Why Does S(gas) > S(liquid) > S(solid) in Benzene?

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The discussion focuses on the relationship between Gibbs free energy and entropy in benzene across its solid, liquid, and gas phases. It highlights that the Gibbs free energy decreases with temperature, with distinct linear segments for each phase. The formula (dG/dT)P = −S is used to demonstrate that the entropy of gas is greater than that of liquid, which in turn is greater than that of solid. Participants express confusion about how to visualize this relationship and suggest using graphs and tangent lines to analyze slopes. The key takeaway is that the increasing slope magnitudes indicate higher entropy in gaseous states compared to liquid and solid states.
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Homework Statement



The Gibbs free energy of benzene decreases continuously with temperature (at fixed pressure) and shows three nearly linear segments corresponding to the solid, liquid and gas phases. The magnitude of the slopes increases as one moves from solid to liquid, and liquid to gas.
Use the formula (dG/dT)P = −S to show that S(gas) > S(liquid) > S(solid).

Homework Equations



(dG/dT)_P = −S

The Attempt at a Solution


I have no idea where to begin sadly =\... I made a graph of G vs T, but i don't think that helps much.
 
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Draw tangent lines in the solid, liquid, and gas regions. Are the slopes positive or negative, and how do the magnitudes compare?
 

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