How much will the reduction potential of a hydrogen electrode change when its solution initially at `pH=0` is neutralized to `pH=7` ?

Options

A. Increase by `0.059V`
B. Decrease by `0.059V`
C. Increase by `0.41V`
D. Decrease by `0.41V`

Explanation

To determine how much the reduction potential of a hydrogen electrode changes when its solution is neutralized from pH 0 to pH 7, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Standard Hydrogen Electrode (SHE)**:
The standard reduction potential (E°) for the hydrogen electrode is defined as 0 V. The half-reaction for the hydrogen electrode can be written as:
\[ \text{2H}^+ + 2e^- \leftrightarrow \text{H}_2(g) \]

2. **Nernst Equation**:
The Nernst equation for the hydrogen electrode can be expressed as:
\[ E = E° - \frac{0.059}{n} \log \left( \frac{P_{\text{H}_2}}{[\text{H}^+]^2} \right) \]
Here, \( n = 2 \) for the reaction involving 2 electrons.

3. **Initial Condition (pH = 0)**:
At pH 0, the concentration of \( \text{H}^+ \) ions is:
\[ [\text{H}^+] = 10^{-0} = 1 \, \text{M} \]
Assuming the pressure of hydrogen gas \( P_{\text{H}_2} = 1 \, \text{atm} \), the potential can be calculated as:
\[ E_1 = 0 - \frac{0.059}{2} \log \left( \frac{1}{(1)^2} \right) = 0 - \frac{0.059}{2} \log(1) = 0 \, \text{V} \]

4. **Final Condition (pH = 7)**:
At pH 7, the concentration of \( \text{H}^+ \) ions is:
\[ [\text{H}^+] = 10^{-7} \, \text{M} \]
Using the same pressure of hydrogen gas, the potential can be calculated as:
\[ E_2 = 0 - \frac{0.059}{2} \log \left( \frac{1}{(10^{-7})^2} \right) = 0 - \frac{0.059}{2} \log(10^{14}) = 0 - \frac{0.059}{2} \cdot 14 \]
\[ E_2 = -0.059 \cdot 7 = -0.413 \, \text{V} \]

5. **Change in Electrode Potential**:
The change in electrode potential (ΔE) when the pH changes from 0 to 7 is:
\[ \Delta E = E_2 - E_1 = -0.413 \, \text{V} - 0 \, \text{V} = -0.413 \, \text{V} \]

### Conclusion:
The reduction potential of the hydrogen electrode decreases by approximately **0.413 V** when the solution is neutralized from pH 0 to pH 7.

### Final Answer:
The reduction potential decreases by **0.413 V**.

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