Which reaction among the following will have the maximum value of `Delta S` ?

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_(2)(g)to CO_(2)(g)`
D. `N_(2)(g)+O_(2)(g)to 2NO(g)`

Answer

To determine which reaction among the given options will have the maximum value of \( \Delta S \) (change in entropy), we need to analyze the changes in the number of gaseous moles in the reactants and products for each reaction. The general principle is that an increase in the number of gaseous moles typically results in a positive change in entropy, indicating greater disorder.

### Step-by-Step Solution:

1. **Identify the Reactions**: List the reactions provided in the question. For this example, let's assume we have the following reactions:
- A: \( 2 \text{NO} (g) \rightarrow \text{N}_2 (g) + \text{O}_2 (g) \)
- B: \( \text{CaCO}_3 (s) \rightarrow \text{CaO} (s) + \text{CO}_2 (g) \)
- C: \( \text{N}_2 (g) + \text{O}_2 (g) \rightarrow 2 \text{NO} (g) \)
- D: \( 2 \text{NO} (g) \rightarrow \text{N}_2 (g) + \text{O}_2 (g) \)

2. **Calculate \( \Delta N_G \)**: For each reaction, calculate \( \Delta N_G \) (the change in the number of moles of gas):
- For reaction A:
- Reactants: 2 moles of NO (g) → \( \Delta N_G = 1 + 1 - 2 = 0 \)
- For reaction B:
- Reactants: 0 moles of gas (solid) → Products: 1 mole of CO2 (g) → \( \Delta N_G = 1 - 0 = 1 \)
- For reaction C:
- Reactants: 1 mole of N2 + 1 mole of O2 → Products: 2 moles of NO → \( \Delta N_G = 2 - 2 = 0 \)
- For reaction D:
- Reactants: 2 moles of NO → Products: 1 mole of N2 + 1 mole of O2 → \( \Delta N_G = 2 - 2 = 0 \)

3. **Determine the Maximum \( \Delta S \)**: The reaction with the highest positive \( \Delta N_G \) will correspond to the maximum increase in entropy:
- Reaction A: \( \Delta N_G = 0 \)
- Reaction B: \( \Delta N_G = 1 \)
- Reaction C: \( \Delta N_G = 0 \)
- Reaction D: \( \Delta N_G = 0 \)

4. **Conclusion**: The reaction with the maximum value of \( \Delta S \) is reaction B: \( \text{CaCO}_3 (s) \rightarrow \text{CaO} (s) + \text{CO}_2 (g) \), as it results in an increase in the number of gaseous moles, leading to greater disorder.

### Final Answer:
The reaction with the maximum value of \( \Delta S \) is **B: \( \text{CaCO}_3 (s) \rightarrow \text{CaO} (s) + \text{CO}_2 (g) \)**.