with the equation B = Nμ_oI / 2R.

Labeled Diagrams

See attached sheet.

Data

Part 1

Current = 7 A

Part 2

Current = 7 A

Diameter of Cylindrical support = 0.130 m

Graphs

Part 1

Part 2

Questions

Part 1

1. Theory states that the magnetic field produced by a long straight current-carrying wire decreases in strength as you get further from the wire. The exact dependence of the magnetic field strength B on radial distance from the wire R is B = μ_oI / 2πR where μ_o is the permeability of free space and has a value of 4π x 10^-7 Tm/A. For your data from Part 1, plot a graph in Graphical Analysis of B vs. 1/R. Your graph should have a linear trend. Perform a Linear Fit on your graph. What is the value of the slope?

The slope is 9.2 x 10^-7 Tm.

2. Calculate your value of μ_oI / 2π. How does it compare to the slope of your graph? What is the percent difference?

The value is 1.4 x10^-6 Tm, which is larger in value in comparison to the slope. The percent difference is 41%.

Part 2

3. Theory states that the magnetic field produced by a circular loop of current- carrying wire increases in strength as the number of turns of wire is increased. The exact dependence of the magnetic field strength B on the number of turns N is B = Nμ_oI/ 2R where R is the radius of the loop of wire. For your data from Part 2, plot a graph in Graphical Analysis of B vs. N. Your graph should have a linear trend. Perform a Linear Fit on your graph. What is the value of the slope?

The graph of the slope is 6.53 x 10^-5 T/turn.

4. Calculate your value of μ_oI / 2R. How does it compare to the slope of your graph? What is the percent difference?

The value is 6.7 x 10^-5 T/turn, which is very similar yet slightly large in value than the slope. The percent difference is 2.6%.

Conclusion

During part one of the experiment, magnetic field strength was measured as a function of radial distance from a conductor. First, a piece of polar graph paper with concentric circles starting at a diameter of 0.5 cm increasing in increments of 0.5 cm to 10 cm was punched through a rigid aluminum conductor at the center of the concentric circles. The paper was placed on the plastic table of the apparatus and was aligned using a compass so that the parallel lines on the sheet were pointing north. The paper was then secured to the apparatus using tape. The high amperage DC power supply was connected in series with a high power resistor and the aluminum wire at the side and on top of the apparatus. The magnetic field sensor was zeroed and the DC power supply was set to 7 A. With the current on and kept constant, the magnetic field strength was recorded at each circle on the polar graph paper by holding the sensor in line with the parallel lines on the sheet and so that the white dot on the sensor was on the left and at a 90^o angle with the parallel lines pointing north. The magnetic field strength was recorded using Vernier Lab Pro. This value was recorded along with the respective radius.

Graphical Analysis was used to plot B vs. 1/R and perform a linear trend. The resulting slope was 9.2 x 10^-7 Tm and the correlation was 0.9734. It was somewhat difficult to get accurate readings at the smaller radii, which negatively affected this correlation. The slope from this plot in comparison to the value of μ_oI / 2π, 1.4 x10^-6 Tm, yielded a percent difference of 41%. The data followed the expected trend of decreasing in magnetic field strength as the radius increased. Possible sources of error include the difficulty of aligning the sensor perfectly along the radius of each circle, and it was also a challenge to get an accurate reading from the sensor as the readings kept jumping around. Additionally, if the sheet was not perfectly aligned northward, there would be interference from the earth’s magnetic pull which would have affected the readings.

During part two of the experiment, magnetic field strength was measured as a function of the number of turns in a wire. First, the power supply was turned off and the center aluminum wire was removed along with the top table of the tangential galvanometer. The magnetic field sensor was inserted into the side of the cylindrical support by screwing it into the side of the top table support using a threaded plastic bushing. The white dot of the sensor was aligned to be in the center of the cylindrical support with the white dot facing upward. The sensor was zeroed and the power supply was turn on to 7 A. A piece of flexible wire was wound around the outside of this support to complete one full turn. The magnetic field sensor measured B using “Events with Entry” on Lab Pro. The magnetic field strength was measured for six full turns of the wire. The diameter of the cylindrical support was also measured, being 0.013 m.

