Consider the decomposition of hydrogen peroxide in alkaline medium which is catalysed by iodide ions :
`2" H"_(2)"O"_(2)overset("OH"^(-))to2" H"_(2)"O"+"O"_(2)`
This reaction takes place in two steps as given below :
Step-I. `"H"_(2)"O"_(2)+I^(-)to"H"_(2)"O"+" IO"^(-)("slow")`
Step-II. `"H"_(2)"O"_(2)+"IO"^(-)to"H"_(2)"O"+I^(-)+"O"_(2)("fast")`
(a) Write the rate law expression and determine the order of reaction w.r.t. `"H"_(2)"O"_(2).`
(b) What is the molecularity of each individual step ?

Answer

To solve the question regarding the decomposition of hydrogen peroxide in an alkaline medium catalyzed by iodide ions, we will break it down into two parts as specified in the question.

### Part (a): Rate Law Expression and Order of Reaction with Respect to H₂O₂

1. **Identify the Rate-Determining Step**:
- The first step of the reaction is the slow step:
\[ \text{Step-I: } \text{H}_2\text{O}_2 + \text{I}^- \rightarrow \text{H}_2\text{O} + \text{IO}^- \quad (\text{slow}) \]
- Since this is the slow step, it will determine the rate of the overall reaction.

2. **Write the Rate Law Expression**:
- The rate law is generally expressed as:
\[ \text{Rate} = k[\text{Reactants}]^{\text{coefficients}} \]
- For Step-I, the rate law can be written as:
\[ \text{Rate} = k[\text{H}_2\text{O}_2]^1[\text{I}^-]^1 \]
- This simplifies to:
\[ \text{Rate} = k[\text{H}_2\text{O}_2][\text{I}^-] \]

3. **Determine the Order of Reaction with Respect to H₂O₂**:
- The order of reaction with respect to a reactant is given by the exponent of that reactant in the rate law expression.
- From the rate law, the order with respect to H₂O₂ is 1.

### Part (b): Molecularity of Each Individual Step

1. **Define Molecularity**:
- Molecularity is defined as the number of reactant species (atoms, molecules, or ions) that collide to form products in an elementary reaction step.

2. **Molecularity of Step-I**:
- The reaction is:
\[ \text{H}_2\text{O}_2 + \text{I}^- \rightarrow \text{H}_2\text{O} + \text{IO}^- \]
- Here, there are 2 reactant species (1 molecule of H₂O₂ and 1 ion of I⁻).
- Therefore, the molecularity of Step-I is 2.

3. **Molecularity of Step-II**:
- The reaction is:
\[ \text{H}_2\text{O}_2 + \text{IO}^- \rightarrow \text{H}_2\text{O} + \text{I}^- + \text{O}_2 \]
- Again, there are 2 reactant species (1 molecule of H₂O₂ and 1 ion of IO⁻).
- Thus, the molecularity of Step-II is also 2.

### Summary of Results:
- **Rate Law Expression**: \(\text{Rate} = k[\text{H}_2\text{O}_2][\text{I}^-]\)
- **Order of Reaction with Respect to H₂O₂**: 1
- **Molecularity of Step-I**: 2
- **Molecularity of Step-II**: 2