In which of the following conditions, a reaction will definitely be spontaneous:

Options

A. Exothermic and increasing disorder
B. Exothermic and decreasing disorder
C. Endothermic and increasing disorder
D. Endothermic and decreasing disorder

Answer

To determine the conditions under which a reaction will definitely be spontaneous, we need to analyze the Gibbs free energy change (ΔG) for the reaction. A reaction is spontaneous if ΔG is negative (ΔG < 0). The relationship between ΔG, enthalpy change (ΔH), and entropy change (ΔS) is given by the equation:

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

Where:
- ΔG = change in Gibbs free energy
- ΔH = change in enthalpy
- T = temperature in Kelvin
- ΔS = change in entropy

### Step-by-Step Solution:

1. **Understand the Conditions for Spontaneity**:
- For a reaction to be spontaneous, ΔG must be negative (ΔG < 0).

2. **Analyze the First Option**:
- **Exothermic Reaction (ΔH < 0) and Increasing Disorder (ΔS > 0)**:
- Here, ΔH is negative and ΔS is positive.
- Substituting into the equation:
\[ \Delta G = \text{(negative)} - T \times \text{(positive)} \]
- This will result in ΔG being negative, hence the reaction is spontaneous.

3. **Analyze the Second Option**:
- **Exothermic Reaction (ΔH < 0) and Decreasing Disorder (ΔS < 0)**:
- Here, ΔH is negative and ΔS is negative.
- Substituting into the equation:
\[ \Delta G = \text{(negative)} - T \times \text{(negative)} \]
- This results in ΔG being positive, hence the reaction is non-spontaneous.

4. **Analyze the Third Option**:
- **Endothermic Reaction (ΔH > 0) and Increasing Disorder (ΔS > 0)**:
- Here, ΔH is positive and ΔS is positive.
- Substituting into the equation:
\[ \Delta G = \text{(positive)} - T \times \text{(positive)} \]
- Depending on the values of ΔH and TΔS, ΔG could be negative or positive, hence we cannot conclude spontaneity.

5. **Analyze the Fourth Option**:
- **Endothermic Reaction (ΔH > 0) and Decreasing Disorder (ΔS < 0)**:
- Here, ΔH is positive and ΔS is negative.
- Substituting into the equation:
\[ \Delta G = \text{(positive)} - T \times \text{(negative)} \]
- This results in ΔG being positive, hence the reaction is non-spontaneous.

### Conclusion:
The only condition that guarantees spontaneity is the first option: **Exothermic Reaction (ΔH < 0) and Increasing Disorder (ΔS > 0)**.

### Final Answer:
**Option 1: Exothermic and Increasing Disorder.**

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