Problem 72 - Chemistry: The Central Science

Question

The decomposition of hydrogen peroxide is catalyzed by iodide ion. The catalyzed reaction is thought to proceed by a two-step mechanism: $$ \begin{aligned} \mathrm{H}_{2} \mathrm{O}_{2}(a q)+\mathrm{I}^{-}(a q) & \longrightarrow \mathrm{H}_{2} \mathrm{O}(l)+\mathrm{IO}^{-}(a q) \quad \text { (slow) } \\ \mathrm{IO}^{-}(a q)+\mathrm{H}_{2} \mathrm{O}_{2}(a q) & \longrightarrow \mathrm{H}_{2} \mathrm{O}(l)+\mathrm{O}_{2}(g)+\mathrm{I}^{-}(a q) \text { (fast) } \end{aligned} $$ (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.

Step-by-Step Solution

Answer

The overall chemical equation for the decomposition of hydrogen peroxide catalyzed by iodide ions is: \( 2\mathrm{H}_{2}\mathrm{O}_{2}(aq) + \mathrm{I}^{-}(aq) → 2\mathrm{H}_{2}\mathrm{O}(l) + \mathrm{O}_{2}(g) + \mathrm{I}^{-}(aq) \). The intermediate in this reaction mechanism is \(\mathrm{IO}^{-}\) as it is formed in the first step and consumed in the second step. Assuming the first step is rate-determining, the rate law for the overall process is given by: \(\text{rate} = k[H_{2}O_{2}][I^{-}]\), where k is the rate constant, and [H₂O₂] and [I⁻] represent the concentrations of hydrogen peroxide and iodide ions, respectively.

Step 1: Combine the two reaction steps

Add both reaction steps together to obtain the overall chemical equation: $$ \mathrm{H}_{2}\mathrm{O}_{2}(aq) + \mathrm{I}^{-}(aq) \longrightarrow \mathrm{H}_{2}\mathrm{O}(l) + \mathrm{IO}^{-}(aq) \\ \mathrm{IO}^{-}(aq) + \mathrm{H}_{2}\mathrm{O}_{2}(aq) \longrightarrow \mathrm{H}_{2}\mathrm{O}(l) + \mathrm{O}_{2}(g) + \mathrm{I}^{-}(aq) $$ Summing them up: $$ \mathrm{H}_{2}\mathrm{O}_{2}(aq) + \mathrm{I}^{-}(aq) + \mathrm{IO}^{-}(aq) + \mathrm{H}_{2}\mathrm{O}_{2}(aq) → \mathrm{H}_{2}\mathrm{O}(l) + \mathrm{IO}^{-}(aq) + \mathrm{H}_{2}\mathrm{O}(l) + \mathrm{O}_{2}(g) + \mathrm{I}^{-}(aq) $$ Now, cancel intermediate species present in both sides (IO⁻): $$ \mathrm{H}_{2}\mathrm{O}_{2}(aq) + \mathrm{I}^{-}(aq) + 2\mathrm{H}_{2}\mathrm{O}_{2}(aq) → 2\mathrm{H}_{2}\mathrm{O}(l) + \mathrm{O}_{2}(g) + \mathrm{I}^{-}(aq) $$ The overall chemical equation is: $$ 2\mathrm{H}_{2}\mathrm{O}_{2}(aq) + \mathrm{I}^{-}(aq) → 2\mathrm{H}_{2}\mathrm{O}(l) + \mathrm{O}_{2}(g) + \mathrm{I}^{-}(aq) $$ #b) Identifying Intermediate#

Step 2: Identify the intermediate

An intermediate is a substance that is produced in one reaction step and consumed in a subsequent step. In this mechanism, the intermediate is IO⁻. It is formed in the slow (first) step and consumed in the fast (second) step. #c) Rate Law Prediction#

Step 3: Determine the rate law

Since the first step is the rate-determining step, the overall rate law will depend on the rate law for the first step. The rate law for a given reaction step is proportional to the concentration of the reactants. In this case, the rate law for the first step is given by: $$ \text{rate} = k[H_{2}O_{2}][I^{-}] $$ Here, k is the rate constant, [H₂O₂] represents the concentration of hydrogen peroxide, and [I⁻] represents the concentration of iodide ions. Hence, the rate law for the overall process is: $$ \text{rate} = k[H_{2}O_{2}][I^{-}] $$

Key Concepts

Reaction Mechanism

Understanding the reaction mechanism is crucial in chemical kinetics as it provides a detailed description of the step-by-step sequence of elementary reactions by which overall chemical change occurs. In the decomposition of hydrogen peroxide catalyzed by iodide ion, two steps describe how reactants are converted into products:

• The first step, which is slow, involves the reaction of hydrogen peroxide with iodide ions to produce water and hypoiodite ions (IO⁻).
• The second step, which is fast, involves the reaction of hypoiodite ions with hydrogen peroxide to produce water, oxygen, and regenerate iodide ions.

Each step is characterized by its own rate, which contributes to the overall rate at which the reaction occurs. Identifying these steps helps chemists understand the complexity of chemical reactions and design ways to influence the overall reaction rate.

Rate-Determining Step

The rate-determining step is the slowest step in a reaction mechanism that acts as a bottleneck, determining the reaction rate. For the hydrogen peroxide decomposition reaction, the first step is considered the rate-determining step because it proceeds more slowly than the subsequent step.

The rate of the overall reaction is essentially controlled by this initial step, as all following reactions depend on its completion. Thus, understanding and identifying the rate-determining step is crucial for predicting how changes in reactant concentration or other conditions will affect the overall reaction speed.

Catalysis

Catalysis is a process in which the rate of a chemical reaction is increased by a substance called a catalyst, which is not consumed in the overall reaction. In our given exercise, the iodide ion (I⁻) serves as a catalyst for the decomposition of hydrogen peroxide. It participates in the reaction mechanism but is regenerated at the end.Catalysts work by providing an alternate reaction pathway with a lower activation energy. This means that at a given temperature, more molecules have the necessary energy to reach the transition state and convert into products. The ability of a catalyst like iodide to accelerate a reaction is a powerful tool in both industrial processes and biological systems.

Intermediate Species

Intermediate species are formed during one step of a reaction mechanism and consumed in another. They are crucial for connecting the steps of a reaction but do not appear in the overall chemical equation. In the decomposition of hydrogen peroxide, IO⁻ is an intermediate species. It is produced in the slow first step and immediately consumed in the fast second step.

Identifying intermediates helps us understand the flow of reactants to products and reveals potential targets for enhanced catalysis or inhibition in pharmaceutical and industrial chemistry applications.

Rate Law

The rate law is an expression that relates the rate of a reaction to the concentration of reactants. It is determined experimentally and reflects the influence of reactant concentrations on the rate of reaction. For a reaction where the first step is rate-determining, as in the decomposition of hydrogen peroxide, the rate law is proportional to the product of the concentrations of the reactants involved in that step.

The rate law for our example is given as:\[\begin{equation}\text{rate} = k[H_{2}O_{2}][I^{-}]\end{equation}\]Here, \(k\) is the rate constant, \([H_{2}O_{2}]\) represents the concentration of hydrogen peroxide, and \([I⁻]\) is the concentration of iodide ions. Understanding the rate law is fundamental for chemists to control and optimize reactions for desired outcomes.