Question

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

Short answer

(a) Rate laws for each elementary reaction: \(rate1 = k_1[\ce{H2O2}][\ce{I-}]\) \(rate2 = k_2[\ce{IO-}][\ce{H2O2}]\) (b) Overall chemical equation: \(\ce{2H2O2} \longrightarrow \ce{2H2O} + \ce{O2}\) (c) Intermediate species identification: The intermediate species is \(\ce{IO-}\). (d) Predicting the rate law for the overall process: \[rate = k_1[\ce{H2O2}][\ce{I-}]\]\[rate = k[\ce{H2O2}][\ce{I-}]\]

Step-by-step solution

(a) Rate laws for each elementary reaction

The rate laws depend on the molecularity of the reaction, so for the slow step, the reaction is bimolecular, as it involves two molecules, \(\ce{H2O2}\) and \(\ce{I-}\), reacting together. For the fast step, it is also bimolecular, as it involves \(\ce{IO-}\) and \(\ce{H2O2}\). For the slow step: \[rate1 = k_1[\ce{H2O2}][\ce{I-}]\] For the fast step: \[rate2 = k_2[\ce{IO-}][\ce{H2O2}]\]

(b) Overall chemical equation

Combine both elementary reactions and cancel any common species on both sides: \[\ce{H2O2} + \ce{I-} \longrightarrow \ce{H2O} + \ce{IO-}\] \[\ce{IO-} + \ce{H2O2} \longrightarrow \ce{H2O} + \ce{O2} + \ce{I-}\] Resulting in the overall reaction: \[\ce{2H2O2} \longrightarrow \ce{2H2O} + \ce{O2}\]

(c) Intermediate species identification

The intermediate species appear in the mechanism but not in the overall reaction. In this case, the intermediate species is \(\ce{IO-}\).

(d) Predicting the rate law for the overall process

Since we assume that the first step is rate-determining, the overall rate depends on the rate of the slow step: \[rate = k_1[\ce{H2O2}][\ce{I-}]\] However, we must express the intermediate, \(\ce{IO-}\), in terms of the reactants. From the fast step: \[rate2 = k_2[\ce{IO-}][\ce{H2O2}]\] Since the fast step is much faster than the slow step, the intermediate concentration is maintained at a steady state, so: \[\frac{d[\ce{IO-}]}{dt} = 0\] Express \(\ce{IO-}\) concentration: \[[\ce{IO-}] = \frac{rate1}{k_2[\ce{H2O2}]}\] Therefore, the overall rate law is: \[rate = k_1[\ce{H2O2}][\ce{I-}]\] For this problem, the rate law remains the same because the assumptions made did not require us to change the rate law. So, the overall rate law for the decomposition of hydrogen peroxide catalyzed by iodide ions is: \[rate = k[\ce{H2O2}][\ce{I-}]\]

Key concepts

Rate Law

In chemical kinetics, the rate law describes how the rate of a chemical reaction depends on the concentration of its reactants. For the decomposition of hydrogen peroxide in the presence of iodide ions, understanding the rate law helps us predict how changes in concentration affect the reaction speed.

For a bimolecular reaction, where two reactant molecules collide, the rate law is of the form:

• Rate = k[ Reactant1] [Reactant2]

Here, *k* is the rate constant, a crucial component that influences the reaction rate. Also, the rate of each elementary step in a reaction mechanism depends on the concentration of the reactants involved in that step.

In the given mechanism, the slow step involving hydrogen peroxide and iodide ions dictates the overall reaction rate. Thus, the rate law for the entire process depends on the concentrations of these two species:

• Rate = k_1[ H₂O₂] [I⁻]

Chemical Equation

A chemical equation provides a concise way to represent a chemical reaction. It shows the reactants transforming into products, often using a balanced equation to reflect the conservation of mass. In this exercise, the elementary steps of the decomposition process split the reaction into more accessible parts.

Combining these steps into a single, overall chemical equation involves adding the sequences together and eliminating intermediates, as they do not appear in the final balanced equation. For the decomposition of hydrogen peroxide catalyzed by iodide ions, the overall balanced equation is:

• 2 H₂O₂ → 2 H₂O + O₂

This equation tells us that two molecules of hydrogen peroxide decompose to form two water molecules and one molecule of oxygen gas.

Reaction Mechanism

A reaction mechanism is a step-by-step sequence of elementary reactions by which an overall chemical change occurs. It offers insight into the specific molecular processes involved, showing how reactants convert to products.

In the reaction mechanism for hydrogen peroxide decomposition catalyzed by iodide ions, we see two elementary steps: a slow one and a fast one. The slow step is crucial because it acts as the rate-determining step, which means it governs the overall reaction rate. Here, iodide ion starts the reaction by transforming hydrogen peroxide into water and the intermediate hypoiodite ion (IO⁻).

The fast step involves the hypoiodite ion reacting with another hydrogen peroxide molecule to finally form water, oxygen, and regenerated iodide ion. This two-step mechanism gives us a complete view of what occurs on a molecular level during this reaction.

Catalysis

Catalysis is an important aspect of this reaction. A catalyst is a substance that increases the rate of a chemical reaction without being consumed in the process. In the decomposition of hydrogen peroxide, iodide ions act as a catalyst. They enable the reaction to proceed at a faster rate by providing an alternative reaction pathway with a lower activation energy.

During the reaction mechanism, iodide ions facilitate the formation of the intermediate hypoiodite ion, which then quickly transforms hydrogen peroxide into products. Although the catalyst is involved in an intermediate form, it is regenerated by the end of the process.

Therefore, the presence of a catalyst like iodide ions is crucial for enhancing the speed of the reaction, confirming that catalysis plays an essential role in many chemical processes.