A cell reaction would be spontaneous if the cell potential and `/_\_rG` are respectively:

Options

A. positive and negative
B. negative,negative
C. zero,zero
D. positive,zero

Answer

To determine the conditions under which a cell reaction is spontaneous, we can use the relationship between Gibbs free energy (ΔG) and cell potential (E). Here’s a step-by-step solution:

### Step 1: Understand the Gibbs Free Energy Equation
The Gibbs free energy change (ΔG) for a cell reaction is given by the equation:

\[ \Delta G = -nFE \]

where:
- \( \Delta G \) is the change in Gibbs free energy,
- \( n \) is the number of moles of electrons transferred,
- \( F \) is the Faraday constant (approximately 96485 C/mol),
- \( E \) is the cell potential (voltage).

### Step 2: Analyze the Conditions for Spontaneity
For a reaction to be spontaneous, the change in Gibbs free energy must be negative:

\[ \Delta G < 0 \]

### Step 3: Determine the Implications for E
From the equation \( \Delta G = -nFE \), we can infer that:

- Since \( n \) (number of moles of electrons) and \( F \) (Faraday constant) are both positive values, for \( \Delta G \) to be negative, the product \( -nFE \) must also be negative.
- This implies that \( E \) must be positive:

\[ E > 0 \quad \text{(for spontaneous reactions)} \]

### Step 4: Conclusion
Thus, for a cell reaction to be spontaneous, the cell potential (E) must be positive, and the Gibbs free energy change (ΔG) must be negative. Therefore, the correct answer is:

- Cell potential (E) is positive, and ΔG is negative.

### Final Answer
The correct option is **A: Cell potential is positive and ΔG is negative.**

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