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Chapter 14: Problem 67

The reaction \(\mathrm{S}_{2} \mathrm{O}_{8}^{2-}+2 \mathrm{I}^{-} \longrightarrow 2 \mathrm{SO}_{4}^{2-}+\mathrm{I}_{2}\) proceeds slowly in aqueous solution, but it can be catalyzed by the \(\mathrm{Fe}^{3+}\) ion. Given that \(\mathrm{Fe}^{3+}\) can oxidize \(\mathrm{I}^{-}\) and \(\mathrm{Fe}^{2+}\) can reduce \(\mathrm{S}_{2} \mathrm{O}_{8}^{2-},\) write a plausible two-step mechanism for this reaction. Explain why the uncatalyzed reaction is slow.

Short Answer

Expert verified
A plausible two-step mechanism for the reaction pioneered by \(Fe^{3+}\) is as follows: 1. Oxidation: \(2Fe^{3+} + 2I^- \longrightarrow 2Fe^{2+} + I_2\) 2. Reduction: \(2Fe^{2+} + S_2O_8^{2-} \longrightarrow 2Fe^{3+} + 2SO_4^{2-}\)The uncatalyzed reaction is slower because the energy barrier for a direct reaction between \(S_2O_8^{2-}\) and \(I^-\) ions is very high, due to their charges and sizes. The catalyst reduces this energy barrier, hence speeding up the reaction.

Step by step solution

01

Understanding the reaction

The given reaction is: \(S_2O_8^{2-} + 2I^- \longrightarrow 2SO_4^{2-} + I_2\). It's mentioned that \(Fe^{3+}\) catalyzes this reaction. Catalysts generally speed up reactions by reducing the energy of the transition state or allowing an alternate (and quicker) path for the reaction to proceed. Here, \(Fe^{3+}\) can oxidize \(I^-\) and \(Fe^{2+}\) can reduce \(S_2O_8^{2-}\).
02

Writing the two-step reaction mechanism

A plausible two-step mechanism for this reaction is as follows: 1. Oxidation: \(2Fe^{3+} + 2I^- \longrightarrow 2Fe^{2+} + I_2\) 2. Reduction: \(2Fe^{2+} + S_2O_8^{2-} \longrightarrow 2Fe^{3+} + 2SO_4^{2-}\)In the first step, \(Fe^{3+}\) oxidizes \(I^-\) to \(I_2\). In the second step, \(Fe^{2+}\) reduces \(S_2O_8^{2-}\) to \(SO_4^{2-}\). Notice that the \(Fe\) ions are regenerated after each cycle, as is normal in a catalytic process.
03

Explaining the slow rate of the uncatalyzed reaction

The uncatalyzed reaction \(S_2O_8^{2-} + 2I^- \longrightarrow 2SO_4^{2-} + I_2\) would involve a direct reaction between the \(S_2O_8^{2-}\) and \(I^-\) ions. Given the charges and large sizes of these ions, it's likely that overcoming the energy barrier for the reaction would be difficult, which would result in a slow rate of reaction. In contrast, the two-step mechanism that involves the \(Fe\) ions allows the reaction to proceed more quickly, as the energy barriers for each of these steps are lower.

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Most popular questions from this chapter

Consider the reaction $$ \begin{aligned} \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{I}(a q)+\mathrm{H}_{2} \mathrm{O}(l) & \\\ & \longrightarrow \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(a q)+\mathrm{H}^{+}(a q)+\mathrm{I}^{-}(a q) \end{aligned} $$ How could you follow the progress of the reaction by measuring the electrical conductance of the solution?

Define the half-life of a reaction. Write the equation relating the half-life of a first-order reaction to the rate constant.

Explain why termolecular reactions are rare.

Distinguish between homogeneous catalysis and heterogeneous catalysis. Describe some important industrial processes that utilize heterogeneous catalysis.

Reactions can be classified as unimolecular, bimolecular, and so on. Why are there no zero-molecular reactions?
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