Chemistry 2710 Spring 2000 Final Examination

Name:

Aids allowed: calculator, one $8\frac{1}{2}\times 11''$ sheet of notes

If you have a graphing calculator, you can use it rather than hand drawing graphs. If you do use your calculator's graphing capabilities, explain in detail what you did (what graphs you drew, how you interpreted them, etc.). If you need to draw graphs by hand, graph paper is included at the end of this exam. Make sure to label your graphs with the question number.

Useful data:

$R = 8.3145\,\mathrm{J\,K^{-1}mol^{-1}}$, $k_B = 1.3807\times 10^{-23}\,\mathrm{J/K}$,
$h = 6.6261\times 10^{-34}\,\mathrm{J/Hz}$.
At 298.15K, $1\,\mathrm{bar} = 0.040339\,\mathrm{mol/L}$.
To convert degrees Celsius to Kelvin, add 273.15.

1.

The rate of a reaction triples when the concentration of a reactant is doubled. What is the order of the reaction with respect to the concentration of this reactant? [4 marks]

2.

Explain briefly the physical meaning of the exponential term in the Arrhenius formula. [4 marks]

3.

A set of initial velocity experiments was performed for the reaction $\mathrm{A}\rightarrow 2\mathrm{P}$ by stopping the reaction after approximately 1min and measuring the concentration of P (initially zero). In one run, the initial concentration of A was 0.04mol/L. The reaction was stopped at 64s, at which time p had reached $1.3\times 10^{-5}\,\mathrm{mol/L}$. What was the initial rate? [4 marks]

4.

Find the reactions in the following list which are either certainly or probably not elementary and explain briefly which features make it so. [4 marks]

(a)

$\mathrm{H_2O_{2(aq)}} + 2\mathrm{Fe^{2+}_{(aq)}} + 2\mathrm{H^+_{(aq)}} \rightarrow 2\mathrm{H_2O_{(l)}} + 2\mathrm{Fe^{3+}_{(aq)}}$

(b)

$\mathrm{Cl_{(g)}} + \mathrm{O_{3(g)}} \rightarrow \mathrm{ClO_{(g)}} + \mathrm{O_{2(g)}}$

(c)

$\mathrm{C_{(s)}} + \mathrm{O_{2(g)}} \rightarrow\mathrm{CO_{2(g)}}$

5.

The rate constant for the reaction of hydroxyl radicals with methanal (formaldehyde) has been measured as a function of temperature:

T (K)	k ( $\mathrm{L\,mol^{-1}s^{-1}}$)
250	$4.02\times 10^7$
286	$8.49\times 10^7$
333	$1.80\times 10^8$
400	$3.99\times 10^8$
500	$8.51\times 10^8$
667	$1.80\times 10^9$

Calculate the activation energy and preexponential factor for this reaction. [10 marks]

6.

Methyl radicals react with ethane to form methane and ethyl radicals:

$$\mathrm{CH_{3(g)}} + \mathrm{C_2H_{6(g)}} \rightarrow \mathrm{CH_{4(g)}} + \mathrm{C_2H_{5(g)}}.$$

The preexponential factor for this elementary reaction is $2.00\times 10^8\,\mathrm{L\,mol^{-1}s^{-1}}$. What is the entropy of activation at 298.15K? What does the value of the entropy of activation of this reaction tell you about the transition state? [8 marks]

7.

Suppose that a certain drug is administered in pill form at a rate of one pill every 6 hours. Each pill, as it is manufactured, contains 18mg of the drug. The minimum effective dose for an adult of average mass is 12mg every 6 hours. The drug is somewhat unstable and breaks down in a pseudo-first-order reaction with a half-life of 47days. What is the shelf life of the drug? In other words, how long does it take before each pill contains less than the minimum effective dose? [5 marks]

8.

