Chapter 11

Sulfuryl chloride \(\left(\mathrm{SO}_{2} \mathrm{Cl}_{2}\right)\) decomposes to sulfur dioxide \(\left(\mathrm{SO}_{2}\right)\) and chlorine \(\left(\mathrm{Cl}_{2}\right)\) by reaction in the gas phase. The following pressure data were obtained when a sample containing \(5.00 \times 10^{-2}\) mol sulfury 1 chloride was heated to \(600 . \mathrm{K}\) in a \(5.00 \times 10^{-1}-\mathrm{L}\) container. Defining the rate as $$-\frac{\Delta\left[\mathrm{SO}_{2} \mathrm{Cl}_{2}\right]}{\Delta t}$$ a. determine the value of the rate constant for the decomposition of sulfuryl chloride at \(600 .\) K. b. what is the half-life of the reaction? c. what fraction of the sulfuryl chloride remains after \(20.0 \mathrm{h} ?\)

Cobra venom helps the snake secure food by binding to acetylcholine receptors on the diaphragm of a bite victim, leading to the loss of function of the diaphragm muscle tissue and eventually death. In order to develop more potent antivenins, scientists have studied what happens to the toxin once it has bound the acetylcholine receptors. They have found that the toxin is released from the receptor in a process that can be described by the rate law $$Rate \(=k[\text { acetylcholine receptor-toxin complex }]$$ If the activation energy of this reaction at \)37.0^{\circ} \mathrm{C}\( is \)26.2 \mathrm{kJ} /\( mol and \)A=0.850 \mathrm{s}^{-1},\( what is the rate of reaction if you have a 0.200-M solution of receptor-toxin complex at \)37.0^{\circ} \mathrm{C} ?$

Experiments during a recent summer on a number of fireflies (small beetles, Lampyridaes photinus) showed that the average interval between flashes of individual insects was \(16.3 \mathrm{s}\) at \(21.0^{\circ} \mathrm{C}\) and \(13.0 \mathrm{s}\) at \(27.8^{\circ} \mathrm{C}\). a. What is the apparent activation energy of the reaction that controls the flashing? b. What would be the average interval between flashes of an individual firefly at \(30.0^{\circ} \mathrm{C} ?\) c. Compare the observed intervals and the one you calculated in part b to the rule of thumb that the Celsius temperature is 54 minus twice the interval between flashes.

The activation energy of a certain uncatalyzed biochemical reaction is \(50.0 \space\mathrm{kJ} / \mathrm{mol} .\) In the presence of a catalyst at \(37^{\circ} \mathrm{C}\) the rate constant for the reaction increases by a factor of \(2.50 \times 10^{3}\) as compared with the uncatalyzed reaction. Assuming the frequency factor \(A\) is the same for both the catalyzed and uncatalyzed reactions, calculate the activation energy for the catalyzed reaction.

Consider the reaction $$3 \mathrm{A}+\mathrm{B}+\mathrm{C} \longrightarrow \mathrm{D}+\mathrm{E}$$ where the rate law is defined as $$-\frac{\Delta[\mathrm{A}]}{\Delta t}=k[\mathrm{A}]^{2}[\mathrm{B}][\mathrm{C}]$$ An experiment is carried out where \([\mathrm{B}]_{0}=[\mathrm{C}]_{0}=1.00 \space M\) and \([\mathrm{A}]_{0}=1.00 \times 10^{-4} \mathrm{M}\) a. If after \(3.00 \min ,[A]=3.26 \times 10^{-5} M,\) calculate the value of \(k\) b. Calculate the half-life for this experiment. c. Calculate the concentration of \(\mathrm{B}\) and the concentration of A after 10.0 min.

The thiosulfate ion \(\left(S_{2} O_{3}^{2-}\right)\) is oxidized by iodine as follows: $$2 \mathrm{S}_{2} \mathrm{O}_{3}^{2-}(a q)+\mathrm{I}_{2}(a q) \longrightarrow \mathrm{S}_{4} \mathrm{O}_{6}^{2-}(a q)+2 \mathrm{I}^{-}(a q)$$ In a certain experiment, \(7.05 \times 10^{-3} \mathrm{mol} / \mathrm{L}\) of \(\mathrm{S}_{2} \mathrm{O}_{3}^{2-}\) is consumed in the first 11.0 seconds of the reaction. Calculate the rate of consumption of \(\mathrm{S}_{2} \mathrm{O}_{3}^{2-} .\) Calculate the rate of production of iodide ion.

The reaction \(\mathrm{A}(a q)+\mathrm{B}(a q) \longrightarrow\) products \((a q)\) was studied, and the following data were obtained: What is the order of the reaction with respect to A? What is the order of the reaction with respect to B? What is the value of the rate constant for the reaction?

