Problem 62
The rate law for the decomposition of ozone to molecular oxygen: $$ 2 \mathrm{O}_{3}(g) \longrightarrow 3 \mathrm{O}_{2}(g) $$ is $$ \text { rate }=k \frac{\left[\mathrm{O}_{3}\right]^{2}}{\left[\mathrm{O}_{2}\right]} $$ The mechanism proposed for this process is: $$ \begin{array}{l} \mathrm{O}_{3} \stackrel{k_{1}}{\rightleftarrows} \mathrm{O}+\mathrm{O}_{2} \\\ \mathrm{O}+\mathrm{O}_{3} \stackrel{k_{2}}{\longrightarrow} 2 \mathrm{O}_{2} \end{array} $$ Derive the rate law from these elementary steps. Clearly state the assumptions you use in the derivation. Explain why the rate decreases with increasing \(\mathrm{O}_{2}\) concentration.
Problem 63
How does a catalyst increase the rate of a reaction?
Problem 64
What are the characteristics of a catalyst?
Problem 65
A certain reaction is known to proceed slowly at room temperature. Is it possible to make the reaction proceed at a faster rate without changing the temperature?
Problem 66
Most reactions, including enzyme-catalyzed reactions, proceed faster at higher temperatures. However, for a given enzyme, the rate drops off abruptly at a certain temperature. Account for this behavior.
Problem 67
Are enzyme-catalyzed reactions examples of homogeneous or heterogeneous catalysis? Explain.
Problem 68
The concentrations of enzymes in cells are usually quite small. What is the biological significance of this fact?
Problem 69
When fruits such as apples and pears are cut, the exposed areas begin to turn brown. This is the result of an enzymecatalyzed reaction. Often the browning can be prevented or slowed by adding a few drops of lemon juice. What is the chemical basis of this treatment?
Problem 70
The first-order rate constant for the dehydration of carbonic acid: $$ \mathrm{H}_{2} \mathrm{CO}_{3} \longrightarrow \mathrm{CO}_{2}+\mathrm{H}_{2} \mathrm{O} $$ is about \(1 \times 10^{2} \mathrm{~s}^{-1}\). In view of this rather high rate constant, explain why it is necessary to have the enzyme carbonic anhydrase to enhance the rate of dehydration in the lungs.
Problem 73
List four factors that influence the rate of a reaction.
