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### Topic: contradiction? equilibrium question  (Read 2888 times)

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#### 21385

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• Mole Snacks: +2/-1 « on: November 18, 2007, 01:06:10 AM »
I don't really get the effects of increasing the temperatures on the equilibrium. Because of le chatelier's principle, the equilibrium of any endothermic reaction will increase if the temperature is increased. However, looking at G=-RTlnK equation, we can see that G can still be negative even if it is endothermic reaction by having a positive entropy change. Thus, if G is negative, negative signs from both sides cancel, and from this equation, we can see that an increase in temperature would actually decrease K. Can anyone explain this to me? Thanks

#### Yggdrasil

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• Gender: • Physical Biochemist « Reply #1 on: November 18, 2007, 01:55:51 AM »
Maybe things will be more clear if we express the equation this way:

K = e^(-ΔG/RT)

So, we want to know how K changes with T.  Specifically, we want to know the sign of dK/dT.  The difficulty is that ΔG also depends on T.  We can write out this explicit dependence on T by writing:

ΔG = ΔH - TΔS

so that

K = e^(-ΔH/RT) e^(ΔS/R)

Assuming that ΔH and ΔS do not depend on temperature

dK/dT = e^(ΔS/R) e^(-ΔH/RT) * ΔH/RT2

Since e^x is always positive and RT2 is always positive, the sign of dK/dT is equal to the sign of ΔH.

#### 21385

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• Mole Snacks: +2/-1 