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When you're solving for k at different temperatures, you're going to be using standard enthalpy and entropy values, so these dont change based on temperature. Thinking back to the first midterm though, we can remember that k does depend on temperature so that's how this concept can be applied to thermochemistry
As the Van't Hoff Equation is used when the temperature is different for a given reaction, the change in enthalpy and entropy for the reaction remains the same as they are independent of temp and therefore t is the only variable that is different in two situations (where t1 is raised or lowered to t2).
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