CHM 2422 (Physical Chemistry Lab II)

Introduction

The proposed particle in a box experiment uses theories from quantum mechanisms in order to determine and prove the behavior of a molecule. In the experiment performed, various dye molecules were observed using a Spectronic 21 spectrophotometer to determine their wavelengths of maximum absorption. The spectrophotometer emits light through the sample and uses a detector to measure the absorbance through a range of wavelengths. The “box” is considered to be the space between the nitrogens of the dye molecules, where the behavior of the molecules is observed. Upon measuring different concentrations of the dye molecules with the Spectronic 21, standard linear plots of absorbance versus concentration could then be graphed. These plots could then be used to establish that the dyes follow Beer’s law, A = εbc. The measured wavelengths of maximum absorption could then be compared to the theoretical values, which can be found using the following equations:

λ_max = 8ml²c (p + 3)² / [h(N+1)]

λ_max = 8ml²c (p + 3 + α)² / [h(p+4)]

where h = Planck’s constant, m = mass of an electron, c = speed of light, l = distance between the nitrogens, N = number of electrons in the entire molecular orbital π system, p = number of carbon atoms, and α = extra distance the conjugate electrons go beyond the terminal nitrogens. These equations are derived from the basics of quantum mechanics. By comparing the measured values to the calculated values, one can validate the theories of quantum mechanics and also determine α.

Procedure

To begin, 1 L of 1 x 10^-6 M solutions were prepared using the following compounds: 1,1’-diethyl-4,4’-cyanine iodide, 1,1’-diethyl-4,4’-carbocyanine iodide, and 1,1’-diethyl-4,4’-dicarbocyanine iodide. Then, the following dilutions of each of those solutions were prepared: 100%, 50%, 25%, 10%, and 5%. Each of the dilutions was then analyzed using a Spectronic 21 spectrophotometer to determine their measured absorbance and wavelength of maximum absorption. These measured values were saved on the computer and later analyzed.

Results

Calculations

λ max _(calculated) =

8 (9.1 x 10^-31 kg) (1.42 x 10^-10 m)² (2.998 x 10⁸ m/s) (7 + 3) ² / [ (6.626 x 10^-34 m²kg/s) (10 + 1) ]

λ max _(calculated) = 6.04 x 10^-7 m (1 nm / 10^-9 m) = 604 nm

 

λ max _(measured) =

8 (9.1 x 10^-31 kg) (1.42 x 10^-10 m)² (2.998 x 10⁸ m/s) (7 + 3 + α) ² / [ (6.626 x 10^-34 m²kg/s) (10 + 1) ]

α = 0.001628

 

Percent Error = | λ max _(calculated) – λ max _(measured) | / λ max _(calculated) x 100%

| 604 -595 | / 604 x 100% = 1.49%

 

Conclusions

The calculated λ max values were extremely close to the measured λ max values. The percent error was 1.49% for cyanine iodide, 3.49% for carbocyanine iodide, and 6.22% for dicarbocyanine iodide. These results seem very good considering the laboratory conditions; they are nearly the best results we could have hoped for. This seems to show the equations derived from quantum mechanics are indeed valid. However, the measured λ max values are all less than the calculated λ max values, which should not have been the case. The measured λ max values should have been greater than the calculated λ max values in order to account for α, the extra length past the terminal nitrogens. This in turn made the values for α all negative. The dyes all seems to follow Beer’s law, as shown by the high R² values calculated by plotting the absorbance versus concentration for each dye. It was odd that the absorbance reading for dicarbocyanine iodide exceeded a value of 1. Normally this should never happen; 1 should be the maximum absorbance value. This may be accounted for by the spectrophotometer not being correctly calibrated.

Introduction

This laboratory experiment placed an emphasis on the determination of the order of reaction and ultimately the rate constant and activation energy of the bromate-bromide reaction. The rate equation of this reaction is represented by:

-d[BrO₃^–] / dt = k [BrO₃^–]^x [Br^–]^y [H⁺]^z

Hence, by using varying and constant amounts of bromate, bromide, and acid in different trial runs, it is possible to determine the x, y, and z exponents of this equation, which are actually the order of the reactions.

In order to better understand the bromate-bromide reaction, it is important to take note of the stoichiometric equation, which is noted as:

BrO₃^– + 5Br^– + 6H⁺ —> 3Br₂ + 3H₂O

This reaction couples with the reaction of Br­₂ and methyl orange, which produces bleach. By combining the two reactions, the basis is built for determining the rate of the reaction. As bromate and bromide react, they produce Br₂, which then reacts with methyl orange to dissipate the color of the solution and show completion of the reaction. This dissipation of color can be timed and used for calculation.

