Problem 50 - Chemical Principles

Question

The mechanism proposed for the oxidation of iodide ion by the hypochlorite ion in aqueous solution is as follows: Step \(1 \mathrm{ClO}^{-}+\mathrm{H}_{2} \mathrm{O} \longrightarrow \mathrm{HClO}+\mathrm{OH}^{-}\)and its reverse (both fast, equilibrium) Step \(2 \mathrm{I}^{-}+\mathrm{HClO} \longrightarrow \mathrm{HIO}+\mathrm{Cl}^{-}\)(slow) Step \(3 \mathrm{HIO}+\mathrm{OH}^{-} \longrightarrow \mathrm{IO}^{-}+\mathrm{H}_{2} \mathrm{O}\) (fast) Write the rate law for the formation of HIO implied by this mechanism.

Step-by-Step Solution

Answer

The rate law for the formation of HIO is \(rate = k[\mathrm{I}^{-}][\mathrm{HClO}]\).

Step 1 - Understanding the Rate-Determining Step

In a reaction mechanism, the rate-determining step is the slowest step and controls the reaction rate. Here, Step 2, \(\mathrm{I}^{-} + \mathrm{HClO} \longrightarrow \mathrm{HIO} + \mathrm{Cl}^{-}\), is the slowest step and therefore determines the rate law of the formation of HIO.

Step 2 - Write the Rate Law Based on the Rate-Determining Step

The rate law is based on the concentrations of the reactants in the rate-determining step. For the given reaction, the rate of formation of HIO is thus proportional to the concentration of \(\mathrm{I}^{-}\) and the concentration of \(\mathrm{HClO}\). The rate law can be written as: \[rate = k[\mathrm{I}^{-}][\mathrm{HClO}]\]

Step 3 - Incorporate the Pre-Equilibrium Condition

Step 1 establishes an equilibrium between \(\mathrm{ClO}^{-}\), \(\mathrm{H}_2\mathrm{O}\), \(\mathrm{HClO}\), and \(\mathrm{OH}^{-}\) because it is fast and reversible. As a result, the concentration of \(\mathrm{HClO}\) can be expressed in terms of the equilibrium concentrations of \(\mathrm{ClO}^{-}\) and \(\mathrm{OH}^{-}\). However, in this case, we only need the concentration of \(\mathrm{HClO}\) for the rate law, and there is no further information to relate \(\mathrm{HClO}\) to \(\mathrm{ClO}^{-}\) and \(\mathrm{OH}^{-}\) concentrations.

Step 4 - Final Rate Law Expression

Without additional information to relate \(\mathrm{HClO}\) to the other substances in the equilibrium, the final rate law for the formation of \(\mathrm{HIO}\) based on the mechanism provided will remain as \[rate = k[\mathrm{I}^{-}][\mathrm{HClO}]\].

Key Concepts

Reaction Mechanism

The term reaction mechanism describes the step-by-step sequence of elementary reactions by which overall chemical change occurs. A mechanism details the actual process through which reactants transform into products, including the intermediates and transition states. In the given oxidation of iodide ions by hypochlorite ions, the mechanism is proposed to consist of three steps, with fast and reversible processes achieving equilibrium quickly, and a significantly slower step. This slower step typically involves a higher energy transition state, hence its lower rate. Understanding the reaction mechanism allows chemists to predict how changing concentrations of reactants will affect the rate of product formation.

Rate-Determining Step

The rate-determining step (RDS) is the slowest step in a reaction mechanism and thus determinants the overall reaction rate. This concept is crucial when deducing the rate law of a chemical reaction. Since other steps occur relatively quickly, they don't significantly limit the speed of the overall reaction. Focusing on this slowest step allows us to develop the rate law expression which is purely based on the reactants involved in the RDS, as seen in the provided exercise. By examining each step of the proposed mechanism, chemists can identify the rate-determining step and use it to predict how the reaction rate will respond to changes in reactant concentrations.

Chemical Kinetics

Chemical kinetics is the study of rates of chemical processes and the factors affecting those rates. It involves understanding how various factors such as concentration, temperature, and presence of catalysts influence the speed of chemical reactions. Kinetics is crucial for the development of chemical processes in industries and laboratories, as it guides the optimization of conditions for the fastest and most efficient reactions. The rate law, deduced from kinetics and mechanisms, mathematically expresses the relationship between the reaction rate and the concentration of reactants. In our oxidation example, we looked at the specific reaction rate and how the concentration of reactants influenced the speed at which HIO is formed.

Equilibrium Condition

The equilibrium condition in a chemical reaction occurs when the forward reaction rate equals the reverse reaction rate, leading to no net change in concentrations of reactants and products. This state is significant when there are steps within a mechanism that reach equilibrium rapidly compared to the rest of the process, which implies that these steps are both fast and reversible. The conditions at equilibrium are described by the equilibrium constant, which relates the concentrations of products and reactants. In our exercise example, the fast first step achieves equilibrium, and normally, this would allow us to express the concentration of a reactant used in the rate-determining step in terms of the other reactants, but the exercise does not provide the necessary equilibrium constants for further simplification of the rate law. However, understanding these equilibrium conditions is essential for comprehending the full dynamic behavior of chemical reactions.