Which is correct for spontaneity of an electrochemical cell ?

Options

A. `DeltaG^0=-ve, E^0=0`
B. `DeltaG^0=+ve,E^0=+ve`
C. `DeltaG^0=0,E^0=0`
D. `DeltaG^0=-ve,E^0=+ve`

Answer

To determine the spontaneity of an electrochemical cell, we need to analyze the relationship between the standard cell potential (E°) and the Gibbs free energy change (ΔG°). Here’s a step-by-step solution:

### Step 1: Understand the relationship between E° and ΔG°
The spontaneity of an electrochemical cell can be assessed using the equation:
\[ \Delta G° = -nFE° \]
where:
- \( \Delta G° \) is the change in Gibbs free energy,
- \( n \) is the number of moles of electrons transferred,
- \( F \) is Faraday's constant (approximately 96485 C/mol),
- \( E° \) is the standard cell potential.

### Step 2: Analyze the condition for spontaneity
For a reaction to be spontaneous:
- \( \Delta G° \) must be negative.

From the equation, for \( \Delta G° \) to be negative:
\[ -nFE° < 0 \]
This implies that:
\[ E° > 0 \]
Thus, the standard cell potential (E°) must be positive for the electrochemical cell to be spontaneous.

### Step 3: Conclusion
Therefore, the conditions for spontaneity of an electrochemical cell are:
1. The standard cell potential \( E° \) must be positive.
2. The Gibbs free energy change \( \Delta G° \) must be negative.

### Final Answer
The correct option regarding the spontaneity of an electrochemical cell is:
- **Option 4: ΔG° Negative, E° Positive.**

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