Spectrophotometry Principles: Electromagnetic Radiation-Matter Interaction, Lecture notes of Law

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CHAPTER - 1

PRINCIPLES OF SPECTROPHOTOMETRY

Spectroscopy is a powerful tool used for quantitative and qualitative analysis of samples, and is the most important of all the instrumental methods of analysis. It is a branch of science dealing with the study of interaction of electromagnetic radiation with matter. Spectrophotometry is one of the most widely applied physico chemical technique, which is remarkable for its sensitivity and precision. Two reasons for the popularity of the spectrophotometric technique are the instrumentation is fairly easy to operate and widely available. The chief advantage of spectrophotometric method is that they provide a simple means for determining minute quantities of substances. « Spectrophotometry in the visible region of electromagnetic spectrum generally considered to extend from 380nm to 780nm, is often called colorimetry. Colorimetry, is defined as a technique of analysis based on comparing the colour intensity of the unknown with that of standard solution.

Spectrophotometry is defined as a technique which involves provisions for continuously varying wavelength of the central band and therefore, measuring the absorption of radiation with wavelength by the sample. This is a convenient and direct technique which does not effect

several types of interactions such as reflection, refraction, diffraction, interference, absorption etc., may occur. Of these interactions, absorption in which certain frequencies are selectively removed by matter is of unique importance. The energy thus absorbed is transferred to atoms or molecules in matter. As a result, these atoms or molecules in the ground state are excited.

There are two fundamental laws governing the fraction of incident radiation absorbed by matter. They are

**1. Lambert's law and

2. Beer's law
3. LAMBERT'S LAW : The relationship between the absorption of radiation and the path length of the absorbing medium was first formulated by Bouguer (1729) and later by Lambert 1 (1760) which is mathematically expressed in the logarithmic form as log T = log P/P Q = -Kb ... 1. Where P Q ” Radiant power of incident radiation**

P = Radiant power of transmitted radiation T = Transmittance K = is a constant.

Lambert's law though exact has only limited applications in chemistry.

2. BEER'S LAW : Beer 2 in 1852, studied the effect of concentration of the coloured constituent in solution upon the light transmission or absorption. He found the same relation between transmission and concentration as Lambert had discovered between transmission andthickness of the absorbing layer. The intensity of a beam of monochromatic radiation decreases exponentially as the concentration of the absorbing substance increases arithmetically. This may be written in the form Lot T = Log P/P Q = - K 1 C ... 1.

Where K 1 is a proportionality constant.

The two laws are combined using a new proportionality constant 'a' and written as

log (P/PQ ) = abc ... 1. The ratio of P/P 0 is known as transmittance (T) which is dimensionless quantity. As, 'abc' is a logarithmic quantity, it is a pure number. The above equation can be written as

A - abc ... 1.

Deviations are termed positive and negative depending on the observed curve is above and below the theoretical straight line respectively. According to Kortum and Seiler 3 the Beer's law is fundamentally a limiting law and is valid and obeyed at low concentrations, but the law does not hold good for solutions of higher concentration. The deviations may be attributed to factors, such as reflection of radiation by the test solution 4 , pure solvent, transmission, non-use of monochromatic radiation, florescence or scattering, change of structure of the coloured species with concentration, reaction of electrolytes with the coloured complex when present in large amount, temperature, ionization, association or dissociation of coloured solutes in solution, inert salts when present even in very low concentration due to the influence of electrostatic interactions.

It is still possible to apply spectrophotometry in quantitative analysis with marked success, provided that necessary precautionary measures are taken to control the experimental conditions.

RINGBOM'S PLOT : There is an element of uncertainty in measurements due to the working of the instrument even in the range of

obedience of Beer's law. A small random error in the reading of percent transmittance (T) causes a large relative error in concentration when 'T' is either very small or very large. The practical range of concentration can be determined spectrophotometrically with the help of Ringbom's plot.

In Ringbom's 5 plot, a graph is drawn between per cent absorptance against logarithm of the concentration, where a 'S' shaped or sigmoid curve is obtained. The term absorptance is defined as

Absorptance = 1 - transmittance = 1 - T ...1. % Absorptance = 100 - % T ... 1. Deviation based on Beer's law, lead Ringbom to arrive at the conclusion that the accuracy is the greatest when^P/( ^c/c) reaches a maximum value i.e., at the point of steepest slope (inflection point) of the curve between P and log C. Thus if a system obeys Beer's law, the inflection point occurs at 36.8 % transmittance or 62.2 % absorptance and the corresponding absorbance value is 0.4343. The Ringbom plot has two advantages.

1. It shows at a glance the concentration range in which the analysis error is minimum. This is the concentration range corresponding to the nearly linear portion of the Ringbom plot and

are referred to as sensitive while those with < 1 X 10 3 as

less sensitive. Sensitivity is sometimes expressed in terms of specific absorptivity denoted by 'a' and is given by the expression.

a - --------^ £ - ---------- ... 1.

At. Wt. X 1000 The unit for specific absorptivity 'a' are ml gm“ 1 cm “ 1 and its value corresponds to the absorbance of 1 jaq/ml (lppm) solution of the determined in a cuvette with an optical path length of 1 cm. very often the sensitivity is expressed in terms of sensitivity index (S) given by Sandell 6. According to Sandell, sensitivity is the amount of obsorbing species in microgram per ml. of the solution (1 ppm), with an absorbance of 0.001 for a path length of 1 cm. The units of 'S' are yug cm -2 and is given by

S = 103 /a ... 1.

where 'a' is specific absorptivity.

