Error!?!? Challenging problem. See if you can solve

[SonhosDaVida]

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For this question, I thought that dG = dH - TdS.

So for endothermic reactions, the dH has to be positive, and if it is spontaneous, the dG has to be negative.

Then dS has to be positive in order to have a negative TdS value and for a chance for dG to be negative. So why in this problem is the dS stated to be positive?

 

[Lawpy]

You're right and the answer listed is wrong. If ΔS is negative, that would mean TΔS is negative (because T > 0). Since ΔG = ΔH - TΔS, a negative TΔS value would mean subtracting a negative, resulting in ΔG > 0.

For an endothermic spontaneous reaction, ΔH > 0 and ΔG < 0. This happens when:

ΔG = ΔH - TΔS < 0 -->
ΔH < TΔS

Since ΔH > 0, TΔS has to be positive and larger than ΔH.