The change in Gibbs free energy of the system along provides a criterion for the spontaneity of a process at constant temperature and pressure. A change in the free energy of a sytem at constant temperature and pressure will be: `DeltaG_("system") = DeltaH_("system") - T DeltaS_("system")`
For a spontaneous reaction `DeltaG`, equilibrium constant K and `E_("cell")^(0)` 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 the change in Gibbs free energy (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 Gibbs Free Energy (ΔG)**:
- For a process to be spontaneous at constant temperature and pressure, the change in Gibbs free energy (ΔG) must be negative.
- Mathematically, this is expressed as:
\[ \Delta G < 0 \]
- This indicates that the system is releasing free energy, which means it can proceed without the need for additional energy input.

2. **Equilibrium Constant (K)**:
- The equilibrium constant (K) is defined as the ratio of the concentration of products to the concentration of reactants at equilibrium.
- For a spontaneous reaction, the concentration of products must be greater than that of reactants, which implies:
\[ K > 1 \]
- This indicates that the formation of products is favored over the reactants at equilibrium.

3. **Standard Cell Potential (E°cell)**:
- The relationship between Gibbs free energy and the standard cell potential is given by the equation:
\[ \Delta G = -nFE°cell \]
- Where:
- \( n \) = number of moles of electrons transferred
- \( F \) = Faraday's constant
- For a spontaneous reaction, ΔG must be negative, which implies:
\[ E°cell > 0 \]
- This means that the standard cell potential must be positive for the reaction to be spontaneous.

### Summary of Relationships:
- For a spontaneous reaction:
- \( \Delta G < 0 \)
- \( K > 1 \)
- \( E°cell > 0 \)

### Final Answer:
Thus, for a spontaneous reaction, the relationships can be summarized as:
- ΔG is negative,
- K is greater than 1,
- E°cell is positive.