Cell reactiomn is spontaneous when

Options

A. `E_"red"^@` is negative
B. `DeltaG^@` is negative
C. `E_"oxide"^@` is positive
D. `DeltaG^@` is positive

Answer

To determine when a cell reaction is spontaneous, we can analyze the relationship between Gibbs free energy (ΔG°) and the standard electrode potential (E°cell). Here’s a step-by-step solution:

### Step 1: Understand the Relationship
The relationship between Gibbs free energy and the standard electrode potential is given by the equation:
\[ \Delta G° = -nFE°_{cell} \]
where:
- \( \Delta G° \) = Gibbs free energy change
- \( n \) = number of moles of electrons exchanged
- \( F \) = Faraday's constant (approximately 96485 C/mol)
- \( E°_{cell} \) = standard electrode potential of the cell

### Step 2: Determine Conditions for Spontaneity
For a reaction to be spontaneous, the Gibbs free energy change must be negative:
\[ \Delta G° < 0 \]
From the equation, if \( \Delta G° < 0 \), then:
\[ -nFE°_{cell} < 0 \]
This implies that:
\[ E°_{cell} > 0 \]
Thus, for a cell reaction to be spontaneous, both conditions must be satisfied:
1. \( \Delta G° < 0 \)
2. \( E°_{cell} > 0 \)

### Step 3: Analyze the Given Options
Now, let’s evaluate the options provided in the question:
- **Option A:** \( E°_{reduction} \) is negative - This is incorrect because the reduction potential does not directly determine spontaneity.
- **Option B:** \( \Delta G° \) is negative - This is correct as we established that for spontaneity, \( \Delta G° \) must be negative.
- **Option C:** \( E°_{oxidation} \) is positive - This is incorrect as the oxidation potential alone does not determine spontaneity.
- **Option D:** \( \Delta G° \) is positive - This is incorrect because a positive \( \Delta G° \) indicates a non-spontaneous reaction.

### Conclusion
The correct answer is:
**Option B: \( \Delta G° \) is negative.**