The EMF of the cell $Cd|CdCl_{2}.5H_{2}O$ (saturated) || $AgCl(s)$ | 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. The formula is:

$$
\Delta G = -nFE
$$

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

For the given cell reaction, 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:
- $E = 0.7 \, \text{V}$

Substituting these values into the formula:

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

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

Rounding to one decimal place, $\Delta G \approx -135.1 \, \text{kJ/mol}$.

Thus, the free energy change for the cell is $-135.1 \, \text{kJ/mol}$, which corresponds to Option 2: $-135.1 \, \text{kJ}$.

**Explanation for Other Options:**

1. **Option 1: 135.1 kJ** - This option is incorrect because it suggests a positive free energy change. A positive $\Delta G$ would imply that the reaction is non-spontaneous, which contradicts the fact that the cell has a positive EMF, indicating a spontaneous reaction.

3. **Option 3: 67.55 kJ** - This option is incorrect because it not only suggests a positive free energy change but also an incorrect magnitude. The calculation clearly shows that the magnitude of $\Delta G$ is much larger.

4. **Option 4: -67.55 kJ** - This option is incorrect because, although it correctly indicates a negative free energy change, the magnitude is incorrect. The calculation shows that the correct magnitude is approximately $-135.1 \, \text{kJ/mol}$.

In conclusion, Option 2 is the correct answer as it accurately reflects the calculated free energy change for the given cell reaction.