`E_("cell")^(@)` and `DeltaG^(0)` are related as:

Options

A. `DeltaG^(0) = nFE_("cell")^(@)`
B. `DeltaG^(0) = -nFE_("cell")^(@)`
C. `DeltaG^(0)=-nFE_("cell")^(@)`
D. `DeltaG^(0)=mFE_("cell")^(@)`

Explanation

To solve the question regarding the relationship between standard cell potential (E°cell) and standard Gibbs free energy change (ΔG°), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Relationship**: The relationship between standard Gibbs free energy change (ΔG°) and standard cell potential (E°cell) is given by the equation:
\[ \Delta G^\circ = -nFE^\circ_{\text{cell}} \]
where:
- ΔG° = standard Gibbs free energy change
- n = number of moles of electrons transferred in the redox reaction
- F = Faraday's constant (approximately 96,485 C/mol)
- E°cell = standard cell potential (or standard electromotive force)

2. **Identify the Variables**: In the equation, identify the components:
- ΔG° is the energy available to do work at standard conditions.
- E°cell represents the potential difference that drives the electrochemical reaction.

3. **Analyze the Options**: The question provides multiple options regarding the relationship. We need to find the one that correctly represents the equation derived above.

4. **Select the Correct Option**: Based on our understanding of the relationship:
- The correct expression is:
\[ \Delta G^\circ = -nFE^\circ_{\text{cell}} \]
- Therefore, if option 2 states this relationship, it is the correct choice.

### Conclusion:
The correct answer is option 2, which states:
\[ \Delta G^\circ = -nFE^\circ_{\text{cell}} \]