Calculate standard free energy change for the reaction `1/2 Cu(s) +1/2 Cl_(2) (g), 1/2 Cu^(2+) + Cl^(-)` taking place at `25^(@)` C in a cell whose standard e.m.f. is volts

Options

A. `-98430 J`
B. `98430 J`
C. `96500 J`
D. `-49215` J

Explanation

To calculate the standard free energy change (ΔG°) for the given electrochemical reaction at 25°C, we can use the following formula:

\[ \Delta G° = -nFE° \]

Where:
- \( \Delta G° \) = standard free energy change (in joules)
- \( n \) = number of moles of electrons transferred in the reaction
- \( F \) = Faraday's constant (approximately \( 96500 \, C/mol \))
- \( E° \) = standard electromotive force (emf) of the cell (in volts)

### Step-by-Step Solution:

1. **Identify the Reaction**:
The reaction given is:
\[ \frac{1}{2} \text{Cu}(s) + \frac{1}{2} \text{Cl}_2(g) \rightarrow \frac{1}{2} \text{Cu}^{2+} + \text{Cl}^- \]

2. **Determine the Number of Electrons Transferred (n)**:
In this reaction, copper (Cu) is being oxidized from Cu(s) to Cu²⁺, which involves the transfer of 2 electrons. Therefore, \( n = 1 \) (since we are considering half the reaction).

3. **Use the Given Standard EMF (E°)**:
The standard emf of the cell is given as \( E° = 1.02 \, V \).

4. **Substitute Values into the Formula**:
Now we can substitute the values into the formula:
\[ \Delta G° = -nFE° \]
\[ \Delta G° = - (1) (96500 \, C/mol) (1.02 \, V) \]

5. **Calculate ΔG°**:
\[ \Delta G° = - (96500) (1.02) \]
\[ \Delta G° = -98310 \, J/mol \]

6. **Convert to kJ/mol**:
Since free energy is often expressed in kJ/mol, we convert:
\[ \Delta G° = -98.31 \, kJ/mol \]

### Final Answer:
The standard free energy change for the reaction is:
\[ \Delta G° = -98.31 \, kJ/mol \]