The iodate ion is reduced by sulfite according to the...

The iodate ion is reduced by sulfite according to the following reaction: $$ \mathrm{IO}_{3}^{-}(a q)+3 \mathrm{SO}_{3}^{2-}(a q) \longrightarrow \mathrm{I}^{-}(a q)+3 \mathrm{SO}_{4}^{2-}(a q) $$ The rate of this reaction is found to be first order in $\mathrm{IO}_{3}^{-}$, first order in $\mathrm{SO}_{3}^{2-}$, and first order in $\mathrm{H}^{+}$. (a) Write the rate law for the reaction. (b) By what factor will the rate of the reaction change if the $\mathrm{pH}$ is lowered from 5.00 to $3.50 ?$ Does the reaction proceed more quickly or more slowly at the lower $\mathrm{pH}$ ? (c) By using the concepts discussed in Section $14.6, \mathrm{ex}-$ plain how the reaction can be pH-dependent even though $\mathrm{H}^{+}$ does not appear in the overall reaction.

The iodate ion is reduced by sulfite according to the following reaction:
$$
\mathrm{IO}_{3}^{-}(a q)+3 \mathrm{SO}_{3}^{2-}(a q) \longrightarrow \mathrm{I}^{-}(a q)+3 \mathrm{SO}_{4}^{2-}(a q)
$$
The rate of this reaction is found to be first order in $\mathrm{IO}_{3}^{-}$, first order in $\mathrm{SO}_{3}^{2-}$, and first order in $\mathrm{H}^{+}$.
(a) Write the rate law for the reaction.
(b) By what factor will the rate of the reaction change if the $\mathrm{pH}$ is lowered from 5.00 to $3.50 ?$ Does the reaction proceed more quickly or more slowly at the lower $\mathrm{pH}$ ?
(c) By using the concepts discussed in Section $14.6, \mathrm{ex}-$ plain how the reaction can be pH-dependent even though $\mathrm{H}^{+}$ does not appear in the overall reaction.

Key Concepts

Rate Law

The rate law is a mathematical expression that relates the rate of a chemical reaction to the concentrations of its reactants raised to specific powers, known as the reaction orders. It provides a compact way to express how changes in reactant concentrations affect the overall rate of the reaction.

Reaction Order

The reaction order indicates the power to which the concentration of each reactant is raised in the rate law. It shows how the rate of reaction responds to changes in the concentration of each reactant and is determined experimentally; in this question, each reactant (IO3–, SO3^2–, and H+) contributes a first-order dependence to the overall rate.

pH and Proton Concentration Effect

pH is a measure of the hydrogen ion concentration in a solution. Even though H+ does not appear in the overall balanced reaction, its presence in the rate law indicates that the reaction rate is sensitive to the acidity of the medium. Changes in pH, by altering the concentration of protons, can significantly speed up or slow down the reaction.

Reaction Mechanism and pH Dependence

A reaction mechanism is a sequence of elementary steps that explains how reactants transform into products. In cases where H+ is involved in intermediate steps or transition states, the reaction rate can become dependent on the proton concentration even if H+ is not consumed in the overall stoichiometry, thereby explaining the pH dependence observed in the rate law.

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