Finding the Temperature for K to Equal A: An Arrhenius Equation Problem

Click For Summary

Discussion Overview

The discussion revolves around determining the temperature at which the rate constant K equals the pre-exponential factor A in the Arrhenius equation. Participants explore theoretical implications, mathematical reasoning, and the conditions under which this equality might hold, including considerations of activation energy and temperature.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Exploratory
  • Debate/contested

Main Points Raised

  • One participant queries what temperature would make K equal A, suggesting that for K to equal A, the exponential term must equal zero.
  • Another participant clarifies that the condition e^{-Ea/RT}=1 does not imply T=0, but rather questions what T must be if -Ea/RT=0.
  • A participant proposes that the activation energy Ea must be zero to achieve the desired equality, though they express skepticism about this approach.
  • Some participants discuss the implications of activation energy being dependent on temperature and the circular reasoning encountered when trying to evaluate Ea.
  • One participant suggests that K=A may not be plausible and questions whether this scenario has been presented as an exercise.
  • A later reply indicates that as temperature approaches infinity, K could be approximated to equal A, but notes that this situation may not reflect a realistic scenario.
  • Another participant acknowledges the possibility of K being approximately A with a very small activation energy at high temperatures, while expressing concern about the practicality of such limits.

Areas of Agreement / Disagreement

Participants express differing views on the feasibility of K equaling A, with some suggesting that it may not be possible while others explore theoretical limits. There is no consensus on the conditions under which K can equal A.

Contextual Notes

Participants note the dependence of activation energy on temperature and the limitations of the Arrhenius equation in certain regimes, which may complicate the evaluation of K and A.

Precursor
Messages
219
Reaction score
0

Homework Statement


At what temperature does K = A?


Homework Equations


[tex]k= Ae^{-Ea/RT}[/tex]


The Attempt at a Solution


In order for K to equal A, then [tex]e=0[/tex]. But at what temperature can [tex]e=0[/tex]? The temperature can't be 0, because that would be impossible. Any help is appreciated?
 
Physics news on Phys.org
Do you mean [itex]e^{-Ea/RT}=1[/itex]? Why would that imply [itex]T=0[/itex]?
 
Mapes said:
Do you mean [itex]e^{-Ea/RT}=1[/itex]? Why would that imply [itex]T=0[/itex]?

I did not say that T should equal 0. I was asking what T must be if [tex]-Ea/RT= 0[/tex].
 
Hello!
Surely, the activiation energy has to be zero, it looks to be the only way to get zero in the equation, for what you're interested in. Since activation energy is dependent on temperature, make Ea zero, perhaps; although that seems highly questionable...

From Wiki, concerning the equation for Ea: "While this equation suggests that the activation energy is dependent on temperature, in regimes in which the Arrhenius equation is valid this is canceled by the temperature dependence of k. Thus Ea can be evaluated from the reaction rate coefficient at any temperature (within the validity of the Arrhenius equation)."
Kind of goes round in a circle when I tried to find an answer. I would hazard a wild and unfounded guess that k=A is not possible. Do you know if it is plausible? Has it been given as an exercise?

I'm interested to know now...
Post if you find the answer! Good luck!
 
Last edited:
nobahar said:
Hello!
Surely, the activiation energy has to be zero, it looks to be the only way to get zero in the equation, for what you're interested in. Since activation energy is dependent on temperature, make Ea zero, perhaps; although that seems highly questionable...

From Wiki, concerning the equation for Ea: "While this equation suggests that the activation energy is dependent on temperature, in regimes in which the Arrhenius equation is valid this is canceled by the temperature dependence of k. Thus Ea can be evaluated from the reaction rate coefficient at any temperature (within the validity of the Arrhenius equation)."
Kind of goes round in a circle when I tried to find an answer. I would hazard a wild and unfounded guess that k=A is not possible. Do you know if it is plausible? Has it been given as an exercise?

I'm interested to know now...
Post if you find the answer! Good luck!

I have found out that temperature must appraoch infinity for K to equal A. In [tex]k= Ae^{-Ea/RT}[/tex], as T approaches infinity, [tex]-Ea/RT[/tex] approaches 0. Basically, this is calculus more than anything.
 
It seems so obvious now that you've pointed it out... I never considered approximating it to equal one...
If you have a very small activation energy, and a very high temperature, I suppose you could argue that k is approximately A. Taking the limit as T tends to infinity doesn't seem to reflect any plausible, real situation, though.
Once again, many thanks.
 

Similar threads

Graph of ln(A/R) vs 1/T: Arrhenius Equation and Homework Equations
  • · Replies 8 ·
Replies
8
Views
4K
Rate constant calculation Using the Arrhenius equation
  • · Replies 1 ·
Replies
1
Views
3K
Solving Kinetics & Arrhenius Equation: Find A & Ea
  • · Replies 1 ·
Replies
1
Views
3K
Chemistry Finding rate constant from pressure change in an experiment
  • · Replies 2 ·
Replies
2
Views
2K
Chemistry What Does Delta Gn Represent in the MIT Chemistry Course Equation?
  • · Replies 2 ·
Replies
2
Views
3K
Calcualting Activation Energy using Arrhenius equation and plot
  • · Replies 2 ·
Replies
2
Views
3K
Why is the Arrhenius plot for the rate constant different from y=e-1/x?
  • · Replies 9 ·
Replies
9
Views
8K
Arrhenius Equation: Can We Substitute k with 1/t?
  • · Replies 3 ·
Replies
3
Views
3K
Arrhenius Equation for parallel reaction
  • · Replies 14 ·
Replies
14
Views
11K
Chemistry A calculation of enthalpy, entropy, and Gibbs energy of vaporization
  • · Replies 1 ·
Replies
1
Views
2K