In the extraction of chlorine from brine_________

Options

A. `DeltaG^(ө)` for the overall reaction is negative
B. `DeltaG^(ө)` for the overall reaction is positive
C. `E^(ө)` for the overall reaction has negative value
D. `E^(ө)` for the overall reaction has positive value

Explanation

**Step-by-Step Solution:**

1. **Identify the Reaction:**
The reaction for the extraction of chlorine from brine can be written as:
\[ 2 \text{Cl}^- + 2 \text{H}_2\text{O} \rightarrow 2 \text{OH}^- + \text{H}_2 + \text{Cl}_2 \]

2. **Determine the Gibbs Free Energy Change (ΔG°):**
For the given reaction, the standard Gibbs free energy change (ΔG°) is provided as +422 kJ. A positive ΔG° indicates that the reaction is non-spontaneous under standard conditions.

3. **Evaluate the EMF of the Cell (E°):**
The relationship between Gibbs free energy change and cell potential (E°) is given by the equation:
\[ \Delta G° = -nFE° \]
Here, \( n \) is the number of moles of electrons transferred, and \( F \) is Faraday's constant (approximately 96485 C/mol).

For this reaction, \( n \) is 2 (since 2 moles of electrons are involved). Therefore, we can rearrange the equation to solve for E°:
\[ E° = -\frac{\Delta G°}{nF} \]
Substituting the values:
\[ E° = -\frac{422 \times 10^3 \text{ J}}{2 \times 96485 \text{ C/mol}} \approx -2.2 \text{ V} \]

4. **Interpret the Results:**
- Since ΔG° is positive (+422 kJ), it indicates that the overall reaction is non-spontaneous.
- The calculated E° is negative (-2.2 V), which confirms that the reaction does not favor the formation of products under standard conditions.

5. **Select the Correct Options:**
Based on the analysis:
- The second option states that ΔG° for the overall reaction is positive, which is correct.
- The third option states that E° for the overall reaction has a negative value, which is also correct.

Thus, the correct answers to the question are the second and third options.

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