The standard electrode potential for Daniel cell is `1.1V`. Calculate the standard Gibbs energy of the reaction (In KJ/mol)
`Zn_((s))+Cu_((aq))^(2+)rarrZn_((aq))^(2+)+Cu_((s))`

Options

A. `106.15`
B. `212.3`
C. `193`
D. `403`

Explanation

To calculate the standard Gibbs energy (ΔG°) for the reaction given the standard electrode potential (E°) of the Daniel cell, we can use the following formula:

\[ \Delta G^\circ = -nFE^\circ_{\text{cell}} \]

Where:
- \( \Delta G^\circ \) = standard Gibbs energy (in joules per mole)
- \( n \) = number of moles of electrons transferred in the balanced equation
- \( F \) = Faraday's constant (approximately \( 96500 \, C/mol \))
- \( E^\circ_{\text{cell}} \) = standard electrode potential (in volts)

### Step-by-step Solution:

1. **Identify the number of electrons transferred (n)**:
In the reaction:
\[ \text{Zn}_{(s)} + \text{Cu}^{2+}_{(aq)} \rightarrow \text{Zn}^{2+}_{(aq)} + \text{Cu}_{(s)} \]
Zinc (Zn) is oxidized from 0 to +2, losing 2 electrons, while copper (Cu²⁺) is reduced from +2 to 0, gaining 2 electrons. Therefore, \( n = 2 \).

**Hint**: Look for the oxidation and reduction half-reactions to determine the number of electrons transferred.

2. **Use Faraday's constant (F)**:
The value of Faraday's constant is \( F = 96500 \, C/mol \).

**Hint**: Remember that Faraday's constant represents the charge of one mole of electrons.

3. **Substitute the values into the Gibbs energy equation**:
Given \( E^\circ_{\text{cell}} = 1.1 \, V \):
\[ \Delta G^\circ = -nFE^\circ_{\text{cell}} = -2 \times 96500 \, C/mol \times 1.1 \, V \]

4. **Calculate ΔG°**:
\[ \Delta G^\circ = -2 \times 96500 \times 1.1 = -212300 \, J/mol \]

5. **Convert to kilojoules**:
Since \( 1 \, kJ = 1000 \, J \):
\[ \Delta G^\circ = -212300 \, J/mol \div 1000 = -212.3 \, kJ/mol \]

### Final Answer:
\[ \Delta G^\circ = -212.3 \, kJ/mol \]

### Summary of Steps:
1. Identify the number of electrons transferred (n).
2. Use the value of Faraday's constant (F).
3. Substitute values into the Gibbs energy equation.
4. Perform the calculation to find ΔG° in joules.
5. Convert the result to kilojoules.