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. 1.78
D. `-1.75`

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 down the given half-reactions and their standard electrode potentials (E°).

1. \( \text{CuI} + e^- \rightarrow \text{Cu}^+ + \text{I}^- \) (E° = -0.17 V)
2. \( \text{Cu}^+ + e^- \rightarrow \text{Cu} \) (E° = 0.53 V)

### Step 2: Reverse the first half-reaction.

Since the desired reaction has \( \text{CuI} \) as a product, we need to reverse the first half-reaction. When we reverse a half-reaction, we also change the sign of its standard potential.

Reversed Reaction:
\[ \text{Cu}^+ + \text{I}^- \rightarrow \text{CuI} + e^- \]
E° becomes +0.17 V.

### Step 3: Add the two half-reactions.

Now we will add the reversed first half-reaction to the second half-reaction:

1. \( \text{Cu}^+ + \text{I}^- \rightarrow \text{CuI} + e^- \) (E° = +0.17 V)
2. \( \text{Cu}^+ + e^- \rightarrow \text{Cu} \) (E° = 0.53 V)

Adding these two reactions:
- The electrons cancel out:
\[ \text{Cu}^+ + \text{I}^- \rightarrow \text{CuI} \]

### Step 4: Calculate the overall standard electrode potential (E°).

The overall standard potential (E°) for the combined reaction is:
\[ E° = 0.17 + 0.53 = 0.70 \, \text{V} \]

### Step 5: Use the formula for standard free energy change (ΔG°).

The relationship between standard free energy change and standard electrode potential is given by:
\[ \Delta G° = -nFE° \]
Where:
- \( n \) = number of moles of electrons transferred (1 mole in this case)
- \( F \) = Faraday's constant (approximately 96500 C/mol)
- \( E° \) = standard electrode potential (0.70 V)

### Step 6: Substitute the values into the equation.

Substituting the values:
\[ \Delta G° = -1 \times 96500 \, \text{C/mol} \times 0.70 \, \text{V} \]
\[ \Delta G° = -1 \times 96500 \times 0.70 \]
\[ \Delta G° = -67,550 \, \text{J} \]

### Step 7: Convert to kilojoules.

To convert joules to kilojoules:
\[ \Delta G° = -67.55 \, \text{kJ} \]

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