Effect of Temperature on Chemical Equilibrium

[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.
[tex]

Suppose that `⇌`(A, B);
print(`output redirected...`); # input placeholder
A ⇌ B
According to the definition of rate laws,
Rate*forward = k[A][A];
and
Rate*reverse = k;


where
k; is the rate constant
[X]; is the respective concentration of substance X.

----------------------------------------------------------------------------------------

Also, according to the Arrhenius Equation, for any reaction,
k = A*exp(-E[a]/RT);where
A; is a constant
E[a]; is the activation energy
R is the gas constant
T is the temperature at which the reaction
------------------------------------------------------------------------------------

According to the definition of the equilibrium constant,

K[c] = k[A]/k and k[A]/k = 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];
Therefore the K[c]; does not depend on T, which contradicts with Le Chatelier's Principle!
How can I resolve this paradox, or what is the fault with my logic?

[/tex]

 

[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 [tex]
`⇌`(A, B);
print(`output redirected...`); # input placeholder
A ⇌ B
According to the definition of rate laws,
> Rate*forward = k[A][A];
and
> Rate*reverse = k;


where
> k;
is the rate constant
[X]
is the respective concentration of substance X.

----------------------------------------------------------------------------------------

Also, according to the Arrhenius Equation, for any reaction,
/ E[a]\
k = A exp|- ----|
\ RT /
where

A
is a constant
E[a]
is the activation energy
R is the gas constant
T is the temperature at which the reaction
------------------------------------------------------------------------------------

According to the definition of the equilibrium constant,

/ E[a1]\ / E[a1]\
A[1] exp|- -----| A[1] exp|- -----|
k[A] k[A] \ RT / \ RT /
K[c] = ---- and ---- = ----------------- and ----------------- =
k k / E[a2]\ / E[a2]\
A[2] exp|- -----| A[2] exp|- -----|
\ RT / \ RT /

A[1] exp(E[a2] - E[a1])
-----------------------
A[2]
Therefore the
K[c]
does not depend on T, which contradicts with Le Chatelier's Principle!
How can I resolve this paradox, or what is the fault with my logic? [/tex]

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.

 

[LudusRex]

I would like to commend you for delving into the complexities of chemical equilibrium and the effect of temperature on it. Your understanding of the basic principles is commendable, and I am happy to help you resolve the paradox you have encountered.

Firstly, it is important to note that the Arrhenius equation is used to determine the rate constant of a reaction, not the equilibrium constant. The equilibrium constant is a measure of the ratio of products to reactants at equilibrium, and it is not affected by changes in temperature. This is in line with Le Chatelier's Principle, which states that a system at equilibrium will respond to changes in external conditions in a way that minimizes the effect of those changes.

In the case of temperature changes, the equilibrium will shift to favor the endothermic or exothermic reaction to maintain a constant equilibrium constant. This means that while the rate of the forward and reverse reactions may change, the equilibrium constant will remain the same.

Your mistake lies in equating the rate constant with the equilibrium constant, which are two separate entities. The Arrhenius equation describes the relationship between the rate constant and temperature, but it does not take into account the equilibrium state of the reaction.

In summary, your understanding of the effect of temperature on equilibrium is correct. However, the Arrhenius equation is not applicable to equilibrium constants, and your logic is faulty in equating the two. I would suggest further studying the concepts of equilibrium and rate laws to gain a deeper understanding of the topic.