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

In summary: Do you know of any other resources that might provide more insight?In summary, according to Wiki, in order for K to equal A, e=0. However, this cannot happen at 0 degrees Celsius, because that would be impossible. Any help is appreciated.
  • #1
Precursor
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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?
 
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  • #2
Do you mean [itex]e^{-Ea/RT}=1[/itex]? Why would that imply [itex]T=0[/itex]?
 
  • #3
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].
 
  • #4
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 excercise?

I'm interested to know now...
Post if you find the answer! Good luck!
 
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  • #5
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 excercise?

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.
 
  • #6
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.
 

1. What is the Arrhenius Equation?

The Arrhenius Equation is a mathematical formula that describes the relationship between the rate of a chemical reaction and the temperature at which it occurs. It was developed by Swedish chemist Svante Arrhenius in 1889.

2. What is the significance of the Arrhenius Equation?

The Arrhenius Equation is significant because it helps us understand and predict how changes in temperature affect the rate of a chemical reaction. This is important in various fields such as industrial processes, environmental studies, and pharmaceutical research.

3. What are the components of the Arrhenius Equation?

The Arrhenius Equation consists of three components: the rate constant (k), the pre-exponential factor (A), and the activation energy (Ea). These components represent the speed of the reaction, the frequency of collisions between molecules, and the minimum energy required for a reaction to occur, respectively.

4. How is the Arrhenius Equation used to solve problems?

The Arrhenius Equation can be used to calculate the rate constant (k) or activation energy (Ea) for a specific reaction. This is done by rearranging the equation and plugging in known values for temperature (T) and reaction rate (R).

5. What are the limitations of the Arrhenius Equation?

The Arrhenius Equation assumes that the reaction occurs in a homogeneous solution and that the rate constant (k) remains constant throughout the reaction. It also does not take into account other factors that may affect the reaction rate, such as catalysts or changes in the reaction mechanism.

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