The relation between `DeltaG` and E for a cell is `DeltaG`=-nFE, the cel reaction will be spontaneous if

Options

A. G is negative
B. G is positive
C. E is negative
D. E is positive

Explanation

To determine the conditions under which a cell reaction will be spontaneous, we can analyze the relationship between Gibbs free energy change (ΔG) and the cell potential (E) using the equation:

\[ \Delta G = -nFE \]

where:
- ΔG = change in Gibbs free energy
- n = number of moles of electrons transferred in the reaction
- F = Faraday's constant (approximately 96500 C/mol)
- E = cell potential (voltage)

### Step-by-Step Solution:

1. **Understanding the Equation**: The equation states that the change in Gibbs free energy (ΔG) is equal to the negative product of the number of moles of electrons (n), Faraday's constant (F), and the cell potential (E).

2. **Condition for Spontaneity**: A reaction is spontaneous when the change in Gibbs free energy (ΔG) is less than zero:
\[ \Delta G < 0 \]

3. **Rearranging the Equation**: From the equation ΔG = -nFE, we can infer:
\[ -nFE < 0 \]
This implies that:
\[ nFE > 0 \]

4. **Analyzing the Components**:
- The number of moles of electrons (n) is always a positive integer.
- Faraday's constant (F) is a positive constant (approximately 96500 C/mol).
- Therefore, for the product \( nF \) to be positive, the cell potential (E) must also be positive.

5. **Conclusion**: Thus, for the cell reaction to be spontaneous, the cell potential (E) must be greater than zero:
\[ E > 0 \]

### Final Answer:
The cell reaction will be spontaneous if:
\[ E > 0 \]