Which one of the following options is correct for the spontaneity of the reaction?

Options

A. `DeltaG="positive (+Ve), "DeltaH="positive (+Ve)"`
B. `DeltaH="positive (+Ve), "DeltaS="negative (-Ve)"`
C. `DeltaG="negative (-Ve), "DeltaS="negative (-Ve)"`
D. `DeltaG="negative (-Ve), "DeltaS="positive (+Ve)"`

Answer

To determine the spontaneity of a reaction, we can use the Gibbs free energy change (ΔG). The spontaneity of a reaction is assessed based on the sign of ΔG:

1. **Understanding ΔG**:
- If ΔG < 0: The reaction is spontaneous.
- If ΔG = 0: The reaction is at equilibrium.
- If ΔG > 0: The reaction is non-spontaneous.

2. **Using the Gibbs Free Energy Equation**:
The relationship between ΔG, ΔH (enthalpy change), and ΔS (entropy change) is given by the equation:
\[ ΔG = ΔH - TΔS \]
where T is the temperature in Kelvin.

3. **Analyzing the Equation**:
To have ΔG < 0 (spontaneous reaction), we can rearrange the equation:
\[ ΔH - TΔS < 0 \]
This implies:
\[ ΔH < TΔS \]

4. **Considering Different Scenarios**:
- If ΔS > 0 (entropy increases), then for ΔG to be negative, ΔH can be either negative or positive, depending on the temperature.
- If ΔS < 0 (entropy decreases), then ΔH must be negative to ensure ΔG is negative, which may not always be the case.

5. **Conclusion**:
For a reaction to be spontaneous (ΔG < 0), we can conclude:
- If ΔS is positive, ΔH can be either positive or negative, but if ΔS is negative, ΔH must be negative for ΔG to be negative.
- Therefore, the correct condition for spontaneity can be summarized as: ΔG < 0 and ΔH > 0.

Based on this analysis, the correct option regarding the spontaneity of the reaction is:
**Option 4: ΔG < 0 and ΔH > 0**.