What is the potential of a half-cell consisting of zinc electrode in `0.01m ZnSO_4` solution at `25^(@) C (E^(@) = 0.763 V)`

Options

A. 0.8221 V
B. 8.221 V
C. 0.5282 V
D. 9.232 V

Explanation

To find the potential of a half-cell consisting of a zinc electrode in a 0.01 M ZnSO₄ solution at 25°C, we will use the Nernst equation. The Nernst equation relates the cell potential to the standard electrode potential and the concentrations of the reactants and products.

### Step 1: Write the half-reaction for the zinc electrode.
The half-reaction for the dissolution of zinc is:
\[ \text{Zn (s)} \rightleftharpoons \text{Zn}^{2+} (aq) + 2e^- \]

### Step 2: Identify the standard electrode potential (E°).
The standard electrode potential for the zinc half-cell is given as:
\[ E^\circ = 0.763 \, \text{V} \]

### Step 3: Write the Nernst equation.
The Nernst equation is given by:
\[ E = E^\circ - \frac{0.059}{n} \log \frac{[\text{Zn}^{2+}]}{[\text{Zn}]} \]
Where:
- \( E \) is the cell potential.
- \( E^\circ \) is the standard electrode potential.
- \( n \) is the number of moles of electrons transferred (which is 2 for zinc).
- \([\text{Zn}^{2+}]\) is the concentration of zinc ions.
- \([\text{Zn}]\) is the activity of solid zinc, which is taken as 1.

### Step 4: Substitute the known values into the Nernst equation.
Given that the concentration of Zn²⁺ is 0.01 M, we can substitute the values:
\[ E = 0.763 \, \text{V} - \frac{0.059}{2} \log \frac{0.01}{1} \]

### Step 5: Calculate the logarithm.
Calculate the logarithm:
\[ \log(0.01) = -2 \]

### Step 6: Substitute the logarithm back into the equation.
Now substitute this value back into the Nernst equation:
\[ E = 0.763 \, \text{V} - \frac{0.059}{2} \times (-2) \]
\[ E = 0.763 \, \text{V} + 0.059 \]

### Step 7: Perform the final calculation.
Now, calculate the final value:
\[ E = 0.763 + 0.059 = 0.822 \, \text{V} \]

### Final Answer:
The potential of the half-cell consisting of a zinc electrode in a 0.01 M ZnSO₄ solution at 25°C is approximately:
\[ E \approx 0.822 \, \text{V} \]

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