Chapter 13

Give an example from everyday experience of (a) a very fast reaction, (b) a moderately fast reaction, and (c) a slow reaction.

What is a homogeneous reaction? What is a heterogeneous reaction? Give examples.

The rate of hardening of epoxy glue depends on the amount of hardener that is mixed into the glue. What factor affecting reaction rates does this illustrate?

How does an instantaneous rate of reaction differ from an average rate of reaction?

Explain how the initial instantaneous rate of reaction can be determined from experimental concentration versus time data.

What are the units of reaction rate? What is the sign of a reaction rate?

What are the units of the rate constant for (a) a firstorder reaction, (b) a second-order reaction, and (c) a zero-order reaction?

How does the dependence of reaction rate on concentration differ between a zero-order and a first-order reaction? Between a first-order and second-order reaction?

If the concentration of a reactant is doubled and the reaction rate is unchanged, what must be the order of the reaction with respect to that reactant?

If the concentration of a reactant is doubled, by what factor will the rate increase if the reaction is second order with respect to that reactant?

In an experiment, the concentration of a reactant was tripled. The rate increased by a factor of \(27 .\) What is the order of the reaction with respect to that reactant?

Biological reactions usually involve the interaction of an enzyme with a substrate, the substance that actually undergoes the chemical change. In many cases, the rate of reaction depends on the concentration of the enzyme but is independent of the substrate concentration. What is the order of the reaction with respect to the substrate in such instances?

Rearrange the integrated rate equations for (a) a first-order reaction, (b) a second-order reaction, and (c) a zero-order reaction to calculate \([A]_{t}\). Use the symbol \([A]_{0}\) to represent the initial concentration if needed.

How is the half-life of a first-order reaction affected by the initial concentration of the reactant?

How is the half-life of a zero-order reaction affected by the initial reactant concentration?

The integrated rate law for a zero-order reaction is $$[A]_{t}=-k t+[A]_{0}$$ Derive an equation for the half-life of a zero-order reaction.

What is the basic postulate of collision theory?

What two factors influence the effectiveness of molecular collisions in producing chemical change?

In terms of the kinetic theory, why does an increase in temperature increase the reaction rate?

What does the transition state theory attempt to describe about chemical reactions?

Draw a potential energy diagram for an exothermic reaction and indicate on the diagram the location of the transition state.

Some might say that the "transition state theory tries to describe what happens from the moment molecules start to collide until they finally separate." Critique this statement, comparing to the collision theory as needed.

The decomposition of carbon dioxide, $$\mathrm{CO}_{2} \longrightarrow \mathrm{CO}+\mathrm{O}$$ has an activation energy of approximately \(460 \mathrm{~kJ} / \mathrm{mol}\). Explain why this large value is consistent with a mechanism that involves the breaking of a \(\mathrm{C}=\mathrm{O}\) bond.

Draw the potential energy diagram for an endothermic reaction. Indicate on the diagram the activation energy for both the forward and reverse reactions. Also indicate the heat of reaction.

What is the definition of an elementary process? How are elementary processes related to the mechanism of a reaction?

What is a rate-determining step?

What is an intermediate in the context of reaction mechanisms?

Suppose we compared two reactions, one requiring the simultaneous collision of three molecules and the other requiring a collision between two molecules. From the standpoint of statistics, and all other factors being equal, which reaction should be faster? Explain your answer.

In what way is the rate law for a reaction related to the rate-determining step?

How does a catalyst increase the rate of a chemical reaction?

What is a homogeneous catalyst? How does it function, in general terms?

What is the purpose of the catalytic converter that most automobiles use today? Is the catalyst heterogeneous or homogeneous?

What is the difference in meaning between the terms adsorption and absorption? Which one applies to heterogeneous catalysts?

Why should leaded gasoline not be used in cars equipped with catalytic converters?

The following data were collected for the decomposition of acetaldehyde. \(\mathrm{CH}_{3} \mathrm{CHO},\) (used in the manufacture of a variety of chemicals including perfumes, dyes, and plastics), into methane and carbon monoxide. The data were collected at \(535^{\circ} \mathrm{C}\). $$\mathrm{CH}_{3} \mathrm{CHO} \longrightarrow \mathrm{CH}_{4}+\mathrm{CO}$$ $$\begin{array}{cc}{\left[\mathrm{CH}_{3} \mathrm{CHO}\right]\left(\mathrm{mol}\mathrm{L}^{-1}\right)} & \text {Time (s) } \\ 0.200 & 0 \\\0.153 & 0.20 \times 10^{2} \\\0.124 & 0.40 \times 10^{2} \\\0.104 & 0.60 \times 10^{2} \\\0.090 & 0.80 \times 10^{2} \\\0.079 & 1.00 \times 10^{2} \\\0.070 & 1.20 \times 10^{2} \\\0.063 & 1.40 \times 10^{2} \\\0.058 & 1.60 \times 10^{2} \\\0.053 & 1.80 \times 10^{2} \\\0049 & 2.00 \times 10^{2} \\\\\hline\end{array}$$ Make a graph of concentration versus time and determine, using the tangent to the curve, the instantaneous rate of reaction of \(\mathrm{CH}_{3} \mathrm{CHO}\) after 60 seconds and after 120 seconds.

