## Qualitative And Quantitative Analyses

A. Qualitative Analysis

The ultraviolet-visible spectra of most compounds are of limited value for qualitative analysis and have been largely superseded by the more definitive infrared and mass spectroscopies. Qualitative analytical use of ultraviolet-visible spectra has largely involved describing compounds in terms of the positions and molar absorptivities of their absorption maxima, occasionally including their absorption minima. Indeed, some organic compounds are still characterized in terms of the number of peaks in the UV-visible spectrum and their absorbance ratios. This is usually the case in phytochemistry and photodiode array chromatography and when the analyst has a limited range of compounds to work with whose spectra are known to differ. In the pharmacopeias, however, absorbance ratios have found use in identity tests, and are referred to as Q-values in the U.S. Pharmacopia (USP).

Ultraviolet-visible spectrophotometry has also been applied to titrimetry. In this case the variation in the absorbance of the analyte with addition of titrant is used to obtain a spectrophotometric profile from which titration end points and/or equilibrium constants, etc., can be determined. This has been applied to the whole range of titrations in which a chromophore is generated. These include acid-base, redox, and complexometric titrations.

### B. Quantitative Analysis

Ultraviolet-visible spectrophotometry is perhaps the most widely used spectro-photometric technique for the quantitative analysis of chemical substances as pure materials and as components of dosage forms. It has found increasing usefulness as a means of assaying pharmaceutical substances described in the pharmacopeias.

Pharmaceuticals are usually marketed as formulations containing more than just the active ingredient(s). The other components, referred to as excipients, are added to the formulation to enhance efficacy, improve the appearance of the product, or facilitate certain stages in production. All of these other materials present in the dosage form can, and often do, complicate the analyses of the active ingredient(s). Hence, in most spectrophotometric analyses of pharmaceuticals, a separation stage is often included in the analytical procedure. Physical isolation of the active ingredient from all other dosage form ingredients is not always possible, and when these other excipients are known to interfere with the spectrum of the analyte they are referred to as interferents. Interferents are broadly considered to be those substances that modify the shape of the absorption spectrum, usually contributing to the absorption measured. The presence of inter-ferents in an analytical sample can be inferred from the failure of the absorption curve to return to zero absorption in regions where the analyte is known not to absorb. For purposes of this discussion we can divide spectrophotometric analyses into single-component and multicomponent analyses. Single-component analysis is more commonly applied, and it involves the isolation of the analyte of interest from other dosage form excipients. Multicomponent analysis, on the other hand, does not involve isolation of the analyte of interest from the all the other possible interferents present in the dosage form, but rather involves the retention of one or more interferents whose spectrophotometric profiles in the analytical solution are known. The use of UV-visible spectrophotometry in quantitative analysis is centered around the Beer-Lambert law, which relates the absorbance of an analyte to its concentration:

where A is the absorbance, e is the molar absorptivity (L mole/cm), c is the concentration (mole/L), and d is the path length (cm). The Beer-Lambert law applies rigorously only to integrated absorption bands from absorption-versus-energy plots. In these cases the area under the curve is directly proportional to the concentration of the absorbing species. It is possible, however, to apply the law to nominal single-wavelength analyses, especially when the analytical wavelength is at the absorption maximum. The Beer Lambert law, however, does not necessarily hold at single wavelengths that are significantly different from the wavelength of maximum absorption, especially when the absorbance is rapidly changing.

### 1. Monocomponent Analysis

In a simple analysis, the analyte can be quantified by measuring its absorbance at a given wavelength, then substituting for absorbance (A) molar absorptivity (e), and pathlength (d) in Eq. (9) and solving for concentration (c). If the molar absorptivity (e) is not known and a pure sample of analyte is available, a calibration curve (of absorbance versus concentration) can be drawn. The slope of the calibration curve is given by the product e d. When the path length (d) is known, the molar absorptivity (e) can be calculated. Occasionally, a single sample may be used, but this is less reliable than drawing a calibration curve. Linear interpola tion on the calibration curve can also be used to read the concentration of an analyte whose absorbance is known. This approach is particularly useful when apparent deviations from the Beer-Lambert law are observed. In applying the Beer-Lambert law to analyses it is important that the solvent does not interfere with the analysis. The solvent must not only dissolve the analyte, but must also have a low volatility and be transparent in the spectral region of interest. Thus volatile solvents necessitate that the sample cell be sealed during the analysis or that the measurements be carried out as quickly as possible. Similarly, solvents with a UV cutoff in the near-UV do not permit analytical measurement at wavelengths shorter than the cutoff wavelength.

Ionizable compounds may have to be dissolved in buffered solutions, to ensure that only one form of the analyte exists in solution. The pH employed is commonly at least two pH units above or below the pKa, depending on which pH yields the optimal chromophore. Just as pH equilibria can be employed, chemical complexation equilibria can also be employed to improve analytical selectivity.

A number of organic compounds have found use as chemical derivatization reagents. Usually these have served as chromogenic reagents that generate a chro-mophore upon interaction with the analyte. Organic compounds used for this purpose include the crown ethers, diazotizing reagents, and the porphyrines. Their uses have been largely for metal analysis, as many metal complexes are chromo-genic. In some cases, however, the complexing reagents have served to enhance selectivity by facilitating extraction of the analyte—usually by ion-pair extraction.