SELECTIVITY :

A reagent which reacts only with a limited number of elements is considered a selective reagent. To achieve the desired degree of selectivity in analytical work, it is usually necessary to exploit difference in two or more physical and chemical properties. The selectivity of a colour reaction and the

corresponding spectrophotometric method depends on

1. The nature of the reagent 2. The oxidation state of the element 3. The pH of the medium 4. The nature of the reagent and to mask the interfering ions. 5. The temperature.

In dilute mineral acid solution Zr and Hf (also Ti, Th, Sn and Al) form intensely coloured but sparingly soluble layer with alizarin. Insertion of sulphomic group into alizarin confers water solubility to few metal complexes without otherwise affecting the complexation reaction. Thus a change in the structure of the reagent imparts some selectivity.

In the determination of niobium by the thiocyanate method, iron does not interfere if reduced to iron (II). Thus exemplifies achieving selectivity by changing the oxidation state of an interfering element, while chelating agent do not exhibit absolute specificity in their reaction with metal ions. They may exhibit varying degree of selectivity depending upon the experimental conditions. 8-Hydroxy-quinoline (Oxine) forms water insoluble precipitates with about thirty different metal ions. This number can be reduced by controlling the pH of the solution

bathophenanthor line for iron (II) may be mentioned as examples to spectrophotometric specific reagents.

DETERMINATION OF THE COMPOSITION OF THE METAL COMPLEXES :

Spectrophotometry is one of the most powerful tools for elucidating the composition of complex ions in solution and for determining their formation constants due to the fact that quantitative absorption measurements can be performed without fear of disturbing the equilibrium under consideration. The three important methods that are widely employed for this purpose of the metal complexes are

1. Job's continuous variation method
2. Mole ratio method
3. Slope ratio method 1. JOB'S CONTINUOUS VARIATION METHOD : In 1928, Job 8 described a method for determination of the composition of complexes. The complex equilibrium can be represented by the general equation.

M + nL (^) ■> 1 irj" MLn ... 1.

Where M and L represents the metal ion and the reagent with identical formal concentrations are mixed in different volume ratios, keeping the total volume of the mixture constant. The absorbance of each mixture is measured at a

3. SLOP RATIO MTHOD :

suitable wavelength and corrected for any absorbance if no reaction occurred. A plot is then constructed with the volume fraction V M/y M + V L (where V M and VL are the volume of the metal ion solution and the reagent solution respectively) and the corrected absorbance. A curve with a maximum is obtained (or minimum if the complex absorbs less than the reactants). The composition of the complex is then given by the volume fraction ratio.

'M VM

V M + V L V M + V L

corresponding to the maximum or minimum point.

The composition bears a simple relation to 'n 7 and is independent of equilibrium constant if equiformal solutions are used. The position of the maximum depends on 'n 7 as well as on the equilibrium constant 1 if the formalities are not equal. While Job's method gave satisfactory results for several complexes, instances of inconclusive results are reported in the literature7-9. This method is not found generally applicable when more than one complex is formed in the concentration range of study under the experimental conditions. Cooper et al10. suggested a method to establish this fact. According to copper's modified procedure the absorbance is measured at various wavelengths covering the

This method is proposed by Harvey and Manning- •^1 1^ -* o and is particular useful for weak complexes. It is applicable if oly a single complex is formed. The method assumes that the complex formation reaction can be forced to completion in the presence of a large excess of either of the reactants and that Beer's law is followed under these circumstances.

For the reaction mM +nL - —A M^ + L n ...1.

The following equation can be written, when 'c' is present in very large excess .......

[Mm Ln] * F M /m ...1.

If Beer's law is obeyed A m = £b [Mm Ln] =£b F M /m ...1. and plot of 'A' with respect to F M will be linear. The slope of the lines S M = £b/m when 'M' is very large with respect to L.

[Mm Ln] 1 ---- 1 F L /n ... 1. and Al = C b [M m Ln ] =? € b FL /n ... 1.

The plot of 'A' against F L will be linear •

The combining ratio between L and M is obtained from the ratio of these slopes £b/m S m /Sn = ----------£b/n = n/m ... 1.

EVALUATION OF STABILITY CONSTANT OF A METAL COMPLEX :

The stability constant of the complex Ln given by the following reaction can be evaluated from the spectrophotometric results obtained in Job's continuous variation method.

mM + nL L n ...1. by using the following mathematical relation

---

m nnn [ (I-A/A m )] m+n [C]m+n — 1 ... 1. where Ajjj = Absorbance corresponding to the point of intersection of the extrapolated lines A = Observed absorbance at concentration 'c' c = Concentration corresponding to the point of intersection. = Stability constant

Ajjj— A = = degree of dissociation ...1.

quantitative evaluation of derivative plots.

The first, second etc. derivatives of the absorption spectrum of an analyte is defined as the first, second etc. derivative of the absorbance as a function of wave number or wave length. The first or the second derivative is easily accessible instrumentally. The higher derivative are calculated on the basis of computer generated functions. The first derivative spectrum is useful for the determination of the components more accurately in presence of matrix component. It is also useful for the multicomponent analysis or identification of derivative with high spectral similarity. Thus the first or the second order derivatives can eliminate unwanted effects such as various scatterings, instrumental effect, differences by replacing cells of base line.

Assuming that the Beer's - Lambert's law are obeyed for the Zero order spectrum, various amplitudes of the derivative are proportional to analyte concentration in a similar way as is the absorbance of the primary absorption peak.

The first and second derivatives of Beer'slaw 1 dl de dA/d A = -0.434 -- ------ I d A ---^ dk^ Cl

1

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McUfular Absorption Sp<cUtncopy U V/VIS, April 1985, by La<juu, k , Mclliuiih W. 11. »nd Zander, M J