**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”.

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__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 __

__λ__

__max in__

Quantitative determinationsQuantitative 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 *A*_{280} values are found to be 0.43 and 0.58. The published

ε_{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

λ_{1} and λ_{2} at which a_{1}_{ λ1} /a_{2}_{ λ1 }maximum and

a_{2}_{ λ2} /a_{1}_{ λ2 }is maximum

• Find

the absorbance of the mixture at λ_{1}

and λ_{2} separately (A1 and A2 respectively)

• A1 = a 1 λ1c_{1} + a_{2}_{ λ1 } c_{2}

……(i)

• A2 = a 1 λ2 c_{1} + a_{2}_{ λ2 } 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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