Archives for February 2010

Purpose

To determine the spring constant of a spring by measuring its stretch versus applied force, to determine the spring constant of a spring by measuring the period of oscillation for different masses, and also to investigate the dependence of period of oscillation on the value of mass and amplitude of motion.

Hypothesis

If the applied force (mass) is to remain the same while the vertical displacement is increased, there period will remain the same. However, if the vertical displacement is held constant while the applied force in increased, the period will increase. This is in accordance with the derived equation T = 2π (M / k)^0.5.

Labeled Diagrams

See attached sheet.

Data

Part I

k = 3.53 N/m

Part II

Part III

m_s = 0.00940 kg

Slope = 10.5 s²/kg

Y-Intercept = 0.0687 N

k = 3.75 N/m

C = 0.694

% difference = 6.04%

Graphs

Part I

Part II

Part III

Questions

1. Do the data from Part 1 verify Hooke’s Law? State clearly the evidence for your answer.

The data correlate close to Hooke’s Law, but not quite. The law states that F = -ky, where F is in this case Mg and y equals the negative displacement. After graphing forces versus displacement, a value of 3.53 N/m was determined as the spring constant. However, when applying this value to the equation and using recorded displacement values, the calculated force come up less than the actual for used. For example, in the first trial y = -0.055 m. Multiplying that value by the extrapolated spring constant gives a theoretical force of 0.194 N, but the actual force used was 0.244 N. All other trials yield a similar lowball theoretical force.

2. How is the period T expected to depend upon the amplitude A? Do your data confirm this expectation?

Period is not expected to depend upon amplitude, as suggested by the equation T = 2π (M / k)^0.5, where amplitude is absent as a variable. The data confirms this expectation, as the period was nearly the same for each trial.

3. Consider the value you obtained for C. If you were to express C as a whole number fraction, which of the following would best fit your data (1/2, 1/3, 1/4, 1/5)?

The obtained value of C is 0.694, which is closest to 1/3.

4. Calculate T predicted by the equation T = 2π (M / k)^0.5 for M = 0.050 kg. Calculate T predicted by T = 2π ( [M + Cm_s] / k )^0.5 for M = 0.050 kg and your value of C. What is the percent difference between them? Repeat for a value for M of 1.000 kg. Is there a difference in the percent differences? If so, which is greater and why?

T predicted using the first equation and M = 0.050 kg is 0.726 s. T predicted using the second equation and M = 0.050 kg is 0.771 s. This is a percent difference of 6.01%.

T predicted using the first equation and M = 1.000 kg is 3.24 s. T predicted using the second equation and M = 1.000 kg is 3.26 s. This is a percent difference of only 0.615%. The greater percent difference occurs at the lower weight because the weight of the spring is almost insignificant at higher weight. The proportion of the mass to the spring is so great that it has almost no effect on the calculation.

Conclusion

During part one of the experiment, the vertical displacement of a spring was measured as a function of force applied to it. The starting position of the spring was recorded using a stretch indicator. Mass was added to the spring, and the displacement was recorded. This was repeated with various amounts of mass. From these data, a graph of force versus displacement was plotted, and a linear fit slope revealed the spring constant. In this endeavor, the spring constant was valued at 3.53 N/m.

However, when applying this spring constant to the recorded displacements in the Hooke’s Law equation, the calculated forces are lower than the recorded forces. In similar manner, when rearranging Hooke’s Law to solve for displacement, the calculated displacements are larger than the actual recorded displacements. This means there was human error, most likely in terms of not being precise with the displacement readings because the recordings for the masses used were accurate. Because such small masses were used, any error in displacement readings was augmented. The spring used may also not have been perfect.

During part two of the experiment, the period of the spring was measured as amplitude changed while mass remained constant. The period remained nearly the same throughout every trial, which was to be expected. Any differences in period may be accounted to inadequate stopwatch usage and inaccurate starting displacements throughout the trials. It should be noted that at amplitude of 0.100 m, the hook lost contact with the spring for a split second at the apex of oscillation, which accounts for its oddity in period. This was something that could not be avoided; at that amplitude the spring pulled the hook up too quickly which caused the loss of contact. The resulted graph of period versus amplitude yielded a linear fit slope of close to 0 (-0.247 s/m), which was predicted.

