Which of the followig statements about the spontaneous reaction occurring in a galvanic cell is always true?

Options

A. `E_(cell)^(@)lt0,triangleG^(@)0` and `QltK`
B. `E_(cell)^(@)gt0,triangleG^(@)lt0`, and `QgtK`
C. `E_(cell)^(@)gt0,triangleG^(@)gt0` and `QgtK`
D. `E_(cell)gt0,triangleGlt0` and `QltK`

Explanation

To determine which statement about spontaneous reactions in a galvanic cell is always true, we need to understand the relationship between Gibbs free energy (ΔG), cell potential (E_cell), and the spontaneity of reactions.

### Step-by-Step Solution:

1. **Understanding Spontaneity**:
- A spontaneous reaction is one that occurs without needing to be driven by an external force. In thermodynamics, spontaneity is often indicated by the sign of Gibbs free energy (ΔG).

2. **Gibbs Free Energy and Spontaneity**:
- For a reaction to be spontaneous, ΔG must be negative (ΔG < 0). This indicates that the reaction can proceed in the forward direction without additional energy input.

3. **Relationship Between ΔG and E_cell**:
- The relationship between Gibbs free energy and the electromotive force (EMF) of a galvanic cell is given by the equation:
\[ ΔG = -nFE_{cell} \]
- Here, n is the number of moles of electrons transferred, F is Faraday's constant, and E_cell is the cell potential.

4. **Analyzing the Equation**:
- From the equation, if ΔG is negative (indicating a spontaneous reaction), then E_cell must be positive (E_cell > 0). This means that for a spontaneous reaction in a galvanic cell, the cell potential must always be positive.

5. **Equilibrium Constant**:
- Additionally, the relationship between the equilibrium constant (K) and the cell potential can also be considered. A positive E_cell corresponds to an equilibrium constant K that is greater than 1, indicating that the products are favored at equilibrium.

6. **Conclusion**:
- Therefore, the statement that is always true for spontaneous reactions occurring in a galvanic cell is: **E_cell is positive**.

### Final Answer:
The statement that is always true about the spontaneous reaction occurring in a galvanic cell is that **E_cell is positive**.