# 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

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 λmax ,
are the wavelengths corresponding to peak absorbance values

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

For
quantitative estimations λmax
values are selected

Reasons for
selection of
λmax in
Quantitative determinations

Interference
of impurities is minimum

The
sensitivity is highest

The
error will be minimum at λmax

The
concentration range over which Beer’s law is obeyed will be widest at λmax

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 μL 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
ε280 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
λ1 and λ2 at which a1 λ1 /a2 λ1 maximum and

a2 λ2 /a1 λ2 is maximum

Find
the absorbance of the mixture at λ1
and λ2  separately (A1 and A2 respectively)

A1 = a 1 λ1c1 + a2 λ1  c2
……(i)

A2 = a 1 λ2 c1 + a2 λ2  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