What will be the reduction potential of a hydrogen electrode which is filled with HCl solution of pH value 1.0? (at 298 Kelvin)

Options

A. `(-59.15V)`
B. `(+59.15)`
C. `(+59.15mV)`
D. `(-59.15mV)`

Explanation

To determine the reduction potential of a hydrogen electrode filled with an HCl solution of pH 1.0 at 298 K, we can follow these steps:

### Step 1: Understand the Reaction
The reduction reaction for the hydrogen electrode can be represented as:
\[ \text{2H}^+ + 2e^- \rightarrow \text{H}_2(g) \]
This indicates that two protons (H⁺ ions) gain two electrons to form hydrogen gas.

### Step 2: Use the Nernst Equation
The Nernst equation relates the reduction potential (E) to the standard reduction potential (E°) and the concentrations of the reactants and products:
\[ E = E^\circ - \frac{0.05915}{n} \log Q \]
Where:
- \( E \) = reduction potential
- \( E^\circ \) = standard reduction potential (0 V for the hydrogen electrode)
- \( n \) = number of moles of electrons transferred (2 for this reaction)
- \( Q \) = reaction quotient

### Step 3: Determine the Concentration of H⁺
Given that the pH of the solution is 1.0, we can find the concentration of H⁺ ions:
\[ \text{pH} = -\log[\text{H}^+] \]
\[ [\text{H}^+] = 10^{-\text{pH}} = 10^{-1} = 0.1 \, \text{M} \]

### Step 4: Calculate the Reaction Quotient (Q)
For the hydrogen electrode, the reaction quotient \( Q \) is given by:
\[ Q = \frac{1}{[\text{H}^+]^2} \]
Substituting the concentration of H⁺:
\[ Q = \frac{1}{(0.1)^2} = \frac{1}{0.01} = 100 \]

### Step 5: Substitute Values into the Nernst Equation
Now we can substitute the values into the Nernst equation:
\[ E = 0 - \frac{0.05915}{2} \log(100) \]
Since \( \log(100) = 2 \):
\[ E = -\frac{0.05915}{2} \times 2 \]
\[ E = -0.05915 \, \text{V} \]

### Step 6: Convert to Millivolts
To express the potential in millivolts:
\[ E = -0.05915 \, \text{V} \times 1000 \, \text{mV/V} = -59.15 \, \text{mV} \]

### Final Answer
The reduction potential of the hydrogen electrode filled with HCl solution of pH 1.0 at 298 K is:
\[ \boxed{-59.15 \, \text{mV}} \]

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