Does the Arrhenius equation contradict Le Chatelier's principle on temperature?

[Bipolarity]

Hi guys I am a student of AP Chemistry. I am trying to understand the effect of temperature on equilibrium. I know that under the change of temperature, the equilibrium will shift to favor the endothermic process if heat is added and vice versa. But employing the Arrhenius Equation, I see a necessary concentration.
$$<br /> Suppose that `&rlhar;`(A, B);<br /> print(`output redirected...`); # input placeholder<br /> A &rlhar; B<br /> According to the definition of rate laws,<br /> Rate*forward = k[A][A];<br /> and<br /> Rate*reverse = k<b><b>;<br /> <br /> <br /> where <br /> k; is the rate constant <br /> [X]; is the respective concentration of substance X.<br /> <br /> ----------------------------------------------------------------------------------------<br /> <br /> Also, according to the Arrhenius Equation, for any reaction,<br /> k = A*exp(-E[a]/RT);where <br /> A; is a constant<br /> E[a]; is the activation energy<br /> R is the gas constant<br /> T is the temperature at which the reaction<br /> ------------------------------------------------------------------------------------<br /> <br /> According to the definition of the equilibrium constant,<br /> <br /> K[c] = k[A]/k<b> and k[A]/k<b> = A[1]*exp(-E[a1]/RT)/(A[2]*exp(-E[a2]/RT)) and A[1]*exp(-E[a1]/RT)/(A[2]*exp(-E[a2]/RT)) = A[1]*exp(E[a2]-E[a1])/A[2];<br /> Therefore the K[c]; does not depend on T, which contradicts with Le Chatelier's Principle!<br /> How can I resolve this paradox, or what is the fault with my logic?<br /> <br /> </b></b></b></b>$$

 

[epenguin]

Hi guys I am a student of AP Chemistry. I am trying to understand the effect of temperature on equilibrium. I know that under the change of temperature, the equilibrium will shift to favor the endothermic process if heat is added and vice versa. But employing the Arrhenius Equation, I see a necessary concentration.
Suppose that $$`&rlhar;`(A, B);<br /> print(`output redirected...`); # input placeholder<br /> A &rlhar; B<br /> According to the definition of rate laws,<br /> > Rate*forward = k[A][A];<br /> and<br /> > Rate*reverse = k<b><b>;<br /> <br /> <br /> where <br /> > k;<br /> is the rate constant <br /> [X]<br /> is the respective concentration of substance X.<br /> <br /> ----------------------------------------------------------------------------------------<br /> <br /> Also, according to the Arrhenius Equation, for any reaction,<br /> / E[a]\<br /> k = A exp|- ----|<br /> \ RT /<br /> where <br /> <br /> A<br /> is a constant<br /> E[a]<br /> is the activation energy<br /> R is the gas constant<br /> T is the temperature at which the reaction<br /> ------------------------------------------------------------------------------------<br /> <br /> According to the definition of the equilibrium constant,<br /> <br /> / E[a1]\ / E[a1]\ <br /> A[1] exp|- -----| A[1] exp|- -----| <br /> k[A] k[A] \ RT / \ RT / <br /> K[c] = ---- and ---- = ----------------- and ----------------- = <br /> k<b> k<b> / E[a2]\ / E[a2]\ <br /> A[2] exp|- -----| A[2] exp|- -----| <br /> \ RT / \ RT / <br /> <br /> A[1] exp(E[a2] - E[a1])<br /> -----------------------<br /> A[2] <br /> Therefore the <br /> K[c]<br /> does not depend on T, which contradicts with Le Chatelier's Principle!<br /> How can I resolve this paradox, or what is the fault with my logic? </b></b></b></b>$$

It's your maths, you are forgetting that e^A/e^B is e^A-B not e^A/B.

 

[Bipolarity]

What?? How were you able to read that?? I can't get LaTeX to work... I'm new to this sorry. I use Maple but don't know how to translate it to LaTeX.

In any case, thank you SO MUCH FOR YOUR POST! IT FINALLY MAKES SENSE!

Regards,

BiP

 

[Borek]

LatTeX here is used just for formulas, besides, what you wrote was not in LaTeX. See our LaTeX guide.