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The second law states that the total entropy of an isolated system always increases. At the same time we talk about how if total entropy is negative, the reaction is not spontaneous or if it's zero, the rxn is at equilibrium. How are these two scenarios possible in the light of the second law, stating that the entropy can only increase?
The second law does not mean that entropy always increases, but that entropy can never decrease. If total entropy is negative, the reaction is not spontaneous as you said. This means the reverse reaction is spontaneous so the total entropy increases. When the reaction is at equilibrium, the entropy is zero so it does not decrease.
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