Question

The decomposition of hydrogen peroxide is catalyzed by iodide ion. The catalyzed reaction is thought to proceed by a two-step mechanism: $$ \begin{aligned} \mathrm{H}_{2} \mathrm{O}_{2}(a q)+\mathrm{I}^{-}(a q) & \longrightarrow \mathrm{H}_{2} \mathrm{O}(l)+\mathrm{IO}^{-}(a q) \\ \mathrm{IO}^{-}(a q)+\mathrm{H}_{2} \mathrm{O}_{2}(a q) & \longrightarrow \mathrm{H}_{2} \mathrm{O}(l)+\mathrm{O}_{2}(g)+\mathrm{I}^{-}(a q) \end{aligned} $$ (a) Write the chemical equation for the overall process. (b) Identify the intermediate, if any, in the mechanism. (c) Assuming that the first step of the mechanism is rate determining, predict the rate law for the overall process.

Short answer

(a) The overall reaction for the decomposition of hydrogen peroxide catalyzed by iodide ion is: \(\mathrm{2H}_2\mathrm{O}_2(aq) \longrightarrow 2\mathrm{H}_2\mathrm{O}(l) + \mathrm{O}_2(g)\) (b) The intermediate species in the mechanism is \(\mathrm{IO}^-(aq)\). (c) The rate law for the overall process, based on the rate-determining first step, is: \(Rate = k[\mathrm{H}_2\mathrm{O}_2][\mathrm{I}^-]\).

Step-by-step solution

Determine the overall chemical equation

To determine the overall reaction, add the two given reactions together, cancel out any species that appear on both sides of the equation, and combine the remaining species into a single equation. Given reactions: 1) \(\mathrm{H}_2\mathrm{O}_2(aq) + \mathrm{I}^-(aq) \longrightarrow \mathrm{H}_2\mathrm{O}(l) + \mathrm{IO}^-(aq)\) 2) \(\mathrm{IO}^-(aq) + \mathrm{H}_2\mathrm{O}_2(aq) \longrightarrow \mathrm{H}_2\mathrm{O}(l) + \mathrm{O}_2(g) + \mathrm{I}^-(aq)\) Adding both reactions: \(\mathrm{H}_2\mathrm{O}_2(aq) + \mathrm{I}^-(aq) + \mathrm{IO}^-(aq) + \mathrm{H}_2\mathrm{O}_2(aq) \longrightarrow \mathrm{H}_2\mathrm{O}(l)+\mathrm{IO}^-(aq) + \mathrm{H}_2\mathrm{O}(l) + \mathrm{O}_2(g) + \mathrm{I}^-(aq)\) Now, we can cancel out the intermediate species \(\mathrm{IO}^-\) and simplify the equation: \(\mathrm{H}_2\mathrm{O}_2(aq) + \mathrm{H}_2\mathrm{O}_2(aq) \longrightarrow 2\mathrm{H}_2\mathrm{O}(l) + \mathrm{O}_2(g)\) The overall reaction is: \(\mathrm{2H}_2\mathrm{O}_2(aq) \longrightarrow 2\mathrm{H}_2\mathrm{O}(l) + \mathrm{O}_2(g)\)

Identify the intermediate species

The intermediate species is a species that is produced in one step and consumed in another step. In this case, \(\mathrm{IO}^-(aq)\) is produced in the first step and consumed in the second step, so it is the intermediate species.

Determine the rate law

Assuming that the first step is rate-determining, we can write the rate law for the overall reaction based on the first step: 1) \(\mathrm{H}_2\mathrm{O}_2(aq) + \mathrm{I}^-(aq) \longrightarrow \mathrm{H}_2\mathrm{O}(l) + \mathrm{IO}^-(aq)\) The rate law based on this step is: \(Rate = k[\mathrm{H}_2\mathrm{O}_2][\mathrm{I}^-]\) where \(k\) is the rate constant, and \([\mathrm{H}_2\mathrm{O}_2]\) and \([\mathrm{I}^-]\) are the concentrations of \(\mathrm{H}_2\mathrm{O}_2\) and \(\mathrm{I}^-\), respectively.

Key concepts

Reaction Mechanism

A reaction mechanism is like a roadmap showing the step-by-step pathway a chemical reaction takes to reach its final products. In our hydrogen peroxide decomposition, the reaction mechanism consists of two steps. First, hydrogen peroxide (\(\mathrm{H}_2\mathrm{O}_2\)) reacts with iodide ions (\(\mathrm{I}^-\)) to create water (\(\mathrm{H}_2\mathrm{O}\)) and hypoiodite ions (\(\mathrm{IO}^-\)). Then, in the second step, the hypoiodite ions react with more hydrogen peroxide, forming water, oxygen (\(\mathrm{O}_2\)), and regenerating the iodide ions. Mechanisms are crucial because they help chemists understand the detailed process of how reactions occur, which can differ significantly from the overall chemical equation. This understanding enables the prediction and control of rates and outcomes in chemical processes.

Rate-Determining Step

The rate-determining step of a reaction mechanism is the slowest step that dictates the overall reaction rate, like a bottleneck on a busy highway. In our studied mechanism, the first step is assumed to be the rate-determining step, meaning it limits how fast the entire reaction can go. This assumption is crucial because it influences the form of the rate law we derive. Since the rate-determining step controls the reaction's speed, the factors affecting this step (like the concentration of reactants involved) will directly affect the overall reaction rate.

Intermediate Species

Intermediate species are temporary molecules or ions that are formed and consumed during a multi-step reaction. They are not present in the overall reaction equation because they do not appear as final products or initial reactants. In the decomposition of hydrogen peroxide catalyzed by iodide ion, the hypoiodite ion (\(\mathrm{IO}^-\)) serves as an intermediate. It is created in the first step and is used up in the second step. Identifying intermediates is essential in understanding the detailed steps of a mechanism because these species often hint at the hidden pathways and arrangements molecules take during the transformation process.

Rate Law

The rate law expresses the mathematical relationship between the rate of a reaction and the concentration of the reactants, highlighting how changes in concentration will affect the reaction speed. For reactions proceeding via a multi-step mechanism, the rate law is typically based on the rate-determining step. In our example, assuming the first step controls the overall rate, the rate law is determined as\(Rate = k[\mathrm{H}_2\mathrm{O}_2][\mathrm{I}^-]\).This indicates the rate depends on the concentration of both hydrogen peroxide and iodide ion. The rate constant, \(k\), is a proportionality factor that depends on temperature and other conditions. Understanding the rate law allows chemists to predict how a reaction's speed changes with varying conditions, which is crucial for both laboratory experiments and industrial applications.