Calculate the cell potential (in V) if `/_\G=-96.5`kJ/mol and `n=1`

Answer

To calculate the cell potential (E_cell) given the change in Gibbs free energy (ΔG) and the number of electrons transferred (n), we can use the following relationship:

\[ \Delta G = -nFE_{cell} \]

Where:
- ΔG is the change in Gibbs free energy (in joules per mole),
- n is the number of moles of electrons transferred,
- F is Faraday's constant (approximately 96500 C/mol),
- E_cell is the cell potential (in volts).

### Step-by-Step Solution:

1. **Convert ΔG from kJ/mol to J/mol**:
\[ \Delta G = -96.5 \text{ kJ/mol} = -96.5 \times 10^3 \text{ J/mol} = -96500 \text{ J/mol} \]

**Hint**: Remember to convert kilojoules to joules by multiplying by 1000.

2. **Identify the values**:
- ΔG = -96500 J/mol
- n = 1 (number of electrons)
- F = 96500 C/mol (Faraday's constant)

3. **Rearrange the formula to solve for E_cell**:
\[ E_{cell} = -\frac{\Delta G}{nF} \]

**Hint**: Make sure to keep track of the negative sign when rearranging the formula.

4. **Substitute the values into the equation**:
\[ E_{cell} = -\frac{-96500 \text{ J/mol}}{1 \times 96500 \text{ C/mol}} \]

5. **Calculate E_cell**:
\[ E_{cell} = \frac{96500}{96500} = 1 \text{ V} \]

**Hint**: When dividing the same numbers, they cancel out, leading to a simple result.

6. **Final Result**:
The cell potential (E_cell) is:
\[ E_{cell} = 1 \text{ V} \]

### Summary of Steps:
- Convert ΔG from kJ to J.
- Identify and substitute values into the rearranged formula.
- Perform the calculation to find E_cell.