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So essentially, the Van't Hoff Equation is used to calculate the equilibrium constant at different temperatures. The equation assumes a constant delta So and a constant delta Ho, as these standard values should not change based upon a temperature change. Thus, given K1 at temperature T1, you can use the Van't Hoff Equation to calculate K2 at any temperature T2 for a reaction. I hope that clarifies things!
I think that the best way to know when to use the Van't Hoff Equation is when you are given 2 equilibrium reactions at two different temperatures. It is part of the thermodynamics chapter and can be found on page 42 in the course reader.
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