However, this reaction happens very quickly, and under normal circumstances would not be able to be timed. By adding phenol to the solution, the reaction of Br₂ with methyl orange can be slowed down with the following side reaction:

C­₆H₅OH + Br₂ —> BrC₆H₄OH + H⁺ + Br^–

This reaction of Br₂ with phenol slows down the reaction with methyl orange enough that it is able to be timed. Otherwise, the reaction would happen very quickly and it would be untimable. Nitrate is added to the solution to also improve the quality of the reaction, by increasing the ionic strength of the ion. In theory, the rate equation of the reaction should equal:

-d[BrO₃^–] / dt = k (a x 2a x (3a)²) = 18ka⁴

Where a is equal to the original bromate concentration, 2a is the initial bromide concentration, and 3a is the initial hydrogen ion concentration. The plot of -∆[BrO₃^–] / t versus time at different temperatures should yield linear plots, with the slopes equaling 18ka⁴. Knowing the value of a, the rate constant (k), can be evaluated at each temperature.

Finally, once the rate constant is found, the activation energy can be determined by using the following equation:

log k = (-E / 2.303R) x (1 / T) + constant

By plotting the log k versus 1 / T° K for each temperature, the slope yielded also will provide the activation energy in terms of calorie per mole.

Procedure

To begin, aqueous solutions of the following reagents were prepared: 0.333 M potassium bromate, 0.667 M potassium bromide, 0.500 M perchloric acid, 0.030 M phenol, 0.500 M sodium nitrate, and 40 mg/L of methyl orange solution. Solutions comprised of these were then prepared according to the given specifications. However, potassium bromate, potassium bromide, perchloric acid, and water were combined in one flask while phenol, sodium nitrate, and methyl orange solution were combined in another flask. The flasks were then placed in the bath and allowed to come to a constant temperature. The flask containing the bromate and bromide was transferred into the flask with methyl orange. As soon as the two solutions made contact, timing began using a stopwatch, and the solutions were mixed using a glass stirring rod to ensure conformity. As soon as the orange color had completely dissipated, timing stopped. This process was repeated for every trial according to the specifications of the following charts:

Table #1 (At 25° C)

Table #2 (At 20° C)

Table #3 (At 25° C)

Table #4 (At 30° C)

Table #5 (At 35° C)

Results and Calculations

Determining the Order of Reaction:

-d[BrO₃^–] / dt = k [BrO₃^–]^x [Br^–]^y [H⁺]^z

Run 1 & Run 3

(0.002M) / (54.25secs) = k [0.333] ^x [0.0667] ^y [0.1] ^z
(0.002M) / (27.15secs) k [0.667] ^x [0.0667] ^y [0.1] ^z

0.5 = 0.499 ^x
x = 1

Run 1 & Run 2

(0.002M) / (54.25 secs) = k [0.0333] ^x [0.0667] ^y [0.1] ^z
(0.002M) / (30.34 secs) k [0.0333] ^x [0.1333] ^y [0.1] ^z

0.559 = 0.5 ^y
ln (0.559) = y ln (0.5)
y = 0.839

Run 1 & 4

(0.002M) / (54.25 secs) = k [0.0333] ^x [0.06667] ^y [0.1] ^z
(0.002M) / (24.47 secs) k [0.0333] ^x [0.06667] ^y [0.2] ^z

0.451 = 0.5^z
ln (0.451) = z ln (0.5)
z = 1.15

Concentrations versus Recorded Times

Determining the rate constant for each temperature

-d[BrO₃^–] / dt = k (a x 2a x (3a)²) = 18ka⁴

20° C: k = 0.0198 = 894.57
(18)(0.0333)⁴

25° C: k = 0.0321 = 1450.29
(18)(0.0333)⁴

30° C: k = 0.056 = 2530.10
(18)(0.0333)⁴

35° C: k = 0.0638 = 2882.51
(18)(0.0333)⁴

Activation Energy:

Slope = – E / (2.303 * R ) , R= 8.3145 J/mol K
-3287.7 = – E / (2.303 * 8.3145)
E = 62953.8 cal/mol

Conclusions

The first objective of this experiment was to determine the orders of the reaction. The values obtained vary in their likeness to the theoretical values. It was found that -d[BrO₃^–] / dt = k [BrO₃^–]¹ [Br^–]^0.839 [H⁺]^1.15 when it really should have been = k [BrO₃^–]¹ [Br^–]¹ [H⁺]². The calculated value for BrO₃^– was dead on, while the value for Br^– was slightly off and the value for H⁺ was significantly different. This error could be attributed to a multitude of sources. For example, the concentrations of solutions used may have been different than believed. If the solutions were old, they may have lost strength, contributing towards this. This would in turn affect the timing with the stopwatch, which would throw off the calculation of the orders of reaction. To go along with this, if the solutions were not made accurately, meaning the exact aliquots were not used, this would also affect the time and ultimately rate.

The next objective was to determine the rate constant for each temperature and then the activation energy. The rate constants calculated seem fairly large, meaning the slopes that resulted from plotting [BrO₃^–] versus time were of small value. If the slopes were larger numbers, then the rate constants would have been smaller. This in turn made the activation energy seem excessive. With smaller rate constant values, the plot would have resulted with a smaller number for the slope, and thus a smaller rate constant. This problem can again be justified due to the fact that the believed concentrations and temperatures of solutions may not have been actually what we were working with.