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Is increase of entropy the criterion for...

Is increase of entropy the criterion for spontaneity ? Why ?

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No. For the spontaneity of the reaction `DeltaG` must be negative. Even though entropy does not increase if the `DeltaH` is more negative than `TDeltaS` in the equation `DeltaG = DeltaH - TDeltaS, DeltaG` becomes negative and the reaction becomes spontaneous.
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