Problem 88
What are the units of the rate constant for a third-order reaction?
Problem 89
The integrated rate law for the zeroth-order reaction \(\mathrm{A} \longrightarrow \mathrm{B}\) is \([\mathrm{A}]_{t}=[\mathrm{A}]_{0}-k t .\) (a) Sketch the following plots: (i) rate versus \([\mathrm{A}]_{t}\) and (ii) \([\mathrm{A}]_{t}\) versus \(t\). (b) Derive an expression for the half-life of the reaction. (c) Calculate the time in half-lives when the integrated rate law is \(n o\) longer valid, that is, when \([\mathrm{A}]_{t}=0\).
Problem 90
A flask contains a mixture of compounds \(\mathrm{A}\) and \(\mathrm{B}\). Both compounds decompose by first-order kinetics. The half-lives are 50.0 min for \(\mathrm{A}\) and 18.0 min for \(\mathrm{B}\). If the concentrations of \(\mathrm{A}\) and \(\mathrm{B}\) are equal initially, how long will it take for the concentration of \(\mathrm{A}\) to be four times that of \(\mathrm{B}\) ?
Problem 92
The rate law for the reaction \(2 \mathrm{NO}_{2}(g) \longrightarrow \mathrm{N}_{2} \mathrm{O}_{4}(g)\) is rate \(=k\left[\mathrm{NO}_{2}\right]^{2}\). Which of the following changes will change the value of \(k ?\) (a) The pressure of \(\mathrm{NO}_{2}\) is doubled. (b) The reaction is run in an organic solvent. (c) The volume of the container is doubled. (d) The temperature is decreased. (e) A catalyst is added to the container.
Problem 93
The reaction of \(\mathrm{G}_{2}\) with \(\mathrm{E}_{2}\) to form \(2 \mathrm{EG}\) is exothermic, and the reaction of \(\mathrm{G}_{2}\) with \(\mathrm{X}_{2}\) to form \(2 \mathrm{XG}\) is endothermic. The activation energy of the exothermic reaction is greater than that of the endothermic reaction. Sketch the potential-energy profile diagrams for these two reactions on the same graph.
Problem 94
The activation energy for the decomposition of hydrogen peroxide: $$ 2 \mathrm{H}_{2} \mathrm{O}_{2}(a q) \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(l)+\mathrm{O}_{2}(g) $$ is \(42 \mathrm{~kJ} / \mathrm{mol}\), whereas when the reaction is catalyzed by the enzyme catalase, it is \(7.0 \mathrm{~kJ} / \mathrm{mol}\). Calculate the temperature that would cause the uncatalyzed decomposition to proceed as rapidly as the enzyme-catalyzed decomposition at \(20^{\circ} \mathrm{C}\). Assume the frequency factor A to be the same in both cases.
Problem 95
Briefly comment on the effect of a catalyst on each of the following: (a) activation energy, (b) reaction mechanism, (c) enthalpy of reaction, (d) rate of forward reaction, (e) rate of reverse reaction.
Problem 96
When \(6 \mathrm{~g}\) of granulated \(\mathrm{Zn}\) is added to a solution of \(2 \mathrm{M}\) \(\mathrm{HCl}\) in a beaker at room temperature, hydrogen gas is generated. For each of the following changes (at constant volume of the acid) state whether the rate of hydrogen gas evolution will be increased, decreased, or unchanged: (a) \(6 \mathrm{~g}\) of powdered \(\mathrm{Zn}\) is used, (b) \(4 \mathrm{~g}\) of granulated \(\mathrm{Zn}\) is used, (c) \(2 M\) acetic acid is used instead of \(2 M \mathrm{HCl}\), (d) temperature is raised to \(40^{\circ} \mathrm{C}\).
Problem 98
A certain first-order reaction is 35.5 percent complete in \(4.90 \mathrm{~min}\) at \(25^{\circ} \mathrm{C}\). What is its rate constant?
Problem 99
The decomposition of dinitrogen pentoxide has been studied in carbon tetrachloride solvent \(\left(\mathrm{CCl}_{4}\right)\) at a certain temperature: $$ \begin{array}{cc} 2 \mathrm{~N}_{2} \mathrm{O}_{5} & \longrightarrow 4 \mathrm{NO}_{2}+\mathrm{O}_{2} \\ {\left[\mathrm{~N}_{2} \mathrm{O}_{5}\right](M)} & \text { Initial Rate }(M / \mathrm{s}) \\ \hline 0.92 & 0.95 \times 10^{-5} \\ 1.23 & 1.20 \times 10^{-5} \\ 1.79 & 1.93 \times 10^{-5} \\ 2.00 & 2.10 \times 10^{-5} \\ 2.21 & 2.26 \times 10^{-5} \end{array} $$ Determine graphically the rate law for the reaction, and calculate the rate constant.
