Which of the following pairs of a chemical reaction is certain to result in a spontaneous reaction ?

Options

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

Explanation

To determine which pair of a chemical reaction is certain to result in a spontaneous reaction, we can use the Gibbs free energy equation:

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

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

A reaction is spontaneous when \(\Delta G < 0\).

Let's analyze each option step by step:

### Step 1: Analyze Option A - Exothermic and Decreasing Disorder
- **Exothermic**: \(\Delta H < 0\) (negative)
- **Decreasing Disorder**: \(\Delta S < 0\) (negative)

Using the Gibbs free energy equation:
\[ \Delta G = \Delta H - T \Delta S \]
Substituting the values:
\[ \Delta G = (-) - T(-) = -\Delta H + T\Delta S \]
Both terms are negative, but since \(\Delta S\) is negative, as temperature increases, \(\Delta G\) can become positive. Thus, this reaction is non-spontaneous at high temperatures.

**Conclusion**: Option A is incorrect.

### Step 2: Analyze Option B - Endothermic and Increasing Disorder
- **Endothermic**: \(\Delta H > 0\) (positive)
- **Increasing Disorder**: \(\Delta S > 0\) (positive)

Using the Gibbs free energy equation:
\[ \Delta G = \Delta H - T \Delta S \]
Substituting the values:
\[ \Delta G = (+) - T(+) \]
At low temperatures, \(\Delta G\) can be negative, but at high temperatures, it will be positive. Thus, this reaction is non-spontaneous at high temperatures.

**Conclusion**: Option B is incorrect.

### Step 3: Analyze Option C - Exothermic and Increasing Disorder
- **Exothermic**: \(\Delta H < 0\) (negative)
- **Increasing Disorder**: \(\Delta S > 0\) (positive)

Using the Gibbs free energy equation:
\[ \Delta G = \Delta H - T \Delta S \]
Substituting the values:
\[ \Delta G = (-) - T(+) \]
Here, \(\Delta G\) will always be negative regardless of the temperature. Thus, this reaction is spontaneous at all temperatures.

**Conclusion**: Option C is correct.

### Step 4: Analyze Option D - Endothermic and Decreasing Disorder
- **Endothermic**: \(\Delta H > 0\) (positive)
- **Decreasing Disorder**: \(\Delta S < 0\) (negative)

Using the Gibbs free energy equation:
\[ \Delta G = \Delta H - T \Delta S \]
Substituting the values:
\[ \Delta G = (+) - T(-) = \Delta H + T\Delta S \]
Both terms are positive, and thus \(\Delta G\) will always be positive. This reaction is non-spontaneous at all temperatures.

**Conclusion**: Option D is incorrect.

### Final Answer:
The correct choice for the question is **Option C: Exothermic and Increasing Disorder**.

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