In Elingham diagrams of `DeltaG` de formation Vs T, which of the following graphs has negative slope?

Options

A. `CtoCO`
B. `FetoFe_2O_3`
C. `MgtoMgO`
D. All of these

Answer

To solve the question regarding which graph in the Ellingham diagram has a negative slope, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Ellingham Diagram**: The Ellingham diagram plots the Gibbs free energy change (ΔG) of a reaction against temperature (T). The slope of the line in this diagram is related to the entropy change (ΔS) of the reaction.

2. **Recall the Gibbs Free Energy Equation**: The relationship between Gibbs free energy, enthalpy, and entropy 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, and ΔS is the entropy change.

3. **Identify the Relationship of Slope**: From the equation, we can see that if ΔS is negative, as temperature (T) increases, the term \( -T \Delta S \) becomes less negative, which means ΔG becomes more negative. Thus, the slope of the graph (ΔG vs. T) will be negative when ΔS is negative.

4. **Analyze the Given Options**:
- **Option 1**: Formation of CO from C (C + 1/2 O2 → CO)
- In this reaction, the entropy change (ΔS) is negative because a solid (carbon) is converting into a gas (carbon monoxide), leading to a decrease in the number of gas molecules.
- Therefore, the slope is negative.
- **Option 2 and 3**: Formation of metal oxides.
- In these cases, the formation of metal oxides typically involves an increase in the number of gas molecules, leading to a positive ΔS.
- Thus, the slopes for these options will be positive.

5. **Conclusion**: Based on the analysis, the only option that results in a negative slope in the Ellingham diagram is **Option 1**, which is the formation of CO from C.

### Final Answer:
The graph that has a negative slope in the Ellingham diagram is the formation of CO from C (Option 1).