Electrolysis of dilute aqueous NaCl solution was carried out by passing 10 mA current. The time required to liberate 0.01 mole of `H_2` gas at the cathode is : `(1f= 96500C mol^(-1)`

Options

A. `9.65 xx10^(4)s`
B. `19.3xx10^(4)S`
C. `28.95xx10^(4)S`
D. `38.6xx10^(4)s`

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 1: Determine the charge required to liberate 0.01 moles of H₂ gas.
The balanced equation for the electrolysis of water (which occurs in dilute NaCl solution) at the cathode is:
\[ 2H_2O + 2e^- \rightarrow H_2 + 2OH^- \]

From this equation, we see that 2 moles of electrons (2e⁻) are required to produce 1 mole of H₂ gas. Therefore, to produce 0.01 moles of H₂ gas, we need:
\[ \text{Moles of electrons} = 2 \times 0.01 = 0.02 \text{ moles of electrons} \]
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