`DeltaG^(Ө)` vs T plot in Ellingham diagram slopes downward for the reaction .

Options

A. `Mg + (1)/(2) O_(2) rarr MgO`
B. `2Ag + (1)/(2) O_(2) rarr Ag_(2) O`
C. `C + (1)/(2) O_(2) rarr CO`
D. `CO + (1)/(2) O_(2) rarr CO_(2)`

Explanation

To determine which reaction corresponds to a downward slope in the ΔG° vs T plot in the Ellingham diagram, we need to analyze the relationship between Gibbs free energy (ΔG), enthalpy (ΔH), and entropy (ΔS).

### Step-by-Step Solution:

1. **Understand the Gibbs Free Energy Equation**:
The Gibbs free energy change at standard conditions is given by the equation:
\[ \Delta G° = \Delta H° - T \Delta S° \]
Here, ΔG° is the Gibbs free energy change, ΔH° is the enthalpy change, T is the temperature in Kelvin, and ΔS° is the entropy change.

2. **Identify the Effect of Entropy on the Slope**:
- If ΔS° is positive, as temperature (T) increases, the term \(T \Delta S°\) becomes larger, which makes ΔG° decrease. This results in a downward slope in the ΔG° vs T plot.
- Conversely, if ΔS° is negative, the slope will be upward since increasing T will make ΔG° increase.

3. **Analyze the Given Reactions**:
- **Reaction 1**: \( \text{Mg (s)} + \frac{1}{2} \text{O}_2 (g) \rightarrow \text{MgO (s)} \)
- Here, a solid and a gas produce a solid. The entropy decreases (ΔS° < 0).
- **Reaction 2**: \( \text{Ag (s)} + \frac{1}{2} \text{O}_2 (g) \rightarrow \text{Ag}_2\text{O (s)} \)
- Similar to Reaction 1, this also results in a decrease in entropy (ΔS° < 0).
- **Reaction 3**: \( \text{C (s)} + \frac{1}{2} \text{O}_2 (g) \rightarrow \text{CO (g)} \)
- Here, a solid and a gas produce a gas. The entropy increases (ΔS° > 0).
- **Reaction 4**: \( \text{CO (g)} + \frac{1}{2} \text{O}_2 (g) \rightarrow \text{CO}_2 (g) \)
- This reaction has gaseous reactants producing a gaseous product, but the number of moles decreases (ΔS° < 0).

4. **Determine the Reaction with Positive Entropy Change**:
From the analysis, only **Reaction 3** (C + 1/2 O2 → CO) shows an increase in entropy (ΔS° > 0). Therefore, this reaction will have a downward slope in the ΔG° vs T plot.

### Conclusion:
The reaction that corresponds to a downward slope in the ΔG° vs T plot in the Ellingham diagram is:
\[ \text{C (s)} + \frac{1}{2} \text{O}_2 (g) \rightarrow \text{CO (g)} \]