`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 change in standard entropy (ΔS°), we need to analyze the changes in the state of matter involved in each reaction. The general principle is that the entropy of a system increases when it transitions from a more ordered state (solid) to a less ordered state (liquid or gas).

### Step-by-Step Solution:

1. **Identify the States of Matter**:
- Recognize the states of the reactants and products in the given reactions. Common states include solid (s), liquid (l), and gas (g).

2. **Determine the Direction of Change**:
- For each reaction, note whether the reaction involves a transition from solid to liquid, solid to gas, liquid to gas, or the reverse.
- Transitions from solid to gas (s → g) or liquid to gas (l → g) indicate an increase in entropy, while transitions from gas to solid (g → s) or gas to liquid (g → l) indicate a decrease in entropy.

3. **Calculate ΔS°**:
- ΔS° can be calculated as ΔS° = S_final - S_initial.
- If S_final (entropy of products) is greater than S_initial (entropy of reactants), then ΔS° is positive, indicating an increase in entropy.

4. **Compare the Reactions**:
- Analyze each reaction to see which one has the greatest increase in entropy. The reaction with the most significant transition towards a gaseous state or the one with the highest number of moles of gas produced will typically have the highest ΔS°.

5. **Conclusion**:
- After evaluating all reactions, select the one that shows the highest increase in entropy.

### Example Reactions:
- Reaction A: Solid → Liquid (ΔS° is positive but moderate)
- Reaction B: Solid → Gas (ΔS° is significantly positive)
- Reaction C: Liquid → Gas (ΔS° is positive)
- Reaction D: Gas → Solid (ΔS° is negative)

From the above example, Reaction B (Solid → Gas) would have the highest ΔS° because it represents the greatest increase in disorder.