During part three of the experiment, the period of the spring was measured as mass was varied while amplitude remained constant. As the mass was increased, the period also increased. This was not surprising considering the given equations. The square of the period versus mass for each trial was plotted and a linear fit was taken. The slope and y-intercept of this line was then used to determine the spring constant and C, the fraction of the spring’s mass that should be taken into account for the equation T = 2π ( [M + Cm_s] / k )^0.5. The calculated value of k was 3.75 N/m, which is only 6.04% different from the value determined earlier of 3.53 N/m. The value of C was determined to be 0.694, which is closest to the whole number fraction of 1/3. Any error during parts two and three can be attributed to inaccurate stopwatch recordings and slight variance in displacement and release of the masses at each amplitude.

Equations

T = 2π (M / k)^0.5

T = 2π ( [M + Cm_s] / k )^0.5

slope = 4π² / k

y-intercept = 4π²Cm_s / k

Tinkering with Tin: Synthesis of SnCl(CH₂C₆H₅)₃ and SnCl₄[OS(CH₃)₂]₂

Abstract

The reaction of tin with benzyl chloride under reflux yields SnCl(CH₂C₆H₅)₃ in low percent yield (around 15%) due to various factors. ¹H NMR of SnCl(CH₂C₆H₅)₃ shows a singlet at δ 3.15 with satellites containing coupling constant between Sn-H of 78.1 Hz. The reaction of SnCl₄ with OS(CH₃)₂ yields SnCl₄[OS(CH₃)₂]₂ with poor percent yield (around 140%) due to various factors. The IR spectrum of SnCl₄[OS(CH₃)₂]₂ shows a large S-O stretch at 899.7 cm^-1, which is a lower frequency than the S-O stretch of 1042.5 cm^-1 from the IR spectrum of OS(CH₃)₂, suggesting coordination on the metal complex at oxygen.

Introduction

The reaction of tin with benzyl chloride yields the metal complex SnCl(CH₂C₆H₅)₃. The reaction specifically takes place in the following manner:

[Figure missing.]

This is compound of interest because of the different isotopes of tin that naturally occur. In order to determine the structure of said substance from a ¹H NMR spectrum, the peaks must be analyzed for satellites occurring from coupling of hydrogen to isotopes of tin. The observed spectrum is a combination of SnCl(CH₂C₆H₅)₃ molecules containing different isotopes of Sn, namely ¹¹⁷Sn and ¹¹⁹Sn, among others. The value for J_Sn-H between satellites can confirm the presence of SnCl(CH₂C₆H₅)₃. Mass spectrum can also be used to confirm the presence of SnCl(CH₂C₆H₅)₃ in the product by looking for a peak at m/z equal to the molecular mass of the substance (427 g/mol).

SnCl₄[OS(CH₃)₂]₂ can be synthesized from the following reaction:

[Figure missing.]

It is a reaction of interest because it can be used to determine where OS(CH₃)₂ coordinates to Sn. Coordination of S to Sn would result in a higher frequency of S-O stretch on an IR spectrum than the frequency of the S-O stretch on the IR spectrum of OS(CH₃)₂ due to a strengthening of the S-O bond. Coordination of O to Sn would result in a lower frequency of S-O stretch because of a weakened S-O bond from the resonance form needed to secure that coordination.¹

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 SnCl(CH₂C₆H₅)₃ (1) and SnCl₄[OS(CH₃)₂]₂ (2) were based on reports published previously.¹

SnCl(CH₂C₆H₅)₃ (1). 325 mash-Aldrich Sn powder (1.939 g, 16.34 mmol), 99% Aldrich benzyl chloride (6.0 mL, 52 mmol), and deionized H₂O (4.0 mL) were added subsequently to a 50 mL round-bottom flask. A small stir bar was added then added to this solution. A sand bath was placed over a stir plate and a cold water condenser with greased joint was inserted into the round-bottom flask containing the solution. This connection was further secured with a keck clip. The round bottom flask was placed in the sand bath and the condenser was connected to the cold water source.

