Beer Lambert's Law derivation and its limitations, Factors affecting UV-Vis spectroscopy and its applications.

1. MOLECULAR
UV AND
VISIBLE
SPECTROSCOPY
PALLAVI KUMBHAR
MSC PART-I

2. CONTENTS
01 Introduction
02 Derivation of Beer Lambert’s Law
03 Limitations
04 Factors Affecting molecular absorption
05 Applications of Ultraviolet and Visible spectroscopy
06 References

3. INTRODUCTION
 Molecular spectroscopy is the study of absorption of light by molecules.
 The principle of molecular absorption spectroscopy is based on electromagnetic
radiation in the wavelength region of 190 to 800 nm.
 Molecular absorption spectroscopy in the ultraviolet and visible spectral regions is
widely used for the quantitative determination of a large number of inorganic, organic,
and biological species in various laborataries throughout the world.

4. Derivation of
Beer- Lambert’s
Law
Po= Radiation of initial radiant power
P = transmitted power
c = number of moles per litre
b = path length in cm.
n = absorbing atoms, ions, or molecules
S = area of the cross section of the block
dx = infinitesimal thickness
dS = The total projected area of capture surfaces within the section
The ratio of the capture area to the total area is dS/S
Px = power of the beam entering the section
dP = power absorbed within the section
-dP/Px represents the ratio of the average probability for capture.
The term is given a minus sign to indicate that the radiant power P
decreases as it passes through the absorbing region. Thus,
−
𝑑𝑃𝑥
𝑃𝑥
=
𝑑𝑆
𝑆
….(1)

5. dS is the sum of the capture areas for particles within the section; it is
therefore proportional to the number of particles,
dS= adn ….(2)
where dn is the number of particles and a is a proportionality constant,
which can be called the capture cross section. Substituting Equation(2) in
equation(1) and integrating over the interval between 0 and n, we obtain
− Po
P d𝑃𝑥
𝑃𝑥
= 0
n adn
S
When these integrals are evaluated, we find that
−ln
P
𝑃0
=
an
S
After converting to base 10 logarithms and inverting the fraction to change
the sign, we obtain
log
Po
P
=
an
2.303S

6. The cross-sectional area S can be expressed as the
ratio of the volume of the block V in cubic cm to its
length b in cm. Thus,
S =
V
b
cm2
Substitution of this quantity to the above equation
yields
𝑙𝑜𝑔
Po
P
=
anb
2.303V
….(3)
n/V can be converted to moles per litre because the
number of moles is given by
No. of moles =
n particles
6.02x1023particles/mol
therefore c in moles per litre is given by
c =
n
6.02x1023 mol ×
1000cm3/L
Vcm3
n
V
=
c×6.02x1023
1000
mol/L
Combining this relationship with Equation (3) yields
log
Po
P
=
6.02x1023abc
2.303 × 1000
Finally, the constants in this equation can be collected into
a single term ε to give
log
Po
P
= εbc = A
which is known as Beer Lambert’s law.

7. LIMITATIONS
1) Beer Lambert's law shows the absorption behavior of media
containing only low analyte concentrations (usually <0.01M).
Therefore it is a limiting law.
2) At high concentrations (usually >0.01 M), the extent of solute-
solvent interactions, solute-solute interactions, or hydrogen
bonding can affect the analyte environment and its
absorptivity.
3) The extent of interaction depends on concentration. Due to
this, deviations from the linear relationship between
absorbance and concentration occur.
4) Absorptivity depends on the refractive index of the medium.
Therefore if concentration changes, significant alterations in
the refractive index n of a solution arises which causes

8. FACTORS AFFECTING MOLECULAR
ABSORPTION
Common factors that influence the absorption spectrum of a substance include
1) the nature of the solvent
2) the pH of the solution
3) the temperature
4) high electrolyte concentrations and
5) the presence of interfering substances.
The effects of these factors must be known and conditions for the analysis must be
chosen such that the absorbance will not be materially influenced by small uncontrolled
variations in their magnitudes.

9. APPLICATIONS
OF
ULTRAVIOLET &
VISIBLE
SPECTROSCOPY
1. Charge transfer absorption
For quantitative purposes, charge-transfer absorption
is particularly important because molar absorptivities
are unusually large (ε >10,000), which leads to high
sensitivity.
2. Derivative spectroscopy
Concentration measurements of an analyte in the
presence of an interference or of two or more analytes
in a mixture can be made more easily or more
accurately using derivative methods.

10. 1. A charge-transfer complex consists of an electron donor group
bonded to an electron acceptor.
2. When this product absorbs radiation, an electron from the donor
is transferred to an orbital which accepts electron. The excited
state is the product of internal oxidation-reduction process.
3. For eg: The red colour of the iron(III)- thiocyanate complex.
4. In most charge-transfer complexes involving a metal ion, the
metal serves as the electron acceptor. But there are some
exceptions where the ligand is the acceptor and the metal ion is
the donor.
CHARGE TRANSFER ABSORPTION

11. 1. In derivative spectroscopy, spectra are obtained by plotting the
first- or a higher-order derivative of absorbance with respect to
wavelength as a function of wavelength.
2. Applications of derivative spectroscopy in the ultraviolet and
visible regions,
a. Used for qualitative identification of species.
b. Useful for the simultaneous determination of two or more
components in mixtures.
c. Used to determine trace metals in mixtures.
d. Widely applied to pharmaceutical preparations and to
vitamin mixtures.
3. Disadvantage of Derivative spectroscopy.
DERIVATIVE SPRECTROSCOPY

12. REFRENCES
• Principles of Instrumental Analysis by Skoog, Holler and Crouch.
• Images from Google.