`Delta S^(@)` will be highest for the reaction

Options

A. `Ca + 1/2 O_(2)(g) rightarrow CaO(s)`
B. `CaCO_(3)(s) rightarrow CaO(s) + CO_(2)(g)`
C. `C(s) + O_(2)(g) rightarrow CO_(2)(g)`
D. `N_(2)(g) + O_(2)(g) rightarrow 2NO(g)`

Answer

To determine which reaction has the highest standard entropy change (ΔS°), we will analyze each of the given reactions based on the states of matter involved (solid, liquid, gas) and how they change from reactants to products.

### Step-by-Step Solution:

1. **Understanding Entropy Change (ΔS°)**:
- ΔS° is defined as the change in entropy from the initial state (reactants) to the final state (products).
- The formula is:
\[ \Delta S° = S_{\text{products}} - S_{\text{reactants}} \]

2. **Analyzing the States of Matter**:
- Entropy increases with the state of matter in the following order:
\[ S_{\text{solid}} < S_{\text{liquid}} < S_{\text{gas}} \]
- Gases have the highest entropy due to greater molecular motion and space between particles.

3. **Evaluating Each Reaction**:
- **Option A**:
\[ \text{Ca (s)} + \frac{1}{2} \text{O}_2 (g) \rightarrow \text{CaO (s)} \]
- Reactants: 1 solid + 1 gas → Products: 1 solid
- Here, a gas is converting to a solid, which results in a decrease in entropy (ΔS° < 0).

- **Option B**:
\[ \text{CaCO}_3 (s) \rightarrow \text{CaO (s)} + \text{CO}_2 (g) \]
- Reactants: 1 solid → Products: 1 solid + 1 gas
- Here, a solid is converting to a solid and a gas, which results in an increase in entropy (ΔS° > 0).

- **Option C**:
\[ \text{C (s)} + \text{O}_2 (g) \rightarrow \text{CO}_2 (g) \]
- Reactants: 1 solid + 1 gas → Products: 1 gas
- Here, there is a transition from solid and gas to gas, which may result in a slight increase in entropy, but not significant.

- **Option D**:
\[ \text{N}_2 (g) + \text{O}_2 (g) \rightarrow 2 \text{NO (g)} \]
- Reactants: 1 gas + 1 gas → Products: 2 gases
- The number of moles of gas is the same on both sides, leading to no significant change in entropy (ΔS° ≈ 0).

4. **Conclusion**:
- Among all options, **Option B** shows the most significant increase in entropy because it involves the formation of a gas from a solid. Therefore, ΔS° will be highest for Option B.

### Final Answer:
**Option B**: \(\text{CaCO}_3 (s) \rightarrow \text{CaO (s)} + \text{CO}_2 (g)\)

---