Equilibrium constants vary with temperature
المؤلف:
Jonathan Clayden , Nick Greeves , Stuart Warren
المصدر:
ORGANIC CHEMISTRY
الجزء والصفحة:
ص248
2025-05-17
512
We have said (p. 245) that the equilibrium constant is a constant only as long as the temperature does not change. We can work out exactly how the equilibrium constant varies with temperature by putting our two all-important equations ΔG = –RTlnK and ΔG = ΔH – TΔS together to make
–RTlnK = ΔH – TΔS
If we divide throughout by –RT we have

This equation separates the equilibrium constant K into enthalpy and entropy terms, but it is the enthalpy term that determines how K varies with temperature. Plotting ln K against 1/T would give us a straight line with slope –ΔH/R and intercept ΔS/R. Since T (the temperature in kelvin) is always positive, whether the slope is positive or negative depends on the sign of ΔH: if ΔH is negative then, as temperature increases, ln K (and hence K) increases. In other words, if the reaction is exothermic (that is, gives out heat) then at higher temperatures the equilibrium constant will be smaller. For an endothermic reaction, as the temperature is increased, the equilibrium constant increases.
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