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You would use this equation when you are trying to find out how a K value would change if you increased the temperature of a reaction (you would need to be given another K value at a lower or higher temp which is why there is K1/K2 and T1/T2).
It would be used in a situation where you are trying to find a K value at a different temperature. For instance, on test 2, we were given the K value at one temp and we were asked to find the K value at a different temperature since the K value changes with temperature. In that situation, we would have to use the Van't Hoff equation.
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