CHEM 341. Fall 2000.   Previous PS   Answers   PS#9.doc (Word 97)  Due Tuesday, Dec. 12

1. At 25° C and at a constant pH of 5, the inversion of sucrose proceeds with a constant half-life of 500 min. At this same temperature, but at a pH of 4, the half-life is constant at 50 min. The rate law is . What are the values of a and b?

2. The rate of acid catalyzed hydrolysis of ethyl acetate in hydrochloric acid solution obeys the following rate law

where k = 0.1 M^-1 h^-1 at 25° C. Neglecting any back reaction, calculate the time required for half of the ester to be hydrolyzed if the initial concentrations of ester and of HCl catalyst are 0.02 M and 0.01 M, respectively.

3. In the study of a first-order reaction

it is found that A/A_o is 0.125 after 1 hour. The system initially consisted of 0.20 mole of gaseous A at STP. Calculate the initial rate of reaction in moles of A reacting per minute.

4. For the following mechanism:

where k₁ = rate of forward Reaction #1; k_-1 = rate of reverse reaction for Reaction #1; k₂ = rate of forward Reaction #2.

Using the steady-state assumption, find the expression for in terms of P_N2O5, P_NO, P_NO2, k₂, k₁, and/or k_-1.

5. Consider the reaction

where k₁ = rate of forward Reaction #1; k_-1 = rate of reverse reaction for Reaction #1; k₂ = rate of forward Reaction #2.

Find the rate law of this reaction in terms of [A], [B], [P], k₂, k₁, and/or k_-1. Now suppose that we set [B] = [A]. Under these conditions, what is the overall order of the reaction if k_-1 >> k₂[A]? What is the overall order of the reaction if k_-1 << k₂[A]?

6. The reaction

obeys the rate law: . It takes 0.5 min for one percent of CH₃CH₂NO₂ to react at 25° C, in the case of a solution 0.002 M in CH₃CH₂NO₂ and 0.3 M in NaOH. Calculate k. Calculate also how long it would take for half of CH₃CH₂NO₂ to react.

7. Complete the following statements:

Plot of ln [A]_t or vs. time yields a straight line of slope _______ for a first-order reaction.

Plot of vs. time gives a straight line of slope ________ for a second-order reaction.

8. Consider the following reaction

where k₁ = rate of forward reaction and k_-1 = rate of reverse reaction.

This reaction is first order in both the forward and the reverse direction.

1. Calculate k₁ if the initial velocity (i.e. while [B] is still insignificant) is 5.1 ´ 10^-4 M s^-1 and the initial concentration of A, [A]_o is 4.7 ´ 10^-2 M.
2. A plot of vs. time has a slope equal to -0.01795 s^-1. Find k_-1. Hint: The information from part (a) is also true for part (b).
3. Calculate the equilibrium constant and the half-life for this reaction.

9. Sketch approximate plots of the concentration of [A], [B], and [C] vs. time for (on the same graph) if both reactions are first order, and is the rate-limiting step (i.e. k₁ << k₂). Repeat these plots on a separate graph for the same reaction but if is the rate limiting step (i.e. k₁ >> k₂).

10. For the following reaction

A plot of vs. time has a slope of 5.0 s^-1. Calculate the rate constant, k, of the forward reaction if the rate of the reverse reaction is insignificant and if [A]_o = 3.1 M and [B]_o = 4.7 M.

11. Suppose a reaction has a rate constant of 1.23 x 10³ s^-1 at 300 K and of 6.45 x 10³ s^-1 at 400 K. Calculate the Arrhenius activation energy and the pre-exponential factor A. Then use these values to predict the rate constant at 500 K.

12. Explain how a plot of ln (k/T) vs. 1/T can be used to determine DH_{transition state} and DS_{transition state} if the values of k_B, k, and h are known. (k_B is Boltzman's constant, k is the tunneling factor, and h is Planck's constant).

13. The chlorination of an organic molecule (M)

with initiation by thermal dissociation of chlorine, may proceed by the following mechanism (in the absence of light).

Find the rate law for the overall reaction in terms of [M], [Cl₂], and various constants (i.e. k₁ and/or k₂ and/or k₃ and/or k₄).