Tro - Chemistry: A Molecular Approach 4th Edition - Chapter 14

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Ch.14 - Chemical Kinetics

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Tro 4th Edition

Ch.14 - Chemical Kinetics

Problem 99b
The kinetics of this reaction were studied as a function of temperature. (The reaction is first order in each reactant and second order overall.)
C₂H₅Br(aq) + OH^- (aq) → C₂H₅OH(l) + Br^- (aq)
Temperature (°C) k (L,mol •s)
25 8.81⨉10^-5
35 0.000285
45 0.000854
55 0.00239
65 0.00633
b. Determine the rate constant at 15 °C.
Problem 99c
The kinetics of this reaction were studied as a function of temperature. (The reaction is first order in each reactant and second order overall.)
C₂H₅Br(aq) + OH^- (aq) → C₂H₅OH(l) + Br^- (aq)
Temperature (°C) k (L,mol •s)
25 8.81⨉10^-5
35 0.000285
45 0.000854
55 0.00239
65 0.00633
c. If a reaction mixture is 0.155 M in C₂H₅Brand 0.250 M in OH^-, what is the initial rate of the reaction at 75 °C?
Problem 100
The reaction 2 N₂O₅ → 2 N₂O₄ + O₂ takes place at around room temperature in solvents such as CCl₄. The rate constant at 293 K is found to be 2.35⨉10^-4 s^-1, and at 303 K the rate constant is found to be 9.15⨉10^-4 s^-1.Calculate the frequency factor for the reaction.
Problem 101
a. This reaction has an activation energy of zero in the gas phase: CH3 + CH3 → C2H6. b. Why might the activation energy be zero? c. What other types of reactions would you expect to have little or no activation energy?
Problem 101a
This reaction has an activation energy of zero in the gas phase: CH₃ + CH₃ → C₂H₆ a. Would you expect the rate of this reaction to change very much with temperature?
Problem 102a
Consider the two reactions:
O + N₂ → NO + N E_a = 315 kJ/mol
Cl + H₂ → HCl + H E_a = 23 kJ/mol
a. Why is the activation barrier for the first reaction so much higher than that for the second?
Problem 102b
Consider the two reactions:
O + N₂ → NO + N E_a = 315 kJ/mol
Cl + H₂ → HCl + H E_a = 23 kJ/mol
b. The frequency factors for these two reactions are very close to each other in value. Assuming that they are the same, calculate the ratio of the reaction rate constants for these two reactions at 25 °C.
Problem 103
Anthropologists can estimate the age of a bone or other sample of organic matter by its carbon-14 content. The carbon-14 in a living organism is constant until the organism dies, after which carbon- 14 decays with first-order kinetics and a half-life of 5730 years. Suppose a bone from an ancient human contains 19.5% of the C-14 found in living organisms. How old is the bone?
Problem 104
How old is a rock that contains 83.2% of the amount of uranium-238 it contained when it was formed?
Problem 105a
Consider the gas-phase reaction: H₂(g) + I₂(g) → 2 HI(g) The reaction was experimentally determined to be first order in H₂ and first order in I₂. Consider the proposed mechanisms. Proposed mechanism I: H₂(g) + I₂(g) → 2 HI(g) Single step Proposed mechanism II: I₂(g) Δk1k-12 I(g) Fast H₂( g) + 2 I( g) → k22 HI( g) Slow a. Show that both of the proposed mechanisms are valid.
Problem 105b
Consider the gas-phase reaction: H₂(g) + I₂(g) → 2 HI(g) The reaction was experimentally determined to be first order in H₂ and first order in I₂. Consider the proposed mechanisms. Proposed mechanism I: H₂(g) + I₂(g) → 2 HI(g) Single step Proposed mechanism II: I₂(g) Δk1k-12 I(g) Fast H₂( g) + 2 I( g) → k22 HI( g) Slow b. What kind of experimental evidence might lead you to favor mechanism II over mechanism I?
Problem 106a
Consider the reaction: 2 NH₃(aq) + OCl^-(aq) → N₂H₄(aq) + H₂O(l) + Cl^- (aq) This three-step mechanism is proposed: NH₃(aq) + OCl^- (aq) Δk1k2 NH₂Cl(aq) + OH- (aq) Fast NH₂Cl(aq) + NH₃(aq) →k3 N₂H₅⁺ (aq) + Cl^- (aq) Slow N₂H₅⁺ (aq) + OH^-(aq) →k4 N₂H₄(aq) + H₂O(l) Fast a. Show that the mechanism sums to the overall reaction.
Problem 107
What rate law corresponds to the proposed mechanism for the formation of hydrogen bromide, which can be written in a simplified form as: Br2(g) → 2Br(g) (Fast) Br(g) + H2(g) → HBr(g) + H(g) (Slow) H(g) + Br2(g) → HBr(g) + Br(g) (Fast)?
Problem 108
What rate law corresponds to the proposed mechanism for the formation of hydrogen iodide, which can be written in simplified form as: I2 Δk1k-1 2I (Fast), I + H2 Δk2k-2 H2I (Fast), H2I + I ¡k3 2HI (Slow)?
Problem 109
A certain substance X decomposes. Fifty percent of X remains after 100 minutes. How much X remains after 200 minutes if the reaction order with respect to X is (c) second order?
Problem 110
The half-life for radioactive decay (a first-order process) of plutonium- 239 is 24,000 years. How many years does it take for one mole of this radioactive material to decay until just one atom remains?
Problem 111
The energy of activation for the decomposition of 2 mol of HI to H2 and I2 in the gas phase is 185 kJ. The heat of formation of HI(g) from H2(g) and I2(g) is -5.65 kJ/mol. Find the energy of activation for the reaction of 1 mol of H2 and 1 mol of I2 to form 2 mol of HI in the gas phase.
Problem 112
Ethyl chloride vapor decomposes by the first-order reaction: C2H5Cl -> C2H4 + HCl. The activation energy is 249 kJ/mol, and the frequency factor is 1.6 * 10^14 s^-1. Find the temperature at which the rate of the reaction would be twice as fast.
Problem 112a
Ethyl chloride vapor decomposes by the first-order reaction: C₂H₅Cl → C₂H₄ + HCl The activation energy is 249 kJ/mol, and the frequency factor is 1.6⨉10¹⁴ s^-1. Find the value of the rate constant at 710 K.
Problem 112b
Ethyl chloride vapor decomposes by the first-order reaction: C₂H₅Cl → C₂H₄ + HCl The activation energy is 249 kJ/mol, and the frequency factor is 1.6⨉10¹⁴ s^-1. What fraction of the ethyl chloride decomposes in 15 minutes at this temperature?