Model Based Chemical Analyses

The very rigid constraints of a chemical model form a framework within which the fit is confined and which results in a robust analysis, in model-free analysis, this framework is dramatically wider and looser and these methods suffer gradually from a sever lack of robustness. It must be remembered, however, that the choice of the wrong model necessarily results in the rung analysis and wrong resulting parameters.

Model Based Analyses

Simple first order kinetics

d[A]dt

= -k [A]

A Bk

[A] = [A]0 exp (-kt)

[B] = [A]0 (1 - exp (-kt))

[A]0=1

k=0.2

Selective region for A Selective region for B

Univariate data

A=440 = A [A]0 exp (-kt) + r

A=540 = B [A]0 (1 - exp (-kt)) + r

Suppose A=1.3 & k=0.25

A=440 = A [A]0 exp (-kt) + r^

How one can determine the parameters of the model?

RSS =(ri2)

RSS =0.15

Suppose A=1.3 & k=0.25

A=440 = A [A]0 exp (-kt) + r^

How one can determine the parameters of the model?

0 2 4 6 8 10 12 14 16 18 200

0.2

0.4

0.6

0.8

1

Time

Abs

orba

nce

Suppose A=1.0 & k=0.20

RSS =1.42 × 10-5

How one can determine the parameters of the model?

A=440 = A [A]0 exp (-kt) + r^

0.5 < A < 1.5

&

0.1 < k < 0.3

0.5 < A < 1.5

&

0.1 < k < 0.3

Direct Fitting

Kinfit1.m

Data which should be fitted

Data set file

Calling kinfit1 function

?Modify the kinfit1 function for fitting a kinetic curve which is selective for product.

A=440 = A [A]0 exp (-kt) + r

= +A

y = A x + r

A = (yTy)-1 yT x

Linear Parameters

r= f (k)

Kinfit2.m

?Investigate the effects of non-correct value of initial concentration on the results of analysis.

Selective multivariate dataA1 = A1 {[A]0 exp (-kt)} + r1

= +A1

A2 = A2 {[A]0 exp (-kt)} + r2

= +A2

=

A1 A2

+

Selective region for ASelective region for A

400 420 440 460 480 500 520 540 560 580 6000

0.2

0.4

0.6

0.8

1

1.2

1.4

Wavelength

Abs

orba

nce

400 420 440 460 480 500 520 540 560 580 6000

0.2

0.4

0.6

0.8

1

1.2

1.4

Wavelength (nm)

Abs

orba

nce

In the absence of selectivity

A Bk

A = A [A] + B [B]

At each non-selective wavelength

= +A B =

A

B

A Bk

A = C ET + R

At each non-selective region

=

A A A A A A

B B B B B B

C = f(k)

R = A – C C+ A

R = f(k)

?Is there any limitation in numbers of wavelengths?

Kinfit3.m

?How one can find the error of calculated parameter?