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 regarding the reaction:

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

we need to analyze the rates of disappearance of reactants and the rates of formation of products based on the stoichiometry of the reaction.

### Step-by-Step Solution:

1. **Write the Rate Expressions:**
The rate of reaction can be expressed in terms of the change in concentration of reactants and products. For the given reaction, we can write:
\[ -\frac{d[H_2O_2]}{dt} = \frac{1}{2} \frac{d[H^+]}{dt} = \frac{1}{3} \frac{d[I^-]}{dt} = \frac{d[I_3^-]}{dt} = \frac{1}{2} \frac{d[H_2O]}{dt} \]

2. **Analyze the Statements:**
Now, we will evaluate each statement based on the rate expressions derived above.

- **Statement 1:** "The rate of disappearance of \( H_2O_2 \) will be 3 times the rate of disappearance of \( I^- \)."
- From the rate expressions, we have:
\[ -\frac{d[H_2O_2]}{dt} = \frac{1}{3} \left(-\frac{d[I^-]}{dt}\right) \]
This implies:
\[ -\frac{d[H_2O_2]}{dt} = \frac{1}{3} \cdot \text{rate of disappearance of } I^- \]
Therefore, this statement is **incorrect**.

- **Statement 2:** "The rate of disappearance of \( H_2O_2 \) is \( \frac{1}{3} \) of the rate of formation of \( I_3^- \)."
- From the rate expressions:
\[ -\frac{d[H_2O_2]}{dt} = \frac{d[I_3^-]}{dt} \]
This means the rate of disappearance of \( H_2O_2 \) is equal to the rate of formation of \( I_3^- \), thus this statement is **incorrect**.

- **Statement 3:** "The rate of disappearance of \( I^- \) will be 3 times the rate of formation of \( I_3^- \)."
- From the rate expressions:
\[ -\frac{d[I^-]}{dt} = 3 \cdot \frac{d[I_3^-]}{dt} \]
This means the rate of disappearance of \( I^- \) is indeed 3 times the rate of formation of \( I_3^- \), hence this statement is **correct**.

- **Statement 4:** "The rate of formation of \( H_2O \) is half of the rate of formation of \( I_3^- \)."
- From the rate expressions:
\[ \frac{d[H_2O]}{dt} = \frac{1}{2} \cdot \frac{d[I_3^-]}{dt} \]
This means the rate of formation of \( H_2O \) is actually equal to half of the rate of formation of \( I_3^- \), thus this statement is **incorrect**.

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