The empirical rate law for the reaction of aniline with iodine

$$\mathrm{C}_6\mathrm{H}_6\mathrm{NH}_2 + \mathrm{I}_2 \rightar... ...m{C}_6\mathrm{H}_5\mathrm{INH}_2 + \mathrm{H}^+ + \mathrm{I}^-$$

is

v = k[aniline][I₂].

The reaction is followed by withdrawing 10mL aliquots of the reaction mixture at roughly equal time intervals. These aliquots are titrated with thiosulfate solution to determine the iodine concentration. The reaction of iodine with thiosulfate is

$$\mathrm{I_2} + 2\mathrm{S_2O_3^{2-}} \rightarrow 2\mathrm{I^-} + \mathrm{S_4O_6^{2-}}.$$

(a)

What is the integrated rate law if the initial concentrations of iodine and aniline are equal? Express your answer in terms of the concentration of iodine. [2 marks]

Note: It is not necessary to show the derivation.

(b)

The following titration data were obtained in one run with $\mathrm{[aniline]}_0 = \mathrm{[I_2]}_0 = 0.0040\,\mathrm{mol/L}$ and $\mathrm{[S_2O_3^{2-}]} = 0.0100\,\mathrm{mol/L}$:

t (min)	V (mL)
0.00	7.23
10.25	5.85
20.60	5.03
29.85	4.40
40.11	3.90
49.63	3.51
59.88	3.21
70.69	2.94
80.80	2.66

Calculate the rate constant for the reaction. [10 marks]

9.

For the elementary reaction

$$\mathrm{H_{(g)}} + \mathrm{Br_{2(g)}} \revreact{k_+}{k_-} \mathrm{HBr_{(g)}} + \mathrm{Br_{(g)}},$$

$k_+ = 8.47\times 10^6\,\mathrm{bar^{-1}s^{-1}}$ and the equilibrium constant $K = 1.18\times 10^{31}$ at 298.15K. What is the value of k_-? [4 marks]

10.

In enzyme reactions, it is not uncommon for the enzyme to be left in an unreactive conformation after release of the product. A subsequent reaction converts the enzyme back to the active form. Symbolically, the mechanism is

$$\begin{array}{c} \mathrm{E}+\mathrm{S}\revreact{k_1}{k_{-1}}... ...{P}\\ \mathrm{F}\revreact{k_3}{k_{-3}}\mathrm{E} \end{array}$$

where E is the active form of the enzyme and F its inactive form, S is the substrate, P the product, and C the enzyme-substrate complex. Derive the rate law for this mechanism using the steady-state and/or equilibrium approximations, as appropriate. Is this mechanism kinetically distinguishable from the Michaelis-Menten mechanism? [10 marks]

11.

Briefly describe how you can recognize competitive inhibition of an enzyme-catalyzed reaction using Eadie-Hofstee plots. [5 marks]

12.

In class, we found that the product ratio for parallel first-order reactions

is just

$$\frac{p_1}{p_2} = \frac{k_1}{k_2}.$$

The product ratio of course varies with T since both k₁ and k₂ vary with T. Suppose that at $20^\circ\mathrm{C}$, p₁/p₂ = 20 while at $35^\circ\mathrm{C}$, p₁/p₂ = 15. What is the difference in the activation energies of the two reactions? Make sure that your answer makes it clear which of the two reactions has the higher activation energy. [10 marks]

13.

Create your own kinetics question and provide an answer for it. You should try to create a question of a similar level of difficulty as questions worth 10 marks on this exam. In other words, your question should require a few solution steps. If the question is in parts, the parts should be intimately interrelated. Moreover, your question should be substantially different from any other question on this exam.

Your question will be judged on the following points:

• Appropriate level of difficulty
• Originality: The question tests different concepts than those covered by other questions in this exam.
• Correctness: The question and associated solution do not contain any conceptual or technical errors.
• Completeness: The question contains all data necessary for its solution. All necessary solution steps are shown.
• Clarity: The question and solution are clearly understandable.

It may be a good idea to rough out your question on scrap paper before writing down the final version. [20 marks]