The document discusses various spectrophotometric methods for analyzing drug samples containing multiple absorbing components, including simultaneous equation method. The simultaneous equation method allows determination of concentration of two drugs (X and Y) that absorb at each other's wavelength maxima. It requires knowing the absorptivity of each drug at the two wavelengths and the sample absorbances at those wavelengths to set up two equations and solve for the unknown concentrations. Certain criteria on absorbance ratios must be met for precise results.

1. Prepared and presented by:
Pinak R. Patel
Assistant Professor
Department of pharmaceutical Chemistry
Dharmaj, degree pharmacy college

2. • The Spectrophotometric assay of drugs rarely
involves the measurement of absorbance of samples
containing only one absorbing component.
• The pharmaceutical analyst frequently encounters
the situation where the concentration of one or
more substances is required in samples known to
contain other absorbing substances, which
potentially interfere in the assay.
• If the formula of the samples is known, the identity
and concentration of the interferents are known and
the extent of interference in the assay may be
determined.

3. Some of the commonly used Spectrophotometric
methods are as follows,
1. Simultaneous equation method (Vierdott’s method)
2. Derivative Spectrophotometric method
3. Absorbance ratio method ( Q-Absorbance method)
4. Solvent extraction method
5. Dual wavelength method
6. Geometric correction method
7. Orthogonal poly nominal method
8. H-point standard addition method
9. Least square approximation method

4. The basis of all the Spectrophotometric techniques for
multicomponent samples is the property that
at all wavelengths:
• The absorbance of a solution is the sum of absorbance of the
individual components
or
• The measured absorbance is the difference between the total
absorbance of the solution in the sample cell and that of the
solution in the reference cell.
And most importantly the excipients present in the formulation are
not absorbing at the wavelength of experiment.
If all of these conditions are satisfied than we can apply these
methods satisfactorily.

5. 1. Simultaneous equation method
• If a sample contain two absorbing drugs (X & Y) each of this
absorbs at the λmax of each other i.e. λ1 and λ2 (figure 2), it
may be possible to determine both the drugs by the
technique of simultaneous equation method provided that
certain criteria apply.

6. • The information required is:
• The absorptivity of X at λ1 and λ2 and ax1 and ax2 respectively.
• The absorptivity of Y at λ1 and ay1 and ay2 respectively.
• The absorbance of the diluted sample at λ1 and λ2, A1 and A2
respectively.
• Let Cx & Cy be the concentration of X & Y respectively in the
diluted sample. Two equations are constructed based upon
the fact that at λ1 and λ2 the absorbance of the mixture is the
sum of the individual absorbance of X& Y.
• At λ1 A1 = ax1 bcx + ay1 bcy ………(1)
• At λ2 A2 = ax2 bcx + ay2 bcy ………(2)

7. • Rearrange eq. (2).
cy = A2 - ax2cx / ay2
• Substituting for cy in eq. (1). And rearranging gives
cx = A2ay1 – A1ay2 / ax2ay1 – ax1ay2
And
cy = A1ax2 – A2ax1 / ax2ay1 – ax1ay2
• Criteria for obtaining maximum precision, based upon
absorbance ratios, have been suggested that place limit on the
relative concentrations of the components of the mixture. The
criteria are that the ratios,
• A2/A1/ ax2/ ax1 and ay2/ay1/ A2/A1
• Should lie outside the range of 0.1-20, for the precise
determination of Y and X respectively

8. • These criteria are satisfied only when the λmax of the two
components are reasonably dissimilar. An additional criterion
is that the two components must not interact
chemically, thereby negating the initial assumption that the
total absorbance is the sum of individual absorbance.