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 equation:

\[ \Delta G = \Delta H - T \Delta S \]

Where:
- \(\Delta G\) = Gibbs free energy change
- \(\Delta H\) = Change in enthalpy
- \(T\) = Temperature in Kelvin
- \(\Delta S\) = Change in entropy

### Step-by-Step Solution:

1. **Understanding Spontaneity**:
- A reaction is spontaneous if it occurs without needing to be driven by an external force. This is indicated by a negative Gibbs free energy change (\(\Delta G < 0\)).

2. **Setting Up the Gibbs Free Energy Equation**:
- We start with the equation:
\[ \Delta G = \Delta H - T \Delta S \]

3. **Analyzing the Conditions for Spontaneity**:
- For \(\Delta G\) to be negative, we can rearrange the equation:
\[ \Delta H - T \Delta S < 0 \]
- This can be rewritten as:
\[ \Delta H < T \Delta S \]

4. **Considering the Signs of \(\Delta H\) and \(\Delta S\)**:
- If \(\Delta S\) (entropy change) is positive, it suggests that the disorder of the system is increasing. This is favorable for spontaneity.
- If \(\Delta H\) (enthalpy change) is negative, it indicates that the reaction is exothermic, which also favors spontaneity.

5. **Conclusion**:
- For a reaction to be spontaneous:
- \(\Delta H\) should be negative (exothermic reaction).
- \(\Delta S\) should be positive (increase in entropy).
- Therefore, we conclude that for a spontaneous reaction, both conditions must be satisfied.

### Final Answer:
- The correct conditions for spontaneity of a reaction are:
- \(\Delta H < 0\) (negative)
- \(\Delta S > 0\) (positive)