The cell reaction as written is spontaneous if the cell potential is:

Options

A. Positive
B. Negative
C. Zero
D. Infinite

Explanation

To determine if a cell reaction is spontaneous, we can analyze the relationship between the cell potential (E_cell) and the Gibbs free energy change (ΔG). Here’s a step-by-step solution:

### Step 1: Understand the relationship between ΔG and E_cell
The Gibbs free energy change (ΔG) for a reaction is related to the cell potential (E_cell) by the equation:
\[ \Delta G = -nFE_{cell} \]
where:
- ΔG = Gibbs free energy change
- n = number of moles of electrons transferred in the reaction
- F = Faraday's constant (approximately 96485 C/mol)
- E_cell = cell potential

### Step 2: Determine the condition for spontaneity
A reaction is spontaneous if the change in Gibbs free energy (ΔG) is negative:
\[ \Delta G < 0 \]
From the equation, if E_cell is positive, then ΔG will be negative, indicating that the reaction is spontaneous.

### Step 3: Analyze the implications of E_cell
If E_cell is:
- **Positive**: ΔG will be negative (spontaneous reaction).
- **Zero**: ΔG will be zero (reaction is at equilibrium, not spontaneous).
- **Negative**: ΔG will be positive (non-spontaneous reaction).

### Step 4: Conclusion
For the cell reaction to be spontaneous, the cell potential (E_cell) must be positive.

Thus, the correct answer is that the cell reaction is spontaneous if the cell potential is **positive**.