Predict which of the following reactions have positive entropy changes.
`(a)` `NH_(3(g))+HCl_((g))rarrNH_(4)Cl_((s))`
`(b)` `Cu_((aq))^(+2)+S_((aq))^(-2)rarrCuS_((s))`
`(c )` `NH_(2)COONH_(4(s))rarr2NH_(3(g))+CO_(2(g))`
`(d)` Condensation of water

Options

A. `b` and `c`
B. `c` and `d`
C. `c`
D. `a`

Explanation

To determine which of the given reactions have positive entropy changes, we need to analyze each reaction based on the states of the reactants and products. Entropy (S) is a measure of disorder or randomness in a system. Generally, gases have higher entropy than liquids, and liquids have higher entropy than solids.

Let's analyze each reaction step by step:

### Reaction (a):
**NH₃(g) + HCl(g) → NH₄Cl(s)**

1. **Reactants**: Both NH₃ and HCl are in the gaseous state.
2. **Products**: NH₄Cl is in the solid state.
3. **Entropy Change**: The reaction goes from 2 moles of gas to 1 mole of solid. Since gases have higher entropy than solids, the entropy decreases.
- **Conclusion**: This reaction has a negative entropy change.

### Reaction (b):
**Cu²⁺(aq) + S²⁻(aq) → CuS(s)**

1. **Reactants**: Cu²⁺ and S²⁻ are both in the aqueous state.
2. **Products**: CuS is in the solid state.
3. **Entropy Change**: The reaction goes from 2 moles of ions in solution (higher entropy) to 1 mole of solid (lower entropy). Thus, the entropy decreases.
- **Conclusion**: This reaction also has a negative entropy change.

### Reaction (c):
**NH₂COONH₄(s) → 2NH₃(g) + CO₂(g)**

1. **Reactants**: NH₂COONH₄ is in the solid state.
2. **Products**: 2 moles of NH₃ and 1 mole of CO₂ are in the gaseous state.
3. **Entropy Change**: The reaction goes from 1 mole of solid to 3 moles of gas. Since gases have much higher entropy than solids, the entropy increases significantly.
- **Conclusion**: This reaction has a positive entropy change.

### Reaction (d):
**Condensation of water**

1. **Reactants**: Water vapor (gas).
2. **Products**: Liquid water.
3. **Entropy Change**: The reaction goes from gas to liquid. Since gas has higher entropy than liquid, the entropy decreases.
- **Conclusion**: This process has a negative entropy change.

### Summary of Entropy Changes:
- (a) Negative
- (b) Negative
- (c) Positive
- (d) Negative

### Final Answer:
The reaction with a positive entropy change is **(c) NH₂COONH₄(s) → 2NH₃(g) + CO₂(g)**.

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