Question

Consider the decomposition of hydrogen peroxide \((H_{2}O_{2})\) as per the equation given below: \[ 2H_{2}O_{2} \overset{I^-}{\longrightarrow} 2H_{2}O + O_{2} \] The mechanism for this reaction was found to be: \[ \textbf{Step I:}\qquad H_{2}O_{2}+I^- \longrightarrow H_{2}O+IO^- \qquad (\text{slow}) \] \[ \textbf{Step II:}\qquad H_{2}O_{2}+IO^- \longrightarrow H_{2}O+I^-+O_{2} \qquad (\text{fast}) \] (a) Write the rate law expression.

Hint:

Even though the overall equation involves 2 moles of \( H_2O_2 \), the rate law only depends on the species in the slowest step.

Answer 1

Concept:

• For a multi-step (complex) reaction, the rate law is determined by the slowest step, known as the Rate Determining Step (RDS).

• The mechanism provided is:
Step I: \( H_2O_2 + I^- \rightarrow H_2O + IO^- \) (slow)
Step II: \( H_2O_2 + IO^- \rightarrow H_2O + I^- + O_2 \) (fast)
Step 1: Identify the Rate Determining Step
Step I is specified as the "slow" step. The kinetics of the overall reaction will follow the stoichiometry of this specific elementary step.

Step 2: Write the rate law based on Step I
The reactants in Step I are one molecule of \( H_2O_2 \) and one ion of \( I^- \).
Therefore, the rate law expression is: \[ \text{Rate} = k [H_2O_2] [I^-] \] The final answer is \( \text{Rate} = k [H_2O_2] [I^-] \).