[Anne74]

I am trying to calculate the absolute uncertainty of the activation energy of a reaction that I have carried out at three different temperatures. I have worked out the standard error of the rate constants at each temperature using Excel:
k₁ = 9.0 ± 0.3 mol^-1 dm³ min^-1
k₂ = 22.69 ±  0.07 mol^-1 dm³ min^-1
k₃ = 80.8 ± 0.1 mol^-1 dm³ min^-1

What I have so far is to calculate the standard error of the slope of the Arrhenius plot ln k = ln A – E_a/RT  that I used to calculate the activation energy and multiplied this value by R, but I have got a smaller uncertainty than I expected using this method (± 2 J mol^-1). Is there a mathematical way of directly propagating the uncertainties of the rate constants to get an absolute uncertainty for the activation energy?

Note: I am only considering the uncertainty in the rate constants and ignoring any errors in temperature measurements.

[Corribus]

There are a number of websites available, through Google search, that explain how to propagate errors through different mathematical manipulations. But bear in mind that these calculations involve a lot of statistical assumptions, e.g., that data is distributed according to Gaussian function, etc. So you should ensure that these assumptions are applicable to your data. You should also define what you mean by the +/-. Is this a standard deviation?