Arrhenius Equation: Can We Substitute k with 1/t?

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Discussion Overview

The discussion revolves around the Arrhenius equation and the possibility of substituting the rate constant k with 1/t, where t represents the time for a reaction to reach a certain point. Participants explore the implications of this substitution in the context of reaction rates and constants.

Discussion Character

  • Debate/contested

Main Points Raised

  • One participant states the Arrhenius equation as k=Ae^-Ea/RT and proposes substituting k with 1/t, leading to the equation 1/t=Ae^-Ea/RT.
  • Another participant asserts that the rate constant k is a constant and does not vary with time, challenging the initial substitution proposal.
  • A participant acknowledges a mistake and clarifies that the rate of reaction is directly proportional to both the rate constant k and 1/t, questioning whether k and 1/t are interchangeable in the Arrhenius equation.
  • One participant reiterates that the rate constant k is a constant and discusses the approximation of reaction rates, noting that k is a function of temperature and can change if temperature varies over time.

Areas of Agreement / Disagreement

Participants express disagreement regarding the interchangeability of k and 1/t, with some arguing that k is a constant while others explore the relationship between reaction rates and time. The discussion remains unresolved.

Contextual Notes

There are limitations in the assumptions made about the relationship between rate constants and time, as well as the conditions under which the Arrhenius equation applies. The discussion does not resolve these complexities.

fhlfw
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I know the Arrhenius equation is k=Ae^-Ea/RT
The rate constant k is directly proportional to 1/t
(t stands for the time for the reaction to reach a point)

So I wonder if we can substitute k by 1/t in the Arrhenius equation to become 1/t=Ae^-Ea/RT ?

Thanks a lot
 
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fhlfw said:
The rate constant k is directly proportional to 1/t
The rate constant is a constant, it doesn't vary with time.
 
My bad, I have made a mistake. It should be:

The rate of reaction is directly proportional to both rate constant k and 1/t
So are k and 1/t interchangeable in the Arrhenius equation?
 
fhlfw said:
The rate constant k is directly proportional to 1/t
(t stands for the time for the reaction to reach a point)

For the case that you mean something like this:

\dot \xi = \frac{{\Delta \xi }}{{\Delta t}}

That is just an approximation (except for zero-order reactions).

DrClaude said:
The rate constant is a constant, it doesn't vary with time.

Accorting to the Arrhenius equation the rate constant is a function of temperature. If temperature changes over time than the rate constant changes over time too.
 

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