`H_2` (gas) is bubbled through an aqueous solution of `HCl(pH = 2.5)` at `25^@C`. If at `P_(H_2(g)) = 10^(-x))` bar the electrode potential will be zero. Then find value of x.

Explanation

To solve the problem, we need to find the value of \( x \) such that the electrode potential of the hydrogen electrode becomes zero when hydrogen gas is bubbled through an aqueous solution of hydrochloric acid (HCl) with a given pH.

### Step-by-Step Solution:

1. **Understand the Reaction**:
The half-reaction for the hydrogen electrode can be represented as:
\[ \text{H}_2(g) \rightleftharpoons 2\text{H}^+(aq) + 2e^- \]

2. **Determine the Concentration of \( \text{H}^+ \)**:
The pH of the solution is given as 2.5. We can find the concentration of \( \text{H}^+ \) ions using the formula:
\[ [\text{H}^+] = 10^{-\text{pH}} = 10^{-2.5} \]

3. **Calculate \( [\text{H}^+] \)**:
\[ [\text{H}^+] = 10^{-2.5} \approx 0.00316 \, \text{mol/L} \]

4. **Write the Reaction Quotient \( Q \)**:
The reaction quotient \( Q \) for the hydrogen electrode can be expressed as:
\[ Q = \frac{[\text{H}^+]^2}{P_{\text{H}_2}} \]
where \( P_{\text{H}_2} \) is the partial pressure of hydrogen gas.

5. **Substitute Values into \( Q \)**:
Substituting the concentration of \( \text{H}^+ \) into the equation for \( Q \):
\[ Q = \frac{(10^{-2.5})^2}{P_{\text{H}_2}} = \frac{10^{-5}}{P_{\text{H}_2}} \]

6. **Set the Electrode Potential to Zero**:
The electrode potential \( E \) is given by the Nernst equation:
\[ E = E^\circ - \frac{RT}{nF} \ln Q \]
For the standard hydrogen electrode, \( E^\circ = 0 \). Setting \( E = 0 \):
\[ 0 = 0 - \frac{RT}{nF} \ln Q \]
This implies:
\[ \ln Q = 0 \implies Q = 1 \]

7. **Equate \( Q \) to 1**:
From our earlier expression for \( Q \):
\[ \frac{10^{-5}}{P_{\text{H}_2}} = 1 \]
Thus, we have:
\[ P_{\text{H}_2} = 10^{-5} \, \text{bar} \]

8. **Relate \( P_{\text{H}_2} \) to \( x \)**:
We are given that \( P_{\text{H}_2} = 10^{-x} \, \text{bar} \). Therefore:
\[ 10^{-x} = 10^{-5} \]
This implies:
\[ x = 5 \]

### Final Answer:
The value of \( x \) is \( 5 \).