Calculate the standard free energy change in kJ for the reaction `Cu^(+) +I^(-) to CuI` Given:
'CuI + e to 'Cu+I^(-)" "E^(0)=-0.17V`
`Cu^(+)+e to Cu" "E^(0)=0.53V`

Options

A. `-67.55`
B. 135.1
C. 1.78V
D. `-1.75V`

Explanation

To calculate the standard free energy change (ΔG°) for the reaction \( \text{Cu}^+ + \text{I}^- \rightarrow \text{CuI} \), we will follow these steps:

### Step 1: Write the half-reactions
We have two half-reactions given:
1. \( \text{Cu}^+ + e^- \rightarrow \text{Cu} \) with \( E^\circ = 0.53 \, \text{V} \)
2. \( \text{CuI} + e^- \rightarrow \text{Cu}^+ + \text{I}^- \) with \( E^\circ = -0.17 \, \text{V} \)

### Step 2: Reverse the second half-reaction
Since we need to form \( \text{CuI} \) from \( \text{Cu}^+ \) and \( \text{I}^- \), we reverse the second half-reaction:
\[ \text{Cu}^+ + \text{I}^- \rightarrow \text{CuI} + e^- \]
The potential for the reversed reaction becomes \( E^\circ = +0.17 \, \text{V} \).

### Step 3: Combine the half-reactions
Now we can combine the two half-reactions:
1. \( \text{Cu}^+ + e^- \rightarrow \text{Cu} \) (from the first half-reaction)
2. \( \text{Cu}^+ + \text{I}^- \rightarrow \text{CuI} + e^- \) (reversed second half-reaction)

The overall reaction is:
\[ \text{Cu}^+ + \text{I}^- \rightarrow \text{CuI} \]

### Step 4: Calculate the standard cell potential (E°cell)
The standard cell potential is calculated by adding the potentials of the half-reactions:
\[ E^\circ_{\text{cell}} = E^\circ_{\text{reduction}} + E^\circ_{\text{oxidation}} \]
\[ E^\circ_{\text{cell}} = 0.53 \, \text{V} + 0.17 \, \text{V} = 0.70 \, \text{V} \]

### Step 5: Calculate the standard free energy change (ΔG°)
The relationship between standard free energy change and cell potential is given by:
\[ \Delta G^\circ = -nFE^\circ_{\text{cell}} \]
Where:
- \( n \) = number of moles of electrons transferred (1 for this reaction)
- \( F \) = Faraday's constant \( \approx 96500 \, \text{C/mol} \)
- \( E^\circ_{\text{cell}} = 0.70 \, \text{V} \)

Substituting the values:
\[ \Delta G^\circ = -1 \times 96500 \, \text{C/mol} \times 0.70 \, \text{V} \]
\[ \Delta G^\circ = -67550 \, \text{J/mol} \]

### Step 6: Convert to kJ
To convert joules to kilojoules:
\[ \Delta G^\circ = -67.55 \, \text{kJ/mol} \]

### Final Answer
Thus, the standard free energy change for the reaction \( \text{Cu}^+ + \text{I}^- \rightarrow \text{CuI} \) is:
\[ \Delta G^\circ = -67.55 \, \text{kJ/mol} \]