Which of the following conditions are satisfied when the cell reaction in the electrochemical cell is spontaneous?

Options

A. ΔG° > 0
B. E°cell < 0
C. E°cell =0
D. ΔG° < 0

Answer

To determine the conditions that indicate a spontaneous reaction in an electrochemical cell, we can follow these steps:

### Step 1: Understand the Gibbs Free Energy (ΔG)
For a reaction to be spontaneous, the change in Gibbs free energy (ΔG) must be negative. This means:
\[ \Delta G < 0 \]

### Step 2: Relate ΔG to Cell Potential (E°cell)
In electrochemical cells, the relationship between Gibbs free energy and cell potential is given by the equation:
\[ \Delta G = -nFE°_{cell} \]
Where:
- \( n \) = number of moles of electrons transferred
- \( F \) = Faraday's constant (approximately 96485 C/mol)
- \( E°_{cell} \) = standard cell potential

### Step 3: Analyze the Equation
From the equation, we can deduce that:
- If \( \Delta G < 0 \), then \( -nFE°_{cell} < 0 \)
- This implies that \( E°_{cell} > 0 \)

### Step 4: Evaluate the Options
Now we can evaluate the provided options based on our understanding:
1. **ΔG > 0**: This is incorrect because it indicates a non-spontaneous reaction.
2. **E°cell < 0**: This is also incorrect since a negative cell potential indicates a non-spontaneous reaction.
3. **E°cell = 0**: This indicates a system at equilibrium, which is not spontaneous.
4. **ΔG < 0**: This is correct as it indicates a spontaneous reaction.

### Conclusion
The condition that satisfies a spontaneous reaction in an electrochemical cell is:
\[ \Delta G < 0 \]

Thus, the correct option is **Option 4**.

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