Chapter 13: Problem 59
How does a catalyst increase the rate of a reaction?
Chapter 13: Problem 59
How does a catalyst increase the rate of a reaction?
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Get started for freeConsider the following mechanism for the enzymecatalyzed reaction: $$ \begin{array}{r} \mathrm{E}+\mathrm{S} \underset{k-1}{\stackrel{k_{1}}{\sum_{-1}}} \mathrm{ES} \\\ \mathrm{ES} \stackrel{k_{2}}{\longrightarrow} \mathrm{E}+\mathrm{P} \end{array} $$ Derive an expression for the rate law of the reaction in terms of the concentrations of \(\mathrm{E}\) and \(\mathrm{S}\). (Hint: To solve for [ES], make use of the fact that, at equilibrium, the rate of forward reaction is equal to the rate of the reverse reaction.
Define activation energy. What role does activation energy play in chemical kinetics?
Some reactions are described as parallel in that the reactant simultaneously forms different products with different rate constants. An example is and $$ \begin{array}{l} \mathrm{A} \stackrel{k_{1}}{k_{2}} \mathrm{~B} \\ \mathrm{~A} \stackrel{\longrightarrow}{\longrightarrow} \mathrm{C} \end{array} $$ The activation energies are \(45.3 \mathrm{~kJ} / \mathrm{mol}\) for \(k_{1}\) and \(69.8 \mathrm{~kJ} / \mathrm{mol}\) for \(k_{2}\). If the rate constants are equal at \(320 \mathrm{~K},\) at what temperature will \(k_{1} / k_{2}=2.00 ?\)
Consider the following elementary steps for a consecutive reaction: $$ \mathrm{A} \stackrel{k_{1}}{\longrightarrow} \mathrm{B} \stackrel{k_{2}}{\longrightarrow} \mathrm{C} $$ (a) Write an expression for the rate of change of \(\mathrm{B}\). (b) Derive an expression for the concentration of \(\mathrm{B}\) under steady- state conditions; that is, when \(\mathrm{B}\) is decomposing to \(\mathrm{C}\) at the same rate as it is formed from \(A\).
The rate law for the reaction $$ \mathrm{NH}_{4}^{+}(a q)+\mathrm{NO}_{2}^{-}(a q) \longrightarrow \mathrm{N}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(l) $$ is given by rate \(=k\left[\mathrm{NH}_{4}^{+}\right]\left[\mathrm{NO}_{2}^{-}\right] .\) At \(25^{\circ} \mathrm{C},\) the rate constant is \(3.0 \times 10^{-4} / M \cdot\) s. Calculate the rate of the reaction at this temperature if \(\left[\mathrm{NH}_{4}^{+}\right]=0.26 M\) and \(\left[\mathrm{NO}_{2}^{-}\right]=0.080 M\)
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