Electrolysis of dilute aqueous NaCl solution was carried out by passing 10A current. The time required (in seconds) to liberate 0.01 mole of H2 gas at the cathode is: [IF = 96500 C]

Explanation

To solve the problem of determining the time required to liberate 0.01 moles of H2 gas at the cathode during the electrolysis of dilute aqueous NaCl solution, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Reaction at the Cathode**:
The reaction occurring at the cathode during the electrolysis of NaCl solution is:
\[ 2H^+ + 2e^- \rightarrow H_2(g) \]
This indicates that 2 moles of electrons are required to produce 1 mole of hydrogen gas (H2).

2. **Calculate Moles of Electrons Required**:
Since we want to liberate 0.01 moles of H2 gas, we can determine the moles of electrons needed:
\[ \text{Moles of electrons} = 0.01 \, \text{moles of H2} \times 2 \, \text{moles of electrons/mole of H2} = 0.02 \, \text{moles of electrons} \]

3. **Convert Moles of Electrons to Charge (Coulombs)**:
Using Faraday's constant (96500 C/mol), we can calculate the total charge (Q) needed:
\[ Q = \text{moles of electrons} \times \text{Faraday's constant} = 0.02 \, \text{moles} \times 96500 \, \text{C/mol} = 1930 \, \text{C} \]

4. **Use the Formula Q = I × T to Find Time (T)**:
Rearranging the formula to solve for time (T):
\[ T = \frac{Q}{I} \]
Substituting the values we have:
\[ T = \frac{1930 \, \text{C}}{10 \, \text{A}} = 193 \, \text{seconds} \]

### Final Answer:
The time required to liberate 0.01 moles of H2 gas at the cathode is **193 seconds**.

---