Assuring an elementary reaction `H_2O_2+3I^(-)+2H^(+)rarr2H_2O+I_3^(-)` . The effect on the rate of this reaction brought about by doubling the concentration of `I^(-)` without changing the order

Options

A. The rate would increase by a factor of 3
B. The rate would increase by a factor of 8
C. The rate would decrease by a factor of 1/3
D. The rate would increase by a factor of 9

Answer

To solve the problem, we need to analyze the given elementary reaction and determine how the rate of the reaction changes when the concentration of \( I^- \) is doubled.

### Step-by-Step Solution:

1. **Identify the Reaction and Rate Law**:
The reaction given is:
\[ H_2O_2 + 3I^- + 2H^+ \rightarrow 2H_2O + I_3^- \]
For an elementary reaction, the rate law can be expressed as:
\[ \text{Rate} = k [H_2O_2]^m [I^-]^n [H^+]^p \]
where \( m, n, \) and \( p \) are the stoichiometric coefficients of the reactants in the balanced equation.

2. **Determine the Order of the Reaction**:
From the balanced equation:
- The order with respect to \( H_2O_2 \) is 1 (coefficient of 1).
- The order with respect to \( I^- \) is 3 (coefficient of 3).
- The order with respect to \( H^+ \) is 2 (coefficient of 2).

Therefore, the overall rate law becomes:
\[ \text{Rate} = k [H_2O_2]^1 [I^-]^3 [H^+]^2 \]

3. **Express the Initial Rate**:
Let’s denote the initial rate of the reaction as \( R \):
\[ R = k [H_2O_2]^1 [I^-]^3 [H^+]^2 \]

4. **Calculate the New Rate When \( [I^-] \) is Doubled**:
If we double the concentration of \( I^- \):
\[ [I^-] \rightarrow 2[I^-] \]
The new rate \( R' \) will be:
\[ R' = k [H_2O_2]^1 (2[I^-])^3 [H^+]^2 \]
Simplifying this gives:
\[ R' = k [H_2O_2]^1 \cdot 8[I^-]^3 [H^+]^2 \]

5. **Relate the New Rate to the Original Rate**:
Since \( R = k [H_2O_2]^1 [I^-]^3 [H^+]^2 \), we can express \( R' \) in terms of \( R \):
\[ R' = 8 \cdot R \]

6. **Conclusion**:
Therefore, when the concentration of \( I^- \) is doubled, the rate of the reaction increases by a factor of 8.

### Final Answer:
The rate of the reaction increases by a factor of 8 when the concentration of \( I^- \) is doubled.

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