# Limitations of Beer Lambert Law and Quantitative methodology - Instrumental Methods of Analysis B. Pharma 7th Semester

Limitations of Beer Lambert Law and Quantitative methodology

Objectives

After this session students will be able to

Discuss the limitations of Beer – Lambert law

Classify the deviations from Beer’s law

Identify the significance of isosbestic point

Explain the quantitative methodology of UV spectrophotometry

Apply  the  principles of quantitative methodology

Limitations of the Beer-Lambert law

The linearity of the Beer-Lambert law is limited by chemical and instrumental factors. Causes of nonlinearity include:

• Deviations in absorption coefficients at high concentrations (>0.01M) are due to electrostatic interactions between molecules in close proximity

• Interaction with solvent: hydrogen bonding

• scattering of light due to particulates in the sample

• fluoresecence or phosphorescence- a positive deviation in % T and negative deviation for A

• Changes in refractive index at high analyte concentration

• Shifts in chemical equilibria as a function of concentration

• Non-monochromatic radiation, deviations can be minimized by using a relatively flat part of the absorption spectrum such as the maximum of an absorption band

• Stray light

Deviations from Beer’s Law

Beer's law is subjected to certain real and apparent deviations.

Real deviations are most usually encountered in relatively more concentrated solutions of the absorbing compound (>0,01 M). These deviations are due to interactions between the absorbing species and to alterations of the refractive index of the medium.

Most common are the apparent deviations. These deviations are due to:

(1)    chemical reasons arising when the absorbing compound, dissociates, associates, or reacts with a solvent to produce a product having a different absorption spectrum,

(2)    the presence of stray radiation, and

isosbestic point

isosbestic point is a specific wavelength, wavenumber or frequency at which the total absorbance of a sample does not change during a chemical reaction or a physical change of the sample. The word derives from two Greek words: "iso", meaning "equal", and "sbestos", meaning "extinguishable".[

Isosbestic point of Bromocresol green

Quantitative methodology

Spectrophotometry is a valuable tool in quantitative analysis. Generally, these analysis procedures include the following steps:

A series of solutions with known concentrations are used to measure absorbance of the analyte and prepare a calibration plot (Beer-Lambert law plot).

The absorbance is measured for the solution of unknown concentration.

The unknown concentration is determined by using the calibration plot.

Absorption Maxima

Each substance has characteristic absorption Maxima

Absorption maxima, also known as Î»max , are the wavelengths corresponding to peak absorbance values

These values are useful for both quantitative as  well as qualitative analysis

For quantitative estimations Î»max values are selected

Reasons for selection of Î»max in Quantitative determinations

Interference of impurities is minimum

The sensitivity is highest

The error will be minimum at Î»max

The concentration range over which Beer’s law is obeyed will be widest at Î»max

A case study of UV determination

Imagine that a pharmacist finds the labels on two insulin prescriptions have fallen off the bottles. To conserve costs and not waste the medication, the pharmacist prepares samples by precisely diluting 1.000 Î¼L from each vial to 10.000 ml water. With a 1.000 cm cuvette and the spectrophotometer set to detect at a wavelength of 280 nm, the pharmacist measures the absorbance of each sample. The A280 values are found to be 0.43 and 0.58. The published Îµ280 for insulin in aqueous solution is 5,510 L/mol•cm, the pharmacist can now determine the unknown concentration of each insulin vial. A basic application of the Beer-Lambert law followed by a M1V1 = M2V2 calculation can solve the problem.

Quantitative determinations of two component systems

Simultaneous equations method

Consider a mixture of two components

Obtain spectra of component 1 and 2 and overlay

Find Î»1 and Î»2 at which a1 Î»1 /a2 Î»1 maximum and

a2 Î»2 /a1 Î»2 is maximum

Find the absorbance of the mixture at Î»1 and Î»2  separately (A1 and A2 respectively)

A1 = a 1 Î»1c1 + a2 Î»1  c2   ……(i)

A2 = a 1 Î»2 c1 + a2 Î»2  c2  ……..(ii)

Where c1 and c2 are the concentrations of component 1 and 2 respectively

By solving the above simultaneous equations, c1 and c2 can be determined.

Summary

The linearity of the Beer-Lambert law is limited by chemical and instrumental factors

Beer's law is subjected to certain real and apparent deviations.

Chemical deviations  due to inter convertible substances can be prevented by selecting isosbestic point

Absorption maxima are useful for quantitative determinations

Two components of a mixture can be simultaneously determined by UV spectrophotometry