### 2. Multicomponent Analysis

Spectrophotometric multicomponent analyses are based on mathematically processing a composite absorption spectrum made up of the spectra several components that contribute additively to the overall spectrum. In all cases, some idea of the nature of the contributing spectra is required for the mathematical processing of the composite sample spectrum. A host of techniques of varying complexity have been reported in the literature.

a. Experimental Techniques Applied to Multicomponent Analysis

Difference spectrophotometry involves the exploitation of the ability to chemically modify the spectrophotometric profile of the analyte alone in the presence of other possible interferents. The analyte may be modified by alteration of pH or through chemical reaction in either the reference or sample cell. pH-induced difference spectrophotometry is most commonly employed, due to its simplicity, though reagents to covalently modify the analyte have also found use. The selective modification of the analyte alone in the presence of interferents permits quan-titation on the basis of spectral differences between the otherwise identical refer ence and test solutions. A useful test for indicating whether selective modification of the analyte alone has been achieved involves confirming that there is zero absorbance at the isosbestic points of the two spectral species of the analyte.

Derivative spectra are literally the derivatives of the normal spectra. Their analytical advantage stems from the fact that the slopes of the spectra of substances of narrow spectral bandwidth are usually higher in magnitude than those of substances with broad spectral bandwidth. As a result, the analyses of substances with narrow spectral bandwidth can often be performed in the presence of substances with broad spectral bandwidth, where the spectrum of the analyte appears as a shoulder on the spectrum of the broad-bandwidth interferant. The differentiation procedure was initially carried out manually. However, electronic differentiation techniques developed more recently have simplified the application of the techniques to pharmaceutical analyses. It is worth noting that though higher derivatives appear to improve resolution, the spectra obtained are also significantly distorted by noise. A trade-off is therefore required.

b. Mathematical Correction Techniques

The simultaneous-equations method is a simple case of multicomponent analysis that is applicable to the simultaneous determination of two absorbing species present in a solution. When two or more absorbing species are present in the cell and the Beer-Lambert law is obeyed, the absorbance at a given wavelength is the sum of the absorbances of the two species at that wavelength. That is,

where Atot is total absorbance and A1 and A2 are the absorbance of species 1 and 2, respectively, at the wavelength of measurement.

From Eq. (10) we can therefore say that

for each wavelength of measurement. Hence, if the molar absorptivities £ and £2 are determined from standard solutions, two simultaneous equations can be written whose solution would afford the concentrations of the absorbing species. For n species, n analogous equations can be drawn, permitting the calculation of the concentrations of all n species. It is worth noting that significant errors may be introduced into the calculation if the individual spectra overlap considerably. A number of modern instruments incorporate microprocessors that are preprogrammed to solve simultaneous equations of this sort. In these cases, the operator specifies the appropriate wavelength values and the predetermined molar absorp-tivities (£) of the species to be determined. The microprocessor then calculates the concentrations. The absorbance ratio method is a modification of the simultaneous-equations method which confers on the analysis the advantage of requiring less stringent experimental technique. In the technique, two wavelengths are employed for measurement, one of which is at an isosbestic point for the two spectra. An equation can be drawn relating the fraction of the absorbing components to the absorption at one wavelength and the absorption at the isosbestic point used to eliminate one concentration variable in the equation drawn for the other wavelength.

Thus it has been shown that in a two-component system, the fraction of a component fp is given by the relation fp = Qm - Qq (12)

QP - Qq where Qm = A2/A1 Qx = ap2/ap1, Qq = aq2/aq1, api and aqi are the absorbances of pure p and q at wavelength i, and A is the absorbance of the mixture. Hence the concentration of component p is given by

because at the isosbestic point the molar absorptivities for the two components p and q are identical.

In most analyses it may be possible to separate the analyte(s) from the other dosage form ingredients, but this is not always the case. When this is not the case, the dosage form excipients may be able to interfere with the analyses. To deal with this problem, a number of specific techniques have been developed for the analysis of a variety of analytes in the presence of interferants.

The absorption spectrum of interferants is commonly linear, but nonlinear interferant absorption has been reported. A number of mathematical techniques have been developed to correct for nonlinear interfering absorption. Most of the correction techniques are based on assuming that the interferents have an absorption profile that can be represented by some mathematical function. The simpler correction techniques, such as the geometric correction technique(s), assume a linear interferant absorption profile. A basic approach to the technique can be seen from the three-point geometric correction technique, a modification of which has found applicability to the analysis of vitamin A in fish oils. Higher-order functions have also been used to describe the interfering absorption, and in these cases more involved formulas have been developed.

More involved mathematical correction techniques have also been developed; these include, among others, the use of orthogonal polynomial techniques to correct for the distortion of spectra induced by interferants.