For the reaction, \(2 A+B \longrightarrow 3 C\), it was found that the rate of disappearance of \(B\) was \(0.30 \mathrm{~mol} \mathrm{~L}^{-1} \mathrm{~s}^{-1}\). What were the rates of disappearance of \(A\) and the rate of appearance of \(C\) ?

In the reaction, \(3 \mathrm{H}_{2}+\mathrm{N}_{2} \longrightarrow 2 \mathrm{NH}_{3}\), how does the rate of disappearance of hydrogen compare to the rate of disappearance of nitrogen? How does the rate of appearance of \(\mathrm{NH}_{3}\) compare to the rate of disappearance of nitrogen?

In the combustion of hexane (a low-boiling component of gasoline),$$2 \mathrm{C}_{6} \mathrm{H}_{14}(g)+19 \mathrm{O}_{2}(g) \longrightarrow 12 \mathrm{CO}_{2}(g)+14 \mathrm{H}_{2} \mathrm{O}(g)$$ it was found that the rate of decrease of \(\mathrm{C}_{6} \mathrm{H}_{14}\) was \(1.20 \mathrm{~mol} \mathrm{~L}^{-1} \mathrm{~s}^{-1}\) (a) What was the rate of reaction with respect to \(\mathrm{O}_{2} ?\) (b) What was the rate of formation of \(\mathrm{CO}_{2}\) ? (c) What was the rate of formation of \(\mathrm{H}_{2} \mathrm{O}\) ?

At a certain moment in the reaction, $$2 \mathrm{~N}_{2} \mathrm{O}_{5} \longrightarrow 4 \mathrm{NO}_{2}+\mathrm{O}_{2}$$ \(\mathrm{N}_{2} \mathrm{O}_{5}\), is decomposing at a rate of \(2.5 \times 10^{-6} \mathrm{~mol} \mathrm{~L}^{-1} \mathrm{~s}^{-1}\). What are the rates of formation of \(\mathrm{NO}_{2}\) and \(\mathrm{O}_{2}\) ?

Consider the reaction, $$\mathrm{CH}_{3} \mathrm{Cl}(g)+3 \mathrm{Cl}_{2}(g) \longrightarrow \mathrm{CCl}_{4}(g)+3 \mathrm{HCl}(g)$$ (a) Express the rate of the reaction with respect to each of the reactants and products. (b) If the instantaneous rate of the reaction with respect to \(\mathrm{HCl}\) is \(0.029 \mathrm{M} \mathrm{s}^{-1}\), what is the instantaneous rate of the reaction?

The decomposition of phosphine, a very toxic gas, forms phosphorus and hydrogen in the following reaction: $$4 \mathrm{PH}_{3}(g) \longrightarrow \mathrm{P}_{4}(g)+6 \mathrm{H}_{2}(g)$$ (a) Express the rate with respect to each of the reactants and products. (b) If the instantaneous rate with respect to \(\mathrm{PH}_{3}\) is \(0.34 M \mathrm{~s}^{-1}\), what is the instantaneous rate of the reaction?

Estimate the rate of the reaction,$$\mathrm{H}_{2} \mathrm{SeO}_{3}+6 \mathrm{I}^{-}+4 \mathrm{H}^{+} \longrightarrow \mathrm{Se}+2 \mathrm{I}_{3}^{-}+3 \mathrm{H}_{2} \mathrm{O}$$given that the rate law for the reaction at \(0^{\circ} \mathrm{C}\) is$$\text { rate }=\left(5.0 \times 10^{5} \mathrm{~L}^{5} \mathrm{~mol}^{-5} \mathrm{~s}^{-1}\right)\left[\mathrm{H}_{2} \mathrm{SeO}_{3}\right]\left[\mathrm{I}^{-}\right]^{3}\left[\mathrm{H}^{+}\right]^{2}$$. The reactant concentrations are \(\left[\mathrm{H}_{2} \mathrm{SeO}_{3}\right]=2.0 \times 10^{-2} M\), \(\left[\mathrm{I}^{-}\right]=2.0 \times 10^{-3} M,\) and \(\left[\mathrm{H}^{+}\right]=1.0 \times 10^{-3} M\).

