Thursday, October 30, 2014
Dissociation Fit Test
The procedure used to fit the computed dissociation data is very sensitive to the value of Aeq so we should do a more rigorous test by adding some random errors to the data. The dissociation products of the diatomic molecule do not have to be the same since the dissociation produces two molecules and the resulting equations end up the same.
An estimate of the equilibrium constant K'eq can be found from the ratio of the products after equilibrium has been reached and averaging eliminates most of the measurement error.
As mentioned before the first reaction rate constant dominates at the start of the dissociation since there are no products. We can estimate it by doing a linear fit of a few of the initial data points. The function F(x) is arbitrary and was chosen to give a good fit for the data. With K'eq and k'0 known we can compute the second reaction rate constant k'1.
Like K'eq, and estimate of A'eq can be found by averaging.
We can then compute D' and λ' with the formulas above from the solution of the first order differential equation and solve for κ' using the first two data points and the formula for A.
The result gives a fairly good fit for the data.
There is an unused relation between A0, Aeq, Keq and D so the one might be able to adjust the values of K' , A'eq and D' for a slightly better fit by assuming that A0 is correct.
Supplemental (Oct 31): Since the value of the first data point, A0, is most likely well known one gets a better estimate of κ' by solving
2(A0 - A'eq) = D'(1 - tanh(κ')) for κ'.