How Does Temperature Affect the Rate Constant in Chemical Reactions?

[retracell]

Homework Statement

How is the rate constant related to temperature when other variables are constant

Homework Equations

Arrhenius equation: k=Ae^Ea/RT

The Attempt at a Solution

I know it is just a matter of rearranging but I can't seem make it end up as k ∝ T in some way.
I tried using logarithms and ln(k2/k1) = -Ea/RT(1/T2 - 1/T1) and can't get it
I think this is the same question as https://www.physicsforums.com/showthread.php?t=203424 and it was tagged as solved but it was not.

 

[Borek]

No idea what you are asking about - Arrhenius equation gives you dependence between rate constant and temperature, isn't it exact answer to your question?

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[Blueshift5]

The rate constant (k) is directly proportional to temperature (T) when other variables are constant. This relationship is described by the Arrhenius equation, which states that k is equal to the pre-exponential factor (A) multiplied by the exponential of the activation energy (Ea) divided by the product of the ideal gas constant (R) and temperature (T). In other words, as temperature increases, the rate constant also increases. This is because at higher temperatures, more molecules have enough energy to overcome the activation energy barrier and participate in the reaction, leading to a higher reaction rate. Therefore, the rate constant and temperature have a direct relationship, where an increase in temperature results in an increase in the rate constant.