What is the electrode potential of a gasous hydrogen electrode dipped in a solution `pH=5.0` relative to the calomel electrode with an electrode potential of `+0.28V` ?

Options

A. `0.0125V`
B. `+0.575V`
C. `+0.015V`
D. `-0.575V`

Explanation

To find the electrode potential of a gaseous hydrogen electrode (GHE) dipped in a solution with a pH of 5.0 relative to a calomel electrode with an electrode potential of +0.28 V, we can follow these steps:

### Step 1: Write the half-reaction for the hydrogen electrode
The half-reaction for the reduction of hydrogen ions (H⁺) to hydrogen gas (H₂) is:
\[ \text{2H}^+ + 2e^- \leftrightarrow \text{H}_2(g) \]

### Step 2: Use the Nernst equation
The standard electrode potential (E°) for the hydrogen electrode is 0 V. The Nernst equation for this reaction at 25°C is:
\[ E = E^\circ - \frac{0.059}{n} \log \frac{1}{[\text{H}^+]^2} \]
Where:
- \( E \) is the electrode potential
- \( E^\circ \) is the standard electrode potential (0 V for hydrogen)
- \( n \) is the number of moles of electrons transferred (2 for this reaction)
- \([\text{H}^+]\) is the concentration of hydrogen ions

### Step 3: Calculate the concentration of H⁺ ions
Given that the pH of the solution is 5.0, we can calculate the concentration of H⁺ ions:
\[ [\text{H}^+] = 10^{-\text{pH}} = 10^{-5} \, \text{M} \]

### Step 4: Substitute the values into the Nernst equation
Since \( n = 2 \) and \([\text{H}^+] = 10^{-5}\):
\[ E = 0 - \frac{0.059}{2} \log \frac{1}{(10^{-5})^2} \]
\[ E = -0.0295 \log \frac{1}{10^{-10}} \]
\[ E = -0.0295 \log(10^{10}) \]
\[ E = -0.0295 \times 10 \]
\[ E = -0.295 \, \text{V} \]

### Step 5: Calculate the relative potential to the calomel electrode
Now, we need to find the potential of the hydrogen electrode relative to the calomel electrode:
\[ E_{\text{relative}} = E_{\text{GHE}} - E_{\text{calomel}} \]
\[ E_{\text{relative}} = -0.295 \, \text{V} - 0.28 \, \text{V} \]
\[ E_{\text{relative}} = -0.295 - 0.28 \]
\[ E_{\text{relative}} = -0.575 \, \text{V} \]

### Final Answer
The electrode potential of the gaseous hydrogen electrode dipped in a solution with pH 5.0 relative to the calomel electrode is:
\[ \text{Answer: } -0.575 \, \text{V} \]

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