Estimate the rate of the reaction, $$ \mathrm{H}^{+}(a q)+\mathrm{OH}^{-}(a q) \longrightarrow \mathrm{H}_{2} \mathrm{O} $$ given the rate law for the reaction is$$\text { rate }=\left(1.3 \times 10^{11} \mathrm{~L} \mathrm{~mol}^{-1} \mathrm{~s}^{-1}\right)\left[\mathrm{OH}^{-}\right]\left[\mathrm{H}^{+}\right]$$ for neutral water, where \(\left[\mathrm{H}^{+}\right]=1.0 \times 10^{-7} M\) and \(\left[\mathrm{OH}^{-}\right]=1.0 \times 10^{-7} M\)

The oxidation of \(\mathrm{NO}\) (released in small amounts in the exhaust of automobiles) produces the brownish-red gas \(\mathrm{NO}_{2},\) which is a component of urban air pollution. $$2 \mathrm{NO}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{NO}_{2}(g)$$ The rate law for the reaction is rate \(=k[\mathrm{NO}]^{2}\left[\mathrm{O}_{2}\right]\) At \(25^{\circ} \mathrm{C}, k=7.1 \times 10^{9} \mathrm{~L}^{2} \mathrm{~mol}^{-2} \mathrm{~s}^{-1}\). What would be the rate of the reaction if \([\mathrm{NO}]=0.0010 \mathrm{~mol} \mathrm{~L}^{-1}\) and \(\left[\mathrm{O}_{2}\right]=0.034 \mathrm{~mol} \mathrm{I}^{-1}\).

The rate law for the decomposition of \(\mathrm{N}_{2} \mathrm{O}_{5}\) is rate \(=\) \(k\left[\mathrm{~N}_{2} \mathrm{O}_{5}\right] .\) If \(k=1.0 \times 10^{-5} \mathrm{~s}^{-1},\) what is the reaction rate when the \(\mathrm{N}_{2} \mathrm{O}_{5}\) concentration is \(0.0010 \mathrm{~mol} \mathrm{~L}^{-1}\) ?

The rate law for a certain enzymatic reaction is zero order with respect to the substrate. The rate constant for the reaction is \(6.4 \times 10^{2} M \mathrm{~s}^{-1}\). If the initial concentration of the substrate is \(0.275 \mathrm{~mol} \mathrm{~L}^{-1}\), what is the initial rate of the reaction?

Radon- 220 is radioactive, and decays into polonium- 216 by emitting an alpha particle. This is a first-order process with a rate constant of \(0.0125 \mathrm{~s}^{-1}\). When the concentration of radon- 220 is \(1.0 \times 10^{-9} \mathrm{~mol} \mathrm{~L}^{-1}\), what is the rate of the reaction?

Cyclopropane, \(\mathrm{C}_{3} \mathrm{H}_{6}\), is a gas used as a general anesthetic. It undergoes a slow molecular rearrangement to propylene. At a certain temperature, the following data were obtained relating concentration and rate: $$\begin{array}{cc}\text { Initial Concentration of } & \text { Initial Rate of Formation } \\\\\text { Cyclopropane }\left(\mathrm{mol} \mathrm{L}^{-1}\right) & \text {of Propylene }\left(\mathrm{mol} \mathrm{L}^{-1} \mathrm{~s}^{-1}\right) \\\0.050 & 2.95 \times 10^{-5} \\\0.100 & 5.90 \times 10^{-5} \\\0.150 & 8.85 \times 10^{-5}\end{array}$$ What is the rate law for the reaction? What is the value of the rate constant, with correct units?

The decomposition of \(\mathrm{SO}_{2} \mathrm{Cl}_{2}\) described in Problem 13.53 has a first-order rate constant, \(k=2.2 \times 10^{-5} \mathrm{~s}^{-1}\) at \(320^{\circ} \mathrm{C}\). If the initial \(\mathrm{SO}_{2} \mathrm{Cl}_{2}\) concentration in a container is \(0.0040 \mathrm{M}\), what will its concentration be (a) after 1.00 hour and \((\mathbf{b})\) after 1.00 day?

If it takes 75.0 min for the concentration of a reactant to drop to \(25.0 \%\) of its initial value in a first-order reaction, what is the rate constant for the reaction in the units \(\min ^{-1} ?\)