The standard free energy change of the reaction `Cu^(2+)+Sn(s)rarrCu(s)+Sn^(2+)`
Given : `E^(@)=0.48V`) is:

Options

A. `-31.8KJmol^(-1)`
B. `-62.1KJmol^(-1)`
C. `-79.2KJmol^(-1)`
D. `92.64KJmol^(-1)`

Explanation

To calculate the standard free energy change (ΔG°) for the reaction:

\[ \text{Cu}^{2+} + \text{Sn}(s) \rightarrow \text{Cu}(s) + \text{Sn}^{2+} \]

we can use the following formula:

\[ \Delta G° = -nFE° \]

where:
- \( n \) = number of moles of electrons transferred in the reaction
- \( F \) = Faraday's constant (approximately \( 96500 \, \text{C/mol} \))
- \( E° \) = standard cell potential (given as \( 0.48 \, \text{V} \))

### Step-by-Step Solution:

1. **Identify the number of electrons transferred (n)**:
- In the reaction, copper ions (\( \text{Cu}^{2+} \)) are reduced to copper metal (\( \text{Cu} \)), which involves the gain of 2 electrons.
- The tin (\( \text{Sn} \)) is oxidized from solid to \( \text{Sn}^{2+} \), which also involves the loss of 2 electrons.
- Therefore, \( n = 2 \).

**Hint**: Look for the oxidation states of the reactants and products to determine how many electrons are involved in the reaction.

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

**Hint**: Remember that Faraday's constant is a fundamental constant used in electrochemistry.

3. **Substitute the values into the equation**:
- Now, substitute \( n \), \( F \), and \( E° \) into the ΔG° equation:
\[ \Delta G° = -nFE° = -2 \times 96500 \, \text{C/mol} \times 0.48 \, \text{V} \]

**Hint**: Ensure that the units are consistent when performing the multiplication.

4. **Calculate ΔG°**:
- Performing the calculation:
\[ \Delta G° = -2 \times 96500 \times 0.48 = -92640 \, \text{J/mol} \]

**Hint**: Keep track of significant figures and units during calculations.

5. **Convert to kilojoules**:
- Since the answer is often required in kilojoules, convert joules to kilojoules by dividing by 1000:
\[ \Delta G° = -92640 \, \text{J/mol} \div 1000 = -92.64 \, \text{kJ/mol} \]

**Hint**: Remember to convert units when necessary, especially in thermodynamic calculations.

### Final Answer:
The standard free energy change of the reaction is:
\[ \Delta G° = -92.64 \, \text{kJ/mol} \]