**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

(3) the polychromatic radiation

__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 *A*_{280} values are found to be 0.43 and 0.58. The published
Îµ_{280} 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 a_{1}_{ Î»1} /a_{2}_{ Î»1 }maximum and

a_{2}_{ Î»2} /a_{1}_{ 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»1c_{1} + a_{2}_{ Î»1 } c_{2}
……(i)

• A2 = a 1 Î»2 c_{1} + a_{2}_{ Î»2 } c_{2}
……..(ii)

Where c_{1 }and
c_{2} are the concentrations of component 1 and 2 respectively

• By
solving the above simultaneous equations, c_{1 }and c_{2} 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

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