Dissolution of ammonium chloride in water is an endothermic reaction, yet it is a spontaneous process. This is due to the fact that

Options

A. `DeltaH" is "+ve, DeltaS" is "-ve`
B. `DeltaH" is "-ve, DeltaS" is "+ve`
C. `DeltaH" is "+ve, DeltaS" is "+ve and DeltaH lt TDeltaS`
D. `DeltaH" is "+ve and DeltaH gt T DeltaS`

Explanation

To solve the question regarding the dissolution of ammonium chloride in water being an endothermic yet spontaneous process, we can follow these steps:

### Step 1: Understand the Nature of the Reaction
The dissolution of ammonium chloride (NH4Cl) in water is an endothermic reaction. This means that the reaction absorbs heat from the surroundings, which results in a decrease in temperature of the solution.

**Hint**: Recall that endothermic reactions absorb heat, leading to a cooling effect.

### Step 2: Relate to Gibbs Free Energy
We can use the Gibbs free energy equation to analyze the spontaneity of the reaction:
\[ \Delta G = \Delta H - T \Delta S \]
where:
- \( \Delta G \) = change in Gibbs free energy
- \( \Delta H \) = change in enthalpy
- \( T \) = temperature in Kelvin
- \( \Delta S \) = change in entropy

**Hint**: Remember that for a reaction to be spontaneous, \( \Delta G \) must be negative.

### Step 3: Analyze the Sign of \( \Delta H \)
Since the dissolution of ammonium chloride is endothermic, we know that:
- \( \Delta H \) is positive.

**Hint**: Identify that a positive \( \Delta H \) indicates heat is absorbed.

### Step 4: Determine the Conditions for Spontaneity
For the reaction to be spontaneous despite \( \Delta H \) being positive, we need to consider the term \( -T \Delta S \):
- For \( \Delta G \) to be negative, \( T \Delta S \) must be greater than \( \Delta H \) in magnitude.

This means:
\[ T \Delta S > \Delta H \]

**Hint**: Think about how increasing temperature or a positive entropy change can help make the reaction spontaneous.

### Step 5: Analyze the Change in Entropy
For the dissolution of ammonium chloride, the process increases the disorder of the system (more particles in solution), which means:
- \( \Delta S \) is positive.

**Hint**: Remember that dissolving a solid in a liquid typically increases entropy.

### Step 6: Conclusion
Given that:
- \( \Delta H \) is positive,
- \( \Delta S \) is positive,
- and for spontaneity, \( T \Delta S \) must be greater than \( \Delta H \),

We conclude that the dissolution of ammonium chloride is spontaneous because the increase in entropy (disorder) is sufficient to overcome the positive enthalpy change.

**Final Answer**: The correct option is that the dissolution is spontaneous because \( \Delta H \) is positive, \( \Delta S \) is positive, and the magnitude of \( T \Delta S \) is greater than \( \Delta H \).