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FanCG1-Visitor
1-Visitor
December 29, 2013
Solved

A question on activation energy determination

  • December 29, 2013
  • 2 replies
  • 6060 views

Having a group of experimental data like following

%E6%8D%95%E8%8E%B7.PNG

where α is conversion of the reaction under research. some important kinetic parameters like (E/R) are needed to be obtained from above data.

and the following model has to be considered,

%E6%8D%95%E8%8E%B72.PNG

Above function will be used to fit the experimental data in order to determine E/R and lncA from slope and interception, respectively.

And this will require that m and n have to be obtained in advance.

according to my solution, lncA， E/R， m and n have to be determined at the same time, I dont know how m and n are got at first.

data are attached

Best answer by RichardJ

Shall I force E/R to be a positive value?

That works if you also (as Harvey suggests) force m to be negative

2 replies

R
RichardJ19-Tanzanite
19-Tanzanite
December 29, 2013

Yes, m and n have to be determined at the same time, but there's more than enough data points to determine the values of 4 unknowns. However, if E/R and lncA are constants, then there should be a linear relationship between the LHS of your equation and 1/T, and that is not the case.

F
FanCG1-VisitorAuthor
1-Visitor
December 30, 2013

Thanks a lot

I found that there was a initial guess value sensitive problem for current example (see attached). I dont know whether there is a good method to avoid this.

A
AlanStevens19-Tanzanite
19-Tanzanite
December 30, 2013

I found that there was a initial guess value sensitive problem for current example (see attached). I dont know whether there is a good method to avoid this.

You need to vectorise the product alpha^m.(1-alpha)^n otherwise it will evaluate to a single number instead of a vector of numbers. The resulting solution is then more robust to changes in initial guesses as well.

Alan

NB Don't forget to vectorise the expression on the graph also.

    H
    HarveyHensley12-Amethyst
    12-Amethyst
    December 30, 2013

    This data set looks like it is from a batch reactor and it is just one run. The rate expression suggests that the reaction rate depends upon the reactant to the n th power and to the product to the m th power. Products can affect the rates via adsorption terms that reduce the rate, or by a decay term. In either case, m is probably negative and n positive. For typical reactions n < 3 and m should be a small negative number.

    I don't think you will be able to determine m and n with these data because the conversion and temperature are correlated. You need several runs with different starting concentrations to determine m and n. If m and n are known, as originally proposed, then you can determine the temperature functions. Also, you might want to try using an integral method instead of the numerical difference method. Numerical diferences can include a lot of error.

    F
    FanCG1-VisitorAuthor
    1-Visitor
    December 30, 2013

    thanks Harvey

    I will consider your suggestion

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