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 free energy change in joules,
- $n$ is the number of moles of electrons transferred in the balanced equation for the cell reaction,
- $F$ is Faraday's constant ($96485 \, \text{C/mol}$),
- $E$ is the EMF of the cell in volts.

For the given cell reaction:

$$
Cd|CdCl_{2}.5H_{2}O \, (saturated) || AgCl(s)|Ag
$$

The cell involves the following half-reactions:

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 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, $\Delta G \approx -135.1 \, \text{kJ/mol}$.

Therefore, the correct answer is Option 2: $-135.1 \, \text{kJ}$.

**Explanation for Incorrect Options:**

1. **Option 1: 135.1 kJ** - This option is incorrect because it suggests a positive free energy change, which would imply a non-spontaneous reaction. However, since the EMF is positive, the reaction is spontaneous, and the free energy change must be negative.

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 should be approximately 135.1 kJ, not 67.55 kJ.

4. **Option 4: -67.55 kJ** - This option is incorrect because, although it has the correct sign (negative), the magnitude is incorrect. The correct calculation shows that the magnitude of the free energy change is approximately 135.1 kJ, not 67.55 kJ.

In conclusion, Option 2 is the correct answer as it accurately reflects the negative free energy change calculated from the given EMF of the cell.