(I moved this into Energy Change in Reactions since the varying KK or kk value is coupled with varying temperatures, and molecules move at different speeds at different temperatures, and so are differently energetic. Thus, DeltaT is proportional to DeltaE.)
There's a useful equation we can use.
ln((K_(p2))/(K_(p1))) = -(DeltaH_R)/R[1/(T_2) - 1/(T_1)]
and its variation:
ln((K_(c1))/(K_(c2))) = -(DeltaH_R)/R[1/(T_2) - 1/(T_1)]
where R = 8.314472*10^(-3) (kJ)/(mol*K) and DeltaH_R is the enthalpy of reaction.
You may also have seen another variation with kinetics:
ln((k_2)/(k_1)) = -(E_a)/R[1/(T_2) - 1/(T_1)]
which is very similar, and just contains the rate constants k_i and the activation energy E_a, and everything else is the same. Anyways:
You can use both values of K (or k), both values of T, and R to solve for DeltaH_R. If the result is negative, the reaction is exothermic, and vice versa.
You should have seen something like this plot before, which is represented by the above first or second equation (lnK vs. 1/T):
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This is derived from the Van't Hoff Equation, (dlnK)/(dT) = (DeltaH)/(RT^2), if you were curious. Just multiply over dT and integrate the function from T_1 to T_2. This works well as long as the temperature range is small enough such that DeltaH varies linearly with temperature in that range.