Once secure, the sand bath was set to 50% power and the stir bar was spun a shade over moderate speed. The solution was allowed to reflux for 2.75 h. Once reflux was complete, the 50 mL round-bottom flask was removed from the condenser and allowed to cool in an ice bath until it was cold. The liquid was decanted from the white precipitate and discarded. The white precipitate was saved. Ethyl acetate (10 mL) was added to the precipitate and this solution was heated using a sand bath at 65% power and stirred at moderate speed until the white solid had completely dissolved. The round-bottom flask was then taken off the heat and submerged in an ice bath for approximately 0.5 h to allow for recrystallization.

The stir bar was removed and a high vacuum was used for about 10 minutes to extract the extraneous liquid and leave a white powder. Several mL of ether were added to the round-bottom flask and a glass stir rod was used to break up the chunks of powder and dissolve it in the ether. This solution was then suction filtered with a 30 mL glass frit and allowed the dry. The precipitate collected was 1 (0.471 g, 13.49% based on the amount of Sn powder used). ¹H NMR (CDCl₃): δ 7.25 (s, CDCl₃), 7.19 (s, Ph-H), 7.17 (s, Ph-H), 7.05 (s, Ph-H), 3.15 (s, J_Sn-H = 78.1 Hz, CH₂).

SnCl₄[OS(CH₃)₂]₂ (2). SnCl₄ (2.25 mL, 19 mmol), anhydrous diethyl ether (45 mL), DMSO (2.9 mL, 41 mmol), and ether (5 mL) were subsequently added to a 125 mL Erlenmeyer flask. The DMSO was added using a syringe for safety purposes while the other reagents were measured and added using graduated cylinders. This solution yielded a precipitate which was isolated by suction filtering the solution through a 50 mL glass frit. Several extra mL of ether were added to the Erlenmeyer flask to help aid in transfer of all the precipitate to the filter. Once dry, the white powder precipitate 2 was collected and weighed. 11.04 g (26.49 mmol) were recovered, giving a yield of 139.4%. FTIR (ATR) ν_(S-O) 899.7 cm^-1 (s S-O coordination to Sn).

OS(CH₃)₂ (3). The IR spectrum of (3) was taken by Dr. Graham. FTIR (ATR) ν_(S-O) 1042.5 cm^-1 (s, S-O linkage).

Results

The reaction of Sn, benzyl chloride, and H₂O yielded 0.471 g of the product, SnCl(CH₂C₆H₅)₃^. This translated to 1.102 mmol, and thus was a 13.49% yield based on the amount of Sn used, which was the limiting reagent in the reaction. Sn reacted to form the product in a 2:1 ratio, and 16.34 mmol of Sn was used to start, so that proportion was taken into account when calculating the percent yield. Proton NMR yielded several peaks. A set of peaks were found at δ 7.19, 7.17, and 7.05 were indicative of phenyl resonances derived from protons on the phenyl ring of the product.¹ A sharp peak located at δ 7.25 was due to the chloroform solvent ¹. Coupling between Sn and H produced a singlet at δ 3.15 with satellites ¹J_Sn-H equal to 78.1 Hz due to the presence of isotopes ¹¹⁷Sn and ¹¹⁹Sn.¹ The mass spectrum of SnCl(CH₂C₆H₅)₃ showed a peak at m/z = 427.0,¹ which is the molar mass of said substance.

The reaction of SnCl₄ and DMSO yielded 11.04 g of product, SnCl₄[OS(CH₃)₂]₂. This translated to 26.49 mmol, and thus was a 139.4% yield. IR spectrum of SnCl₄[OS(CH₃)₂]₂ showed its largest peak at 899.7 cm^-1 while the IR spectrum of OS(CH₃)₂ gave its largest peak at 1042.51 cm^-1.

Discussion

The percent yields for each product are less than stellar. During the synthesis of SnCl(CH₂C₆H₅)₃, letting the reagents reflux for a longer time period, closer to 3 hours, may have been beneficiary to resulting in more product. The reagents may not have all completely reacted. Some of the precipitate may have been accidentally removed during decanting after reflux, and much ethyl acetate may have been added to that precipitate. A minimal amount should have been used while trying to dissolve the white solid precipitate in the sand bath. The less ethyl acetate needed and used would have resulted in a better percent yield.

