Question

Is a reaction that is exothermic and becomes more positionally random spontaneous or non spontaneous? What about less positionally random? Is there enough information to tell?

Answer 1

See this answer for the endothermic case.

For the exothermic case, the change in enthalpy `DeltaH < 0`, and if the reaction becomes more "positionally random", then the change in entropy `DeltaS > 0` since there is more motion.

Therefore, the Gibbs' free energy is:

`color(blue)(DeltaG) = DeltaH - TDeltaS`

`= (-) - (+)(+)`

`= (-) - (+)`

`= color(blue)((-))`

which if you recall, is negative for a spontaneous reaction.

So, an exothermic reaction with increased motion (more "positional randomness") is spontaneous at all temperatures.

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Less "positionally random" implies less motion and thus `DeltaS < 0`. I think you are at the point where you can guess what the sign of `DeltaG` would conditionally be (hint: it's analogous to having `DeltaH > 0` and `DeltaS > 0`; how would the magnitude of `T` affect the sign of `DeltaG`?).