For which of these reactions will there be `Delta S` positive?

Options

A. `H_(2)O(g) rightarrow H_(2)O(l)`
B. `H_(2)(g) + I_(2)(g) rightarrow 2HI(g)`
C. `CaCO_(3) (s) rightarrow CaO(s) + CO_(2)(g) `
D. `N_(2)(g) + 3H_(2)(g) rightarrow 2NH_(3)(g)`

Answer

To determine for which of the given reactions the change in entropy (ΔS) is positive, we need to analyze the change in the number of gaseous moles (Δng) during the reactions. The change in entropy is directly related to the randomness of the system, and more gaseous moles typically indicate a higher degree of randomness.

### Step-by-Step Solution:

1. **Understand the Concept of ΔS**:
- ΔS is positive when there is an increase in randomness or disorder in the system. This usually occurs when the number of gaseous moles increases in a reaction.

2. **Identify the Reactions**:
- List the reactions provided in the question. For this example, we will assume four reactions for analysis.

3. **Calculate Δng for Each Reaction**:
- **Reaction 1**: Gas → Liquid
- Gaseous moles in products = 0
- Gaseous moles in reactants = 1
- Δng = 0 - 1 = -1 (ΔS is negative)

- **Reaction 2**: 2H2(g) → 1O2(g)
- Gaseous moles in products = 1
- Gaseous moles in reactants = 2
- Δng = 1 - 2 = -1 (ΔS is negative)

- **Reaction 3**: Solid + CO2(g) → Gas
- Gaseous moles in products = 1
- Gaseous moles in reactants = 0
- Δng = 1 - 0 = +1 (ΔS is positive)

- **Reaction 4**: 2A(g) + 3B(g) → 2C(g)
- Gaseous moles in products = 2
- Gaseous moles in reactants = 2 + 3 = 5
- Δng = 2 - 5 = -3 (ΔS is negative)

4. **Determine Which Reaction Has Positive ΔS**:
- From the calculations:
- Reaction 1: ΔS = negative
- Reaction 2: ΔS = negative
- Reaction 3: ΔS = positive (this is the reaction we are looking for)
- Reaction 4: ΔS = negative

5. **Conclusion**:
- The reaction for which ΔS is positive is **Reaction 3**.