difficult question about Le Chat's principle

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flyingwarthog

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Le chatilier's principle says that increasing the temperature of an endothermic reaction will drive the reaction forward and increase the equilibrium constant. well thats great but i'm confused about this...

we know that the equilibrium constant is derived from the rate law. for example, for the reaction A+B->C+D, the equilibrium expression comes from the fact that

rate forward reaction = rate reverse reaction
k(forward)*[A](B) = k(reverse)*[C][D]

and therefore,

k(forward) / k(reverse) = [C][D] / [A](B)

This expression equals the equilibrium constant:

K(eq) = k(forward) / k(reverse) = [C][D] / [A](B)

why doesn't increasing temperature increase the forward and reverse rate to the same extent? the arrenhieus equation says that the rate constant of a reaction increases with increasing temperature. therefore, wouldn't we predict that BOTH the forward and reverse reaction rates for any reaction would increase with increasing temperature? I'm so confused as to why Le Chats principle predicts that, for example, increasing the temperature of an endothermic reaction will drive it forward. wouldn't the k(forward) and k(reverse) both increase to the same extent, and therefore the equilibrium would not change, meaning that there would be no change in the concentrations of the reactants and products precisely because the forward and reverse reaction rates increased the same amount.

I feel like i'm missing something important here. I would like to understand the chemistry going on here rather than just memorize the effects of temperature changes on exo/endothermic reactions.

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So you understand the qualitative aspect of Le Chatilier's principle but are trying to see the math behind it?

I don't think the principle strictly accounts for temperature change other than by envisioning "heat" as a product or reactant.

I think it is best to look at the derived equation (from delta G) that:
DeltaG_from_K.JPG

DeltaG_from_DelH&DelS.JPG

K_delH&delS.JPG


Linear_Eq_with_K_delH&delS.JPG

Source (http://www.chem.purdue.edu/gchelp/howtosolveit/Thermodynamics/TemperatureDependanceOfK.html)
 
If I'm understanding your question correctly then I think you are asking why Le Chats principle says that increasing the temperature of an endothermic reaction increases the rate of the forward reaction.

We know that Endothermic reaction absorb heat in order to complete the reaction so heat can be thought of as being one of the reactants ex: Heat + {A} + {B} --->[C] + [D]. So If we increase the temp we are adding in more heat, in other words we are increasing one of the reactants. Le Chats principle tells us more product will be produced as a result so overall the forward rate is increased while the reverse rate is not

Same principle for Exothermic reactions. Heat is given off by the reaction which means heat is one of the products. ex: {A} + {B} --->[C] + [D] + Heat. If we increase the temp of an exothermic reaction we are essentially adding in more product so the reverse rate is increased and more reactants are produced.
 
Le chatilier's principle says that increasing the temperature of an endothermic reaction will drive the reaction forward and increase the equilibrium constant. well thats great but i'm confused about this...

we know that the equilibrium constant is derived from the rate law. for example, for the reaction A+B->C+D, the equilibrium expression comes from the fact that

rate forward reaction = rate reverse reaction
k(forward)*[A](B) = k(reverse)*[C][D]

and therefore,

k(forward) / k(reverse) = [C][D] / [A](B)

This expression equals the equilibrium constant:

K(eq) = k(forward) / k(reverse) = [C][D] / [A](B)

why doesn't increasing temperature increase the forward and reverse rate to the same extent? the arrenhieus equation says that the rate constant of a reaction increases with increasing temperature. therefore, wouldn't we predict that BOTH the forward and reverse reaction rates for any reaction would increase with increasing temperature? I'm so confused as to why Le Chats principle predicts that, for example, increasing the temperature of an endothermic reaction will drive it forward. wouldn't the k(forward) and k(reverse) both increase to the same extent, and therefore the equilibrium would not change, meaning that there would be no change in the concentrations of the reactants and products precisely because the forward and reverse reaction rates increased the same amount.

I feel like i'm missing something important here. I would like to understand the chemistry going on here rather than just memorize the effects of temperature changes on exo/endothermic reactions.

1) K(eq) = k(forward) / k(reverse) = [C][D] / [A](B) cannot be used for all reactions. It ONLY applies to SINGLE STEP reactions, i.e. reactions in which the rate determining step is also the original reaction. For such reactions, the rate law can be written using stoichiometric coefficients, like the equilibrium constant equation. In general, however, the rate law should be written using the rate determining step, in which case K(eq) = k(forward) / k(reverse) = [C][D] / [A](B) doesn't work.

2) Increasing the temperature changes both forward and reverse rate constants, but since you have different activation energies for forward and reverse reactions the changes will not necessarily cancel each other out, so Keq can change.
 
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