Chapter 13

Indicate whether each statement is true or false. Rewrite each false statement to make it true. (a) The exponents in the rate law for a reaction that has a one-step mechanism can be determined from the balanced equation for the reaction. (b) A rate law can be used to prove that a proposed mechanism is correct. (c) The step \(\mathrm{A}+\mathrm{X}+\mathrm{Y} \rightarrow \mathrm{AX}+\mathrm{Y}\) in a reaction mechanism is plausible. (d) A reaction intermediate appears first as a reactant and then as a product in a reaction mechanism.

Consider the basic hydrolysis (reaction with aqueous base) of \(\left(\mathrm{CH}_{3}\right){ }_{3} \mathrm{CBr}\). \(\left(\mathrm{CH}_{3}\right)_{3} \mathrm{CBr}(a q)+\mathrm{OH}^{-}(a q) \rightarrow\) $$\left(\mathrm{CH}_{3}\right){ }_{3} \mathrm{COH}(a q)+\mathrm{Br}^{-}(a q)$$ The rate law is first order with respect to \(\left(\mathrm{CH}_{3}\right)_{3} \mathrm{CBr}\) and zero order with respect to \(\mathrm{OH}^{-}\). What does this imply about the mechanism of this reaction?

Consider the decomposition of ozone \(\left(\mathrm{O}_{3}\right)\) to oxygen \(\left(\mathrm{O}_{2}\right)\) \(2 \mathrm{O}_{3}(g) \rightarrow 3 \mathrm{O}_{2}(g)\) The rate law for this reaction is: Rate \(=k\left[\mathrm{O}_{3}\right]^{2} /\left[\mathrm{O}_{2}\right] .\) How is the rate of this reaction affected by the concentration of oxygen?

The following is a two-step mechanism for how chlorine atoms in the upper atmosphere react with and decompose ozone. \(\mathrm{Cl}+\mathrm{O}_{3} \rightarrow \mathrm{ClO}+\mathrm{O}_{2}\) \(\mathrm{O}+\mathrm{ClO} \rightarrow \mathrm{Cl}+\mathrm{O}_{2}\) According to the mechanism, which is the intermediate and which is the catalyst? Justify your choices. (Hint: Write the overall reaction.)

A student claims that an endothermic reaction will always have a higher activation energy than an exothermic reaction, because an endothermic reaction ends up with the products at a higher energy than the reactants. Is this correct or incorrect? Justify your answer.

Consider the reaction: \(2 \mathrm{NO}(g)+2 \mathrm{H}_{2}(g) \rightarrow\) \(\mathrm{N}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(g)\) Initial concentrations and rates for this reaction are given in the table below. $$\begin{array}{|c|c|c|c|} \hline {\text { Experiment }} & {\begin{array}{c} \text { Initial concentration } \\ \text { (mol/L) } \\ \text { [NO] } \end{array}} & \begin{array}{c} \text { Initial rate of } \\ \text { [ } \mathbf{H}_{2} \text { ] } \end{array} & \begin{array}{c} \text { formation of } \mathbf{N}_{2} \\ (\mathbf{m o l} / \mathbf{L} \text { min } \mathbf{)} \end{array} \\ \hline 1 & 0.0060 & 0.0010 & 1.8 \times 10^{-4} \\ 2 & 0.0060 & 0.0020 & 3.6 \times 10^{-4} \\ 3 & 0.0010 & 0.0060 & 0.30 \times 10^{-4} \\ 4 & 0.0020 & 0.0060 & 1.2 \times 10^{-4} \\ \hline \end{array}$$ (a) From the data given, determine the order for each of the reactants, \(\mathrm{NO}\) and \(\mathrm{H}_{2}\), show your reasoning, and write the overall rate law for the reaction. (b) Calculate the value of the rate constant, \(k\), for the reaction. Include units. (c) For experiment 2, calculate the concentration of NO remaining when exactly one-half of the original amount of \(\mathrm{H}_{2}\) has been consumed. (d) The following sequence of elementary steps is a proposed mechanism for the reaction. I. \(\mathrm{NO}+\mathrm{NO} \rightarrow \mathrm{N}_{2} \mathrm{O}_{2}\) II. \(\quad \mathrm{N}_{2} \mathrm{O}_{2}+\mathrm{H}_{2} \rightarrow \mathrm{H}_{2} \mathrm{O}+\mathrm{N}_{2} \mathrm{O}\) III. \(\quad \mathrm{N}_{2} \mathrm{O}+\mathrm{H}_{2} \rightarrow \mathrm{N}_{2}+\mathrm{H}_{2} \mathrm{O}\) Based on the data present, explain why the first step cannot be the rate determining step.

Ace chemistry student Sidney Einstein (no relation) was carrying out a kinetics experiment in lab which produces iodine and uses starch as an indicator. In the first minute after mixing, Sidney spilled some of the solution. Rather than start over, he decided to pour out more solution until he had exactly half the original volume in the tube. Given that the particular reaction under investigation was second order in the reactant being investigated and was supposed to change color after 10 minutes, approximately how long (minutes) will it be before Sidney sees a color change? Explain briefly!

Why is it unlikely that the reaction \(\mathrm{A}+2 \mathrm{~B}+\mathrm{C} \rightarrow \mathrm{P}\) occurs in one step?

True or false? The orders in a rate law are equal to the balancing coefficients in the slowest elementary step in a mechanism.

What is meant by the term rate-determining step?

Why can we ignore other steps and use only the rate-determining step in a mechanism to write the predicted rate law?

Is it wise to postulate a three-molecule collision as an elementary step in a reaction mechanism? Explain your answer.

Suppose a postulated reaction mechanism generates a rate law that does not agree with the experimentally determined rate law. What does this say about the postulated mechanism?

Suppose a postulated mechanism does generate the experimental rate law, but the elementary steps, when added together, do not generate the balanced equation for the overall reaction. What can you say about the postulated mechanism?

Suppose a postulated mechanism does generate the experimental rate law, and when the elementary steps are added together, the balanced equation for the overall reaction is generated. What can you say about the postulated mechanism?

Consider the reaction. Kinetics studies reveal a first-order rate dependence on the concentration of the \(\left(\mathrm{CH}_{3}\right)_{3} \mathrm{C}-\mathrm{Br}\) and a zero-order dependence on the concentration of \(\mathrm{H}_{2} \mathrm{O}\). (a) What happens to the reaction rate as the \(\left(\mathrm{CH}_{3}\right)_{3} \mathrm{C}-\mathrm{Br}\) concentration is changed? What happens to the reaction rate as the \(\mathrm{H}_{2} \mathrm{O}\) concentration is changed? (b) Two mechanisms for this reaction are offered below. Can you rule out either of them? Is either mechanism plausible, given the overall balanced equation and kinetic data? Explain your answer fully.

Write the overall balanced chemical equation that goes along with the mechanism: Elementary step 1: \(\mathrm{Cl}_{2} \rightarrow 2 \mathrm{Cl}\) Elementary step \(2: \mathrm{Cl}+\mathrm{CHCl}_{3} \rightarrow \mathrm{HCl}+\mathrm{CCl}_{3}\) Elementary step \(3: \mathrm{Cl}+\mathrm{CCl}_{3} \rightarrow \mathrm{CCl}_{4}\)