For which reaction change of entropy be positive ?

Options

A. `H_2(g)+I(g)hArr2HI(g)`
B. `MgO(s)+H_2(g)hArrMg(g)+H_2O(l)`
C. `NH_4NO_3(s)hArrN_2O(g)+2H_2O(g)`
D. `HCl(g)+NH_3(g)hArrNH_4Cl(s)`

Answer

To determine for which reaction the change of entropy (ΔS) is positive, we need to analyze the states of the reactants and products involved in each reaction. Entropy is a measure of the disorder or randomness in a system, and it generally increases when a system transitions from a more ordered state (solid) to a less ordered state (liquid or gas).

### Step-by-Step Solution:

1. **Understand the States of Matter**:
- Solids have the lowest entropy due to their ordered structure.
- Liquids have higher entropy than solids because they have more freedom of movement.
- Gases have the highest entropy because the molecules are far apart and can move freely.

2. **Identify the Reactions**:
- We need to evaluate the given reactions to see which ones involve a transition from a solid to a liquid or gas, or from a liquid to a gas.

3. **Analyze Each Reaction**:
- **Reaction 1**: Gas → Gas
- The entropy change is likely negligible since both reactants and products are gases.
- **Reaction 2**: Solid + Gas → Gas + Liquid
- Here, a solid is converting to a liquid and a gas. The entropy increases due to the formation of a liquid from a solid.
- **Reaction 3**: Solid → Gas + Gas (e.g., NH4NO3 → N2O + 2H2O)
- This reaction involves a solid converting into two moles of gas. The entropy increases significantly because we are moving from a solid (low entropy) to gases (high entropy).
- **Reaction 4**: Solid → Liquid
- This reaction also results in an increase in entropy, but not as much as the third reaction.

4. **Determine the Reaction with Maximum Positive Entropy Change**:
- Among the analyzed reactions, the third reaction shows the most significant increase in entropy as it converts one mole of solid into two moles of gas, leading to a substantial increase in randomness.

5. **Conclusion**:
- The reaction with the most positive change in entropy is the third reaction, where a solid converts into two gaseous products.

### Final Answer:
The reaction for which the change of entropy (ΔS) is positive is the third reaction (solid → gas + gas).