Rate constant and temperature

In summary, the Arrhenius equation, which states that k=Ae^(-Ea/RT), shows that the rate constant is directly proportional to temperature when all other variables are constant. This can be seen by rearranging the equation to k ∝ T.
  • #1
retracell
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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.
 
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  • #2
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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  • #3


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.
 

1. What is the relationship between rate constant and temperature?

As temperature increases, the rate constant also increases. This is because at higher temperatures, particles have more kinetic energy and are moving faster, resulting in more frequent collisions and a higher likelihood of successful reactions.

2. How does temperature affect the rate of a reaction?

As mentioned above, an increase in temperature leads to an increase in the rate of a reaction. This is because higher temperatures provide more energy for particles to overcome the activation energy barrier and react with each other.

3. What is the Arrhenius equation and how is it related to rate constant and temperature?

The Arrhenius equation is k = Ae-Ea/RT, where k is the rate constant, A is the frequency factor, Ea is the activation energy, R is the gas constant, and T is the temperature in Kelvin. This equation shows the relationship between rate constant and temperature, as an increase in temperature results in a decrease in the exponential factor, leading to an increase in the rate constant.

4. Can the rate constant change at a constant temperature?

Yes, the rate constant can change at a constant temperature if there are any changes in the reaction conditions, such as concentration or presence of a catalyst. However, at a constant temperature and with no other changes, the rate constant will remain constant.

5. How does temperature affect the activation energy of a reaction?

An increase in temperature decreases the activation energy of a reaction. This is because at higher temperatures, particles have more kinetic energy and are more likely to overcome the activation energy barrier, making the reaction occur more quickly.

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