Calculate the standard free energy change for the reaction :
`Zn(s)|Zn^(2+)(1 M)||Cu^(2+)(1 M)|Cu(s)`
Given `E_(cell)^(@)=1.10" V "`.

Explanation

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

\[ \Delta G° = -nFE°_{cell} \]

Where:
- \( n \) = number of moles of electrons transferred in the reaction
- \( F \) = Faraday's constant (approximately \( 96,500 \, C/mol \))
- \( E°_{cell} \) = standard cell potential (given as \( 1.10 \, V \))

### Step-by-Step Solution:

**Step 1: Determine the number of moles of electrons (n)**

For the reaction involving zinc and copper:
- Zinc (Zn) is oxidized from \( Zn(s) \) to \( Zn^{2+} \), which involves the loss of 2 electrons.
- Copper (Cu) is reduced from \( Cu^{2+} \) to \( Cu(s) \), which involves the gain of 2 electrons.

Thus, the total number of moles of electrons transferred (n) is 2.

**Step 2: Use the formula to calculate ΔG°**

Now, substituting the values into the equation:

\[ \Delta G° = -nFE°_{cell} \]

Substituting \( n = 2 \), \( F = 96,500 \, C/mol \), and \( E°_{cell} = 1.10 \, V \):

\[ \Delta G° = -2 \times 96,500 \, C/mol \times 1.10 \, V \]

**Step 3: Calculate ΔG°**

Calculating the right side:

\[ \Delta G° = -2 \times 96,500 \times 1.10 \]

\[ \Delta G° = -2 \times 106150 \, J/mol \]

\[ \Delta G° = -212300 \, J/mol \]

**Step 4: Convert ΔG° to kilojoules**

To convert from joules to kilojoules, divide by 1000:

\[ \Delta G° = -212.3 \, kJ/mol \]

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

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