A reaction of the form $$aA \longrightarrow Products$$gives a plot of \(\ln [\mathrm{A}]\) versus time (in seconds), which is a straight line with a slope of \(-7.35 \times 10^{-3} .\) Assuming \([\mathrm{A}]_{0}=\) \(0.0100 M,\) calculate the time (in seconds) required for the reaction to reach \(22.9 \%\) completion.

A reaction of the form $$aA \longrightarrow Products$$gives a plot of \(\ln [\mathrm{A}]\) versus time (in seconds), which is a straight line with a slope of \(-7.35 \times 10^{-3} .\) Assuming \([\mathrm{A}]_{0}=\) \(0.0100 M,\) calculate the time (in seconds) required for the reaction to reach \(22.9 \%\) completion.

Which of the following statement(s) is(are) true? a. The half-life for a zero-order reaction increases as the reaction proceeds. b. A catalyst does not change the value of the rate constant. c. The half-life for a reaction, a \(A \longrightarrow\) products, that is first order in A increases with increasing \([\mathrm{A}]_{0}\) d. The half-life for a second-order reaction increases as the reaction proceeds.

Consider the hypothetical reaction \(\mathrm{A}_{2}(g)+\mathrm{B}_{2}(g) \longrightarrow\) \(2 \mathrm{AB}(g),\) where the rate law is: $$-\frac{\Delta\left[\mathrm{A}_{2}\right]}{\Delta t}=k\left[\mathrm{A}_{2}\right]\left[\mathrm{B}_{2}\right]$$ The value of the rate constant at \(302^{\circ} \mathrm{C}\) is \(2.45 \times 10^{-4} \mathrm{L} / \mathrm{mol}\). s, and at \(508^{\circ} \mathrm{C}\) the rate constant is \(0.891 \mathrm{L} / \mathrm{mol} \cdot \mathrm{s}\). What is the activation energy for this reaction? What is the value of the rate constant for this reaction at \(375^{\circ} \mathrm{C} ?\)

Consider a reaction of the type aA \(\longrightarrow\) products, in which the rate law is found to be rate \(=k[\mathrm{A}]^{3}\) (termolecular reactions are improbable but possible). If the first half-life of the reaction is found to be \(40 .\) s, what is the time for the second half-life? Hint: Using your calculus knowledge, derive the integrated rate law from the differential rate law for a termolecular reaction: $$\text { Rate }=\frac{-d[\mathrm{A}]}{d t}=k[\mathrm{A}]^{3}$$

Two isomers \((A \text { and } B)\) of a given compound dimerize as follows: $$\begin{aligned} &2 \mathrm{A} \stackrel{k_{1}}{\longrightarrow} \mathrm{A}_{2}\\\ &2 \mathrm{B} \stackrel{k_{2}}{\longrightarrow} \mathrm{B}_{2} \end{aligned}$$ Both processes are known to be second order in reactant, and \(k_{1}\) is known to be 0.250 \(\mathrm{L} / \mathrm{mol} \cdot \mathrm{s}\) at \(25^{\circ} \mathrm{C} .\) In a particular experiment \(\mathrm{A}\) and \(\mathrm{B}\) were placed in separate containers at \(25^{\circ} \mathrm{C}\) where \([\mathrm{A}]_{0}=1.00 \times 10^{-2} \mathrm{M}\) and \([\mathrm{B}]_{0}=2.50 \times 10^{-2} \mathrm{M} .\) It was found that after each reaction had progressed for 3.00 min, \([\mathrm{A}]=3.00[\mathrm{B}] .\) In this case the rate laws are defined as $$\begin{array}{l} \text { Rate }=-\frac{\Delta[\mathrm{A}]}{\Delta t}=k_{1}[\mathrm{A}]^{2} \\ \text { Rate }=-\frac{\Delta[\mathrm{B}]}{\Delta t}=k_{2}[\mathrm{B}]^{2} \end{array}$$ a. Calculate the concentration of \(\mathrm{A}_{2}\) after 3.00 min. b. Calculate the value of \(k_{2}\) c. Calculate the half-life for the experiment involving A.

