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I believe we assume that entropy remains constant because I think we would normally use that equation to find equilibrium constants based on temperature. Also, entropy gets cancelled when you try to find K at two different temperatures if delta H is know
The reason we assume the entropy is constant is not that we think that the entropy is the same value, but that the difference in that entropy between reactants and products is the same at two different temperatures. The entropy may indeed be higher or lower at given temperatures, but the difference still remains the same, which is why we can cancel them out when we prove Van't Hoff's equation by subtracting lnK2 - lnK1.
The change in entropy is constant because the difference in entropy between the reactants and products at 2 different temperatures is the same. The entropy is different at two different temperatures, but for Van't Hoff we are using the net change go entry which is constant.
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