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Question

In an Ellingham diagram, the slope of the line for the formation of a metal oxide is positive. This indicates that:

Mr. S M HUSSAIN · Accepted Answer

## CORE INFORMATION
✓ **Answer**: A
## CONCEPT FRAMEWORK
 **Primary Concept**: Ellingham diagrams and Gibbs Free Energy
 **Related Topics**: Thermodynamics, Entropy, Enthalpy, Free Energy
 **Prerequisites**: Understanding of Gibbs Free Energy equation and its relation to spontaneity.
## SOLUTION PATHWAY
**Given Information**:
The slope of the line in an Ellingham diagram is positive for the formation of a metal oxide.
**Method & Steps**:
1. Understanding Ellingham Diagrams: Ellingham diagrams plot the standard Gibbs free energy change ($\Delta G^\circ$) for the formation of metal oxides as a function of temperature.  The equation is given by:
	$ \Delta G^\circ = \Delta H^\circ - T\Delta S^\circ $
	where:
		$\Delta G^\circ$ is the standard Gibbs free energy change
		$\Delta H^\circ$ is the standard enthalpy change
		$\Delta S^\circ$ is the standard entropy change
		$T$ is the temperature in Kelvin
2. Interpreting the Slope: The equation above represents a straight line with a slope of $-\Delta S^\circ$ and a y-intercept of $\Delta H^\circ$. A positive slope indicates a negative $\Delta S^\circ$.
3. Conclusion: Since the slope is positive, the entropy change ($\Delta S^\circ$) for the reaction is negative. This means the reaction leads to a decrease in disorder.
	Result: The entropy change for the reaction is negative.
	Verification: A positive slope directly translates to a negative entropy change from the equation of the line.
## OPTION ANALYSIS
A ✓: The entropy change for the reaction is negative.  This is correct, as explained above.
B :x: The reaction becomes less spontaneous at higher temperatures. This is not necessarily true. While a negative entropy change can make a reaction less spontaneous at higher temperatures, it depends on the magnitude of the enthalpy change and the temperature.
 C :x: The free energy change becomes more negative at higher temperatures. This is incorrect. A positive slope indicates that $\Delta G^\circ$ becomes less negative (or more positive) with increasing temperature.
D :x: The enthalpy change for the reaction is positive. The enthalpy change is represented by the y-intercept; a positive slope doesn't determine the sign of the enthalpy change.
## LEARNING AIDS
 **Common Mistakes**:
  1.Confusing the slope with enthalpy change: The slope is related to entropy, not enthalpy.
		How to avoid: Carefully examine the equation for the Gibbs free energy and understand the linear relationship between $\Delta G^\circ$, $\Delta H^\circ$, $\Delta S^\circ$ and T.
  2.Incorrectly interpreting the sign of the slope: A positive slope means a negative entropy change.
		How to avoid: Remember that the slope is $- \Delta S^\circ$.
 **Quick Tips**:
  1.Remember the equation $\Delta G^\circ = \Delta H^\circ - T\Delta S^\circ$ and how it relates to Ellingham diagrams.
  2.Visualize the slope of the line in an Ellingham diagram; a positive slope indicates a negative entropy change.

Mr. S M HUSSAIN · Answer

The correct Option is "The entropy change for the reaction is negative."

Mr. S M HUSSAIN · Answer

The reaction becomes less spontaneous at higher temperatures.

Mr. S M HUSSAIN · Answer

The free energy change becomes more negative at higher temperatures.

Mr. S M HUSSAIN · Answer

The enthalpy change for the reaction is positive.

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