The orthogonal function method has been used for the correction of irrelevant absorption in multicomponent spectrophotometric analysis. Each component makes a fundamental contribution shape to the overall shape of the spectrum, the spectrum being considered as a composite of these contributing spectra. The contribution of each component is represented by a coefficient whose magnitude is in part linearly concentration-dependent. In applying the method a part of the spectrum is selected in which the analyte and interferent show significant variation in their contributions to the overall shape of the spectrum. Since being suggested in the 1960s, the orthogonal polynomial method has been applied to the analyses of a number of compound preparations. Algorithms have also been proposed for computerization of the calculations.

Multivariate analytical methods have also been applied to the analysis of drug substances. The methods have a significant component of matrix analysis, and the Beer-Lambert law is basically rewritten in matrix form, permitting matrix analysis of absorbance data. A number of other mathematical algorithms have also been developed for the quantitation of analytes in multicomponent mixtures. These have either been iterative methods or methods based on multiple least-squares regression. The multiple least-squares regression methods require a knowledge of all the components of the multicomponent mixture, whereas the iterative methods such as the Kalman or the simplex method are less restrictive in the sense that interferents whose spectra are not known need not be included in the database.

The general protocol is transformation of the absorption data to reduce noise. Then, for an «-dimensional data matrix a square covariance matrix is obtained by a series of transformations. If the data matrix is not square, its square is obtained by multiplying the matrix by its transpose. The covariance matrix is then analyzed relative to the calibration matrix to determine concentrations in the unknown mixture. The eigenanalysis performed on the covariance matrix generates eigenvectors, the number of which should correspond to the number of components in the mixture. When the number of eigenvalues is greater than the number of components, this suggests interaction.

Analyte-analyte and analyte-matrix interactions can and often do complicate the analysis, usually showing up as additional significant eigenvalues. A heavy reliance on appropriate choice of working wavelength is a drawback of these techniques. The wavelength range should include 10-20% of the baseline, but application to quantitative UV-visible analysis has been reported with varying degrees of success.

### 3. Errors in Spectrophotometric Measurements

The errors that arise in spectrophotometric measurements arise from either of two sources. They may arise from instrumental factors or from chemical factors.

Instrumental errors can arise from several sources. Electronic noise in the detector, referred to as Johnson or shot noise, is a primary source of error. A less important source of error is flicker in the light source.

The ideal absorbance range for most measurements is in the region of 0.5 to 1.5 absorbance units for most modern instruments, as the concentration-versus-absorbance curve is relatively linear between these absorbance values.

Other instrumental factors affecting analytical accuracy include spectral slit width. As slit width is increased,the fine structure of absorption bands is lost as the incident light is no longer monochromatic, a requirement for the Beer-lambert law to hold. The area under the absorption band is less affected by the monochromaticity of light than the intensity at a particular wavelength, and for this reason, more accurate measurements tend to make use of integrated areas under the absorption band rather than intensities at the peak maxima. Therefore it is useful to indicate the slit width employed in calculating molar absorptivities. The scan rate is another instrumental factor that can introduce error in measurement. This is an important consideration when entire spectra are employed. Generally, fast scan rates tend to distort spectra in the direction of the scan, altering the positions of both maxima and minima as well as diminishing peak intensities. This introduces both qualitative and quantitative errors into the measurement. The distortions arise from the relatively slower response time of the recorder as compared to the rate of signal change. The distortion is best countered by slowing down the scan rate, to give the instrument time to average out instrumental noise. This provides a more accurate measurement.

The combination of instrumental factors that gives rise to measurement errors forms the basis for the greater tolerances seen in pharmacopeial limits set for compounds determined by instrumental techniques when compared to those determined by, say, titrimetry.

A number of chemical factors may also contribute to errors in measurement. These factors generally lead to deviations from the Beer-Lambert law, and can largely be controlled once they are recognized as potential sources of error. Solute-solute interaction, for example, whether it leads to aggregation or precipitation of the aggregate, diminishes the apparent concentration of the analyte of interest. Aggregation of hydrophobic polycyclic aromatics at high concentrations in aqueous media is one such example where deviation from the Beer-Lambert law would be seen. Similarly, dimerization of molecules, for example, carboxylic acids, or even polymerization of analyte in solution may also lead to apparent deviation from the Beer-Lambert law. Both can be controlled to some extent by use of appropriately diluted solutions.

Ionization or even complexation of the analyte in solution can also lead to apparent deviation from the Beer-Lambert law. Again, by appropriate control of pH or complexation conditions it is possible to ensure that only one form predominates in solution, permitting quantitation of the absorbing species. Measurement of absorbance at the isosbestic point has been used to counter this problem. However, this approach is limited by the fact that the absorbance of the analyte at this point is frequently not high enough.

Fluorescence from absorbing species in solution may also contribute to interference. However, this kind of interference is rare and minimal because, first, the lower source intensities employed in UV-visible spectrophotometry imply that fewer fluorescent species become excited, and second, the fluorescence emitted, if any, will be too weak to significantly influence the accuracy of measurement.

It is perhaps for all these possible contributions to analytical error that it is important to carry out a quantitative analysis by employing a calibration curve obtained from a calibration series, as this will not only confirm adherence to the Beer-Lambert law, but also correct for errors introduced by the various factos described.

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