For the reaction \(\mathrm{I}^{-}(a q)+\mathrm{OCl}^{-}(a q)
\rightleftharpoons\) \(\mathrm{OI}^{-}(a q)+\mathrm{Cl}^{-}(a q)\) occurring in
aqueous solution, the following mechanism has been proposed:
\\[
\begin{array}{l}
\mathrm{OCl}^{-}(a q)+\mathrm{H}_{2} \mathrm{O}(l) \quad
\frac{k_{1}}{\overrightarrow{k_{-1}}} \quad \mathrm{HOCl}(a
q)+\mathrm{OH}^{-}(a q) \\
\mathrm{I}(a q)+\mathrm{HOCl}(a q) \stackrel{k_{2}}{\longrightarrow}
\mathrm{HOI}(a q)+\mathrm{Cl}^{-}(a q) \\
\mathrm{HOI}(a q)+\mathrm{OH}^{-}(a q) \stackrel{k_{3}}{\longrightarrow}
\mathrm{H}_{2} \mathrm{O}(l)+\mathrm{OI}^{-}(a q)
\end{array}
\\]
a. Derive the rate law expression for this reaction based on this mechanism.
(Hint: \(\left[\mathrm{OH}^{-}\right]\) should appear in the rate law.
b. The initial rate of reaction was studied as a function of concentration by
Chia and Connick [J. Physical Chemistry \(63(1959): 1518]\), and the following
data were obtained:
$$\begin{array}{lccc}
& & & \text { Initial Rate } \\
{\left[\mathbf{I}^{-}\right]_{0}(\mathbf{M})} & {\left[\mathbf{O C
l}^{-}\right]_{0}(\mathbf{M})} & {\left[\mathbf{O
H}^{-}\right]_{0}(\mathbf{M})} & \left(\mathbf{M} \mathrm{s}^{-1}\right) \\
\hline 2.0 \times 10^{-3} & 1.5 \times 10^{-3} & 1.00 & 1.8 \times 10^{-4} \\
4.0 \times 10^{-3} & 1.5 \times 10^{-3} & 1.00 & 3.6 \times 10^{-4} \\
2.0 \times 10^{-3} & 3.0 \times 10^{-3} & 2.00 & 1.8 \times 10^{-4} \\
4.0 \times 10^{-3} & 3.0 \times 10^{-3} & 1.00 & 7.2 \times 10^{-4}
\end{array}$$
Is the predicted rate law expression derived from the mechanism consistent
with these data?
