For the reaction,
`H_2O_2+2H^++3l^(-) rarrl_3^(-)+2H_2O`
select the correct statement

Options

A. Rate of disappearance of `H_2O_2` will be three times the rate of disappearance of `l^-`
B. Rate of disappearance of `H_2O_2` is `1/3` of rate of formation of `l_3^-`
C. Rate of disappearance of `l^-` ions will be three times the rate of formation `l_3^-` ions
D. Rate of formation of `H_2O` is `1/2` of rate formation of `l_3^-`

Answer

To solve the problem, we need to analyze the given reaction and derive the rate expressions for the reactants and products. The reaction is:

\[ H_2O_2 + 2H^+ + 3I^- \rightarrow I_3^- + 2H_2O \]

### Step 1: Write the Rate Law Expression

For the reaction, we can express the rate of disappearance of the reactants and the rate of formation of the products. The rate law can be expressed as:

\[ \text{Rate} = -\frac{d[H_2O_2]}{dt} = \frac{1}{2} \frac{d[H^+]}{dt} = -\frac{1}{3} \frac{d[I^-]}{dt} = \frac{1}{2} \frac{d[H_2O]}{dt} = \frac{1}{3} \frac{d[I_3^-]}{dt} \]

### Step 2: Analyze Each Statement

Now, we will analyze the provided statements one by one:

1. **Statement 1**: The rate of disappearance of \( H_2O_2 \) is 3 times the rate of disappearance of \( I^- \).
- From the rate law, we see that the rate of disappearance of \( H_2O_2 \) is actually \( \frac{1}{3} \) of the rate of disappearance of \( I^- \). Therefore, this statement is **incorrect**.

2. **Statement 2**: The rate of disappearance of \( H_2O_2 \) is equal to \( \frac{1}{3} \) of the rate of formation of \( I_3^- \).
- The rate of disappearance of \( H_2O_2 \) is \( -\frac{d[H_2O_2]}{dt} \) and the rate of formation of \( I_3^- \) is \( \frac{d[I_3^-]}{dt} \). The correct relationship is that the rate of disappearance of \( H_2O_2 \) is \( \frac{1}{3} \) of the rate of disappearance of \( I^- \), not the rate of formation of \( I_3^- \). Therefore, this statement is **incorrect**.

3. **Statement 3**: The rate of disappearance of \( I^- \) is 3 times the rate of formation of \( I_3^- \).
- According to the rate law, the rate of disappearance of \( I^- \) is indeed 3 times the rate of formation of \( I_3^- \). This statement is **correct**.

4. **Statement 4**: The rate of formation of \( H_2O \) is half of the rate of formation of \( I_3^- \).
- The rate of formation of \( H_2O \) is \( \frac{1}{2} \) of the rate of formation of \( I_3^- \). Therefore, this statement is **incorrect**.

### Conclusion

The correct statement is **Statement 3**: The rate of disappearance of \( I^- \) is 3 times the rate of formation of \( I_3^- \).