The reaction $$\mathrm{NO}(g)+\mathrm{O}_{3}(g) \longrightarrow \mathrm{NO}_{2}(g)+\mathrm{O}_{2}(g)$$ was studied by performing two experiments. In the first experiment the rate of disappearance of NO was followed in the presence of a large excess of \(\mathrm{O}_{3}\). The results were as follows \(\left(\left[\mathrm{O}_{3}\right]\right.\) remains effectively constant at \(1.0 \times 10^{14}\) molecules/cm \(^{3}\) ): In the second experiment [NO] was held constant at \(2.0 \times 10^{14}\) molecules/cm \(^{3}\). The data for the disappearance of \(\mathbf{O}_{3}\) are as follows: a. What is the order with respect to each reactant? b. What is the overall rate law? c. What is the value of the rate constant from each set of experiments? $$\text { Rate }=k^{\prime}[\mathrm{NO}]^{x} \quad \text { Rate }=k^{\prime \prime}\left[\mathrm{O}_{3}\right]^{y}$$ d. What is the value of the rate constant for the overall rate law? $$\text { Rate }=k[\mathrm{NO}]^{\mathrm{x}}\left[\mathrm{O}_{3}\right]^y$$

Hydrogen peroxide and the iodide ion react in acidic solution as follows: $$\mathrm{H}_{2} \mathrm{O}_{2}(a q)+3 \mathrm{I}^{-}(a q)+2 \mathrm{H}^{+}(a q) \longrightarrow \mathrm{I}_{3}^{-}(a q)+2 \mathrm{H}_{2} \mathrm{O}(l)$$ The kinetics of this reaction were studied by following the decay of the concentration of \(\mathrm{H}_{2} \mathrm{O}_{2}\) and constructing plots of \(\ln \left[\mathrm{H}_{2} \mathrm{O}_{2}\right]\) versus time. All the plots were linear and all solutions had \(\left[\mathrm{H}_{2} \mathrm{O}_{2}\right]_{0}=8.0 \times 10^{-4} \mathrm{mol} / \mathrm{L} .\) The slopes of these straight lines depended on the initial concentrations of \(\mathrm{I}^{-}\) and \(\mathrm{H}^{+} .\) The results follow: The rate law for this reaction has the form $$\text { Rate }=\frac{-\Delta\left[\mathrm{H}_{2} \mathrm{O}_{2}\right]}{\Delta t}=\left(k_{1}+k_{2}\left[\mathrm{H}^{+}\right]\right)\left[\mathrm{I}^{-}\right]^{m}\left[\mathrm{H}_{2} \mathrm{O}_{2}\right]^{n}$$ a. Specify the order of this reaction with respect to \(\left[\mathrm{H}_{2} \mathrm{O}_{2}\right]\) and \(\left[\mathrm{I}^{-}\right]\) b. Calculate the values of the rate constants, \(k_{1}\) and \(k_{2}\) c. What reason could there be for the two-term dependence of the rate on \(\left[\mathrm{H}^{+}\right] ?\)

Sulfuryl chloride undergoes first-order decomposition at \(320 .^{\circ} \mathrm{C}\) with a half-life of \(8.75 \mathrm{h}\) $$\mathrm{SO}_{2} \mathrm{Cl}_{2}(g) \longrightarrow \mathrm{SO}_{2}(g)+\mathrm{Cl}_{2}(g)$$ What is the value of the rate constant, \(k\), in \(s^{-1}\) ? If the initial pressure of \(\mathrm{SO}_{2} \mathrm{Cl}_{2}\) is 791 torr and the decomposition occurs in a \(1.25-\mathrm{L}\) container, how many molecules of \(\mathrm{SO}_{2} \mathrm{Cl}_{2}\) remain after \(12.5 \mathrm{h} ?\)

Upon dissolving \(\operatorname{InCl}(s)\) in \(\mathrm{HCl}, \operatorname{In}^{+}(a q)\) undergoes a disproportionation reaction according to the following unbalanced equation: $$\operatorname{In}^{+}(a q) \longrightarrow \operatorname{In}(s)+\operatorname{In}^{3+}(a q)$$ This disproportionation follows first-order kinetics with a half-life of 667 s. What is the concentration of \(\operatorname{In}^{+}(a q)\) after \(1.25 \mathrm{h}\) if the initial solution of \(\operatorname{In}^{+}(a q)\) was prepared by dissolving \(2.38 \mathrm{g}\) InCl \((s)\) in dilute HCl to make \(5.00 \times 10^{2} \mathrm{mL}\) of solution? What mass of \(\operatorname{In}(s)\) is formed after \(1.25 \mathrm{h} ?\)

The decomposition of iodoethane in the gas phase proceeds according to the following equation: $$\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{I}(g) \longrightarrow \mathrm{C}_{2} \mathrm{H}_{4}(g)+\mathrm{HI}(g)$$ At \(660 . \mathrm{K}, k=7.2 \times 10^{-4} \mathrm{s}^{-1} ;\) at \(720 . \mathrm{K}, k=1.7 \times 10^{-2} \mathrm{s}^{-1}\) What is the value of the rate constant for this first-order decomposition at \(325^{\circ} \mathrm{C} ?\) If the initial pressure of iodoethane is 894 torr at \(245^{\circ} \mathrm{C},\) what is the pressure of iodoethane after three half-lives?