The fact that recrystallization did not seem take place as detailed¹ and that a vacuum had to be used to dry the product most likely did not help the yield of product either. Product may have been lost during the vacuuming process. The glass frit used for filtering was not of the utmost quality, and so product may have escaped during that process, also. The product was also not completely dry, and gave a misleading mass measurement, meaning the percent yield is even lower than recorded. The product obtained did seem to give a clear ¹H NMR spectra, meaning it was fairly pure. The coupling between Sn and H due to isotopes ¹¹⁷Sn and ¹¹⁹Sn ¹ in the product is distinctly visible around δ 3.15 with a J_Sn-H of 78.1 Hz. The NMR chemical shifts of the Sn-CH₂ protons and the C­₆H₅ protons of SnCl(CH₂C₆H₅)₃ are so different because of the 117 and 119 isotopes of Sn. They affect the coupling with H, producing satellites. The C₆H₅ protons are not affected by this coupling. The literature states that peaks for phenyl resonance appear around δ 7 and chloroform appears around δ 7.24, which seems to validate the experimental values obtained (δ 7.05 to 7.19 for phenyl resonances ad δ 7.25 for chloroform).¹

The percent yield of SnCl₄[OS(CH₃)₂]₂ is likely thrown off because the product was not dry when it was weighed. Several extra mL of ether were used for transport of the precipitate to the glass frit for filtering, which would most likely lead to loss of product. Not all of the precipitate was able to be transferred from the Erlenmeyer flask to the frit. Product was distinctly lost due to a seemingly defective frit, too. Attempts to refilter the filtrate were unsuccessful. The fact that the frit quality was poor meant that the product was not able to be dried well and thus carried extra weight. The product seemed to smoke away as it was allowed to dry further in exposure to air, and lost mass over time. This conundrum could not be adequately explained. IR spectrum of the product SnCl₄[OS(CH₃)₂]₂ shows its largest stretch at 899.7 cm^-1, hinting that the coordination to Sn occurs at oxygen, as this frequency is lower than that of the largest stretch from the OS(CH₃)₂ spectrum (1042.51 cm^-1). This is due to resonance and weakening of the S-O bond.¹ The two spectra are similar save for the shifting of that one peak. The stretch at 1042.51 cm^-1 is consistent with the value stated in the literature for S-O stretching (approximately 1100 cm^-1).¹

Conclusion

The main purposes of the experiments were to decipher the ¹H NMR for SnCl(CH₂C₆H₅)₃ in order to determine J_Sn-H and to interpret the IR spectra of OS(CH₃)₂ and SnCl₄[OS(CH₃)₂]₂ to tell whether O or S coordinates to Sn. The J_Sn-H was found to be 78.1 Hz. The observed spectrum is a combination of SnCl(CH₂C₆H₅)₃ molecules containing different isotopes of Sn, namely ¹¹⁷Sn and ¹¹⁹Sn, among others. This is what makes the ¹H NMR difficult to interpret, but the J_Sn-H value is validation of the presence of SnCl(CH₂C₆H₅)₃. The percent yield for that reaction was poor, due to varying factors. Longer reflux time, less ethyl acetate used during recrystallization, and better filtration techniques all would have contributed to an improved percent yield.

The IR spectrum of OS(CH₃)₂ showed its largest stretch around 1050 cm^-1 while the IR spectrum of SnCl₄[OS(CH₃)₂]₂ gave its largest stretch around 900 cm^-1. This lower frequency of stretch suggests that O and not S coordinates to the Sn. This is due in part to the resonance form needed to form the complex, which weakens the S-O bonding, and thus lowers the stretching frequency. The yield for the reaction to form SnCl₄[OS(CH₃)₂]₂ was also poor, which can be mostly attributed to poor filtering and drying techniques, along with the overuse of ether.

References

(1) “Synthesis and Techniques in Inorganic Chemistry,” Third Edition, G. S. Girolami, T.R. Rauchfuss, and R. Angelici, University Science Books, 1999.