Graphical Analysis was used to plot B vs N and perform a linear trend. The resulting slope was 6.53 x 10^-5 T/turn and the correlation was 0.9943. The data followed the expected trend of increasing in magnetic field strength as the number of turns increased. The slope from this plot in comparison to the value of μ_oI / 2R, 6.7 x 10^-5 T/turn, yielded a percent difference of only 2.6%. Possible error could have resulted from the earth’s magnetic field. Additionally, the wire was not perfectly wrapped around the base, which would throw the readings off as it would not have been an exact turn of the wire. Finally, it was difficult to align the sensor perfectly in the middle of the support, so again this would contribute to some error in the readings.

Equations

Percent Difference = |E2 – E1| / [ (E1 + E2) / 2 ] x 100%

B x R = μ_oI / 2π

B / N = μ_oI / 2R

Purpose

To investigate the current flow and voltages in series and parallel circuits, and also to use Ohm’s law to calculate equivalent resistances of series and parallel circuits.

Hypothesis

The calculated equivalent resistances for the series circuits will abide by the equation R_eq = R₁ + R₂ and for the parallel circuits the value will be similar to 1/R_eq = 1/R₁ + 1/R₂. The current flow is expected to be uniform throughout the series circuits, but will be stronger through the smaller resistor in the parallel circuits. The voltages across each resistor should add up to V_TOT in the series circuits, and the voltages should be uniform throughout the parallel circuits.

Labeled Diagrams

See attached sheet.

Data

Part 1: Series Circuits

Power supply: 2.5 V

Part 2: Parallel Circuits

Power supply: 2.5 V

Part 3: Currents

Power supply: 5 V

Graphs

Part 3: Currents

Trial 1:

Average current through 10 Ω: 0.0655 A

Average current through 51 Ω: 0.0656 A

Trial 2:

Average current through 68 Ω: 0.0648 A

Average current through 51 Ω: 0.0925 A

Questions

Part 1:

1. Examine the results of Part 1. What is the relationship between the three voltage readings: V₁, V₂, and V_TOT?

V₁ plus V₂ is about equal to V_TOT.

2. Using the measurements you have made above and your knowledge of Ohm’s law, calculate the equivalent resistance (R_eq) of the circuit for each of the three series circuits you tested.

See data table.

3. Study the equivalent resistance readings for the series circuits. For each of the three series circuits, compare the experimental results with the resistance calculated using the rule for calculating equivalent resistance outlined in the Theory section. In evaluating your results, consider the tolerance of each resistor by using the minimum and maximum values in your calculations.

The range for the 10 Ω resistor is 9.5 Ω to 10.5 Ω. This gives a theoretical R_eq range of 19.0 Ω to 21.0 Ω for trial 1. The calculated value of 19.0 Ω falls just on the edge of this range. For trial 2, the 10 Ω resistor has the same range and the 51 Ω resistor has a range of 48.45 Ω to 53.55 Ω. This gives a theoretical R_eq range of 57.95 Ω to 64.05 Ω. The calculated value of 58.2 Ω again falls just on the edge of that range. For trial 3, the theoretical R_eq range is 96.9 Ω to 107.1 Ω, and the calculated R_eq value of 106 yet again falls within that range.

Part 2:

4. Using the measurements you have made above and your knowledge of Ohm’s law, calculate the equivalent resistance (R_eq) of the circuit for each of the three parallel circuits you tested.

See data table.

5. Study the equivalent resistance readings for the parallel circuits. Do your results verify what is expected for R_eq from the Theory section?

Yes, the calculated equivalent resistances have about the same value as 1/R_eq = 1/R₁ + 1/R₂.

6. Examine the results of Part 2. What do you notice about the relationship between the three voltage readings V₁, V₂, and V_TOT in parallel circuits?

V₁, V₂, and V_TOT are all about equal.

Part 3:

7. What did you discover about the current flow in a series circuit in Part 3?

The current flow through each resistor is equal.

8. What did you discover about the current flow in a parallel circuit in Part 3?

The current flow through each resistor differs.

9. If the two measured currents in your parallel circuit were not the same, which resistor had the large current going through it? Why?

The smaller resistor had the largest current going through it because current prefers to go through the path of least resistance.

Conclusion

During part 1 of the experiment….procedure (what was done), results, expectations and sources of error.

During part 2 of the experiment….procedure (what was done), results, expectations and sources of error.

During part 3 of the experiment…procedure (what was done), results, expectations and sources of error.

Equations

R = V / I

R_eq = R₁ + R₂ + R₃ + …

1/R_eq = 1/R₁ + 1/R₂ + 1/R₃ + …

V_TOT = V₁ + V₂ + V₃ + …