For a spontaneous reaction, `DeltaG,` equilibrium constant (K) and `E_(cell)^(@)` will be respectively:

Options

A. `-ve, gt 1, +ve`
B. `+ve, gt 1, -ve`
C. `-ve, lt 1, -ve`
D. `-ve, gt 1, -ve`

Answer

To determine the relationship between Gibbs free energy change (ΔG), the equilibrium constant (K), and the standard cell potential (E°_cell) for a spontaneous reaction, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Spontaneous Reactions**:
- A spontaneous reaction is one that occurs without needing to be driven by an external force. For a reaction to be spontaneous, the change in Gibbs free energy (ΔG) must be negative (ΔG < 0).

2. **Relationship Between ΔG and E°_cell**:
- The relationship between Gibbs free energy change and the standard cell potential is given by the equation:
\[ \Delta G = -nFE^\circ_{\text{cell}} \]
- Here, n is the number of moles of electrons transferred, F is Faraday's constant, and E°_cell is the standard cell potential.
- Since ΔG is negative for spontaneous reactions, it follows that E°_cell must be positive (E°_cell > 0) because a negative ΔG implies that the product of -nF and E°_cell is negative.

3. **Relationship Between ΔG and Equilibrium Constant (K)**:
- The relationship between ΔG and the equilibrium constant K is given by the equation:
\[ \Delta G = \Delta G^\circ + RT \ln K \]
- At equilibrium, ΔG = 0, which leads to:
\[ 0 = \Delta G^\circ + RT \ln K \]
- Rearranging gives:
\[ \Delta G^\circ = -RT \ln K \]
- For a spontaneous reaction, ΔG° is negative, which means that K must be greater than 1 (K > 1) because the natural logarithm of a number greater than 1 is positive, making the product -RT ln K negative.

4. **Summarizing the Relationships**:
- From the above relationships, we conclude:
- ΔG < 0 (negative)
- E°_cell > 0 (positive)
- K > 1 (greater than one)

### Final Answer:
For a spontaneous reaction:
- ΔG: Negative
- K: Greater than one
- E°_cell: Positive