The EMF of the cell $Cd|CdCl_{2}.5H_{2}O$ (saturated) || $AgCl|Ag$ is 0.7 Volt at $25^{\circ}C$ The free energy change for it, is:

Question

Accepted Answer

To determine the free energy change ($\Delta G$) for the given electrochemical cell, we use the relationship between the electromotive force (EMF) of the cell and the free energy change, given by the equation:

$$
\Delta G = -nFE
$$

where:
- $\Delta G$ is the change in free energy,
- $n$ is the number of moles of electrons transferred in the reaction,
- $F$ is Faraday's constant ($96485 \, \text{C/mol}$),
- $E$ is the EMF of the cell.

For the cell reaction involving cadmium and silver chloride, the half-reactions are:

1. $ \text{Cd} \rightarrow \text{Cd}^{2+} + 2e^- $
2. $ \text{AgCl} + e^- \rightarrow \text{Ag} + \text{Cl}^- $

The overall cell reaction involves the transfer of 2 moles of electrons ($n = 2$).

Given:
- EMF ($E$) = 0.7 V

Substituting the values into the equation:

$$
\Delta G = -2 \times 96485 \, \text{C/mol} \times 0.7 \, \text{V}
$$

$$
\Delta G = -135079 \, \text{J/mol} = -135.079 \, \text{kJ/mol}
$$

Rounding to three significant figures, we get $-135.1 \, \text{kJ/mol}$.

Thus, the free energy change for the cell is $-135.1 \, \text{kJ/mol}$, which corresponds to Option 4.

### Explanation for Other Options:

1. **Option 1: 67.55 kJ**
   - This option is incorrect because it suggests a positive free energy change, which is not consistent with the spontaneous nature of the cell reaction. The calculation clearly shows a negative value.

2. **Option 2: -67.55 kJ**
   - This option is incorrect because it underestimates the magnitude of the free energy change. The calculation shows that the correct magnitude is approximately $-135.1 \, \text{kJ/mol}$.

3. **Option 3: 135.1 kJ**
   - This option is incorrect because it suggests a positive free energy change, which contradicts the spontaneous nature of the cell reaction. The correct value is negative, as calculated.

In conclusion, the correct answer is Option 4, $-135.1 \, \text{kJ/mol}$, as it accurately reflects the calculated free energy change for the given cell reaction.