For which reaction among the following, is `DeltaS` maximum ?

Options

A. `Ca(s) + 1/2 O_2(g) to CaO (s)`
B. `CaCO_3 (s) to CaO (s) + CO_2(g)`
C. `C(s) + O_29g) to CO_2(g)`
D. `N_2(g) + O_2(g) to 2NO(g)`

Explanation

To determine which reaction has the maximum change in entropy (ΔS), we need to analyze the changes in the number of gaseous moles (ΔNG) for each reaction. The change in entropy is generally associated with the increase in randomness or disorder of a system, which is greater when there are more gaseous molecules produced in a reaction.

### Step-by-Step Solution:

1. **Identify the Reactions:**
- Reaction 1: Ca(s) + 1/2 O2(g) → CaO(s)
- Reaction 2: CaCO3(s) → CaO(s) + CO2(g)
- Reaction 3: C(s) + O2(g) → CO2(g)
- Reaction 4: N2(g) + O2(g) → 2 NO(g)

2. **Calculate ΔNG for Each Reaction:**
- **Reaction 1:**
- Reactants: 0 moles of gas (Ca(s) + 1/2 O2(g) = 0 + 0.5 = 0.5)
- Products: 0 moles of gas (CaO(s) = 0)
- ΔNG = Products - Reactants = 0 - 0.5 = -0.5 (decrease in gas moles)

- **Reaction 2:**
- Reactants: 0 moles of gas (CaCO3(s) = 0)
- Products: 1 mole of gas (CO2(g) = 1)
- ΔNG = 1 - 0 = 1 (increase in gas moles)

- **Reaction 3:**
- Reactants: 1 mole of gas (O2(g) = 1)
- Products: 1 mole of gas (CO2(g) = 1)
- ΔNG = 1 - 1 = 0 (no change in gas moles)

- **Reaction 4:**
- Reactants: 2 moles of gas (N2(g) + O2(g) = 1 + 1 = 2)
- Products: 2 moles of gas (2 NO(g) = 2)
- ΔNG = 2 - 2 = 0 (no change in gas moles)

3. **Compare ΔNG Values:**
- Reaction 1: ΔNG = -0.5
- Reaction 2: ΔNG = 1
- Reaction 3: ΔNG = 0
- Reaction 4: ΔNG = 0

4. **Determine Maximum ΔS:**
- The reaction with the highest ΔNG (which corresponds to the maximum increase in entropy, ΔS) is Reaction 2, where calcium carbonate decomposes into calcium oxide and carbon dioxide gas.

### Conclusion:
The reaction for which ΔS is maximum is:
**Reaction 2: CaCO3(s) → CaO(s) + CO2(g)**