CHEMOMETRICS ASSISTED UV-SPECTROPHOTOMETRIC ...

4.3. Derivative ratio method
Calculations in this technique rely on the following basis;
Consider a mixture M of two components X and Y. If Beer’s law is obeyed for both
components over the whole wavelength range used and the path length is 1 cm, the
absorption spectrum, of the mixture Ax,y is defined by the Equation
Ax,y = αxi CX + βYi CY .....................................[14]
Where Ax,y is the absorbance of the mixture at wavelength i; αXi and βYi are the A (1%, 1cm)
of X and Y at a given wavelength i ; CX and CY are the concentrations of X and Y
respectively. If such equation 14 is divided by the corresponding equation for the spectrum of
a standard solution of X (the same is correct for the component Y) of concentration C o X, the
following Equation can be written.
Ax,y / αXi C o X = CX / C o X + CY βYi / C o X αXi .................[15]
Which can be simplified to
Ax,y / αXi = CX + CY ( βYi / αXi)........................................[16]
By plotting Ax,y / αXi as a function of βYi / αXi a straight line is obtained. The intercept of
the straight line provides the value of CX and the slope of the straight line is CY . To obtain
the ratio βYi / αXi at each wavelength, the absorption spectra of equimolar standard solutions
of Y and X are measured and the absorbance ratio at each wavelength is calculated. At the
same time the differentiation of equation 15 to its first derivative, give the following
equation:-
d/dλ (AMi / αXi C o X) = (CY / C o X) d/dλ (βYi / αXi)..................[17]
Equation 17 indicates that the derivative ratio spectrum of the mixture is dependent only on
the values of CY and C o X and independent on the values of CX in the mixture. A calibration
graph is obtained by recording and storing the spectra of solution of pure Y at different
concentrations, and the spectrum of a solution of pure X, of concentration C o X. The
amplitudes of Y are then divided (wavelength by wavelength) by the corresponding
amplitudes for X.
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