Engineering Chemistry S Datta

520 ENGINEERING CHEMISTRY
or – ln I t
= k 1
b – ln I 0
or ln I 0
It
= k 1
b
k b 1
or log I 0
10
=
It
2303 .
where, log 10
I 0
/I t
is called the absorbance (A).
Absorbance is reciprocal of common logarithms of transmittance.
F
A = log I 1
0 I
10
= log
I 10 HG
T
t K J = – log 10
T = 2 – log (% T).
Beer in 1852 put forward another relationship which is between absorbance and
concentration which is mathematically expressed as:
log I 0
10
It
Beer’s law is defined as:
= k 2 C
2.
303
The intensity of a beam of parallel monochromatic radiation decreases
exponentially with the number of absorbing molecules. It may be stated also as: the
absorbance is proportional to the concentration.
The combination of these two laws leads to Beer–Lambert’s law, which is mathematically
expressed as:
I0
A = log 10
= abc in which the proportionality constants k
I
1
/2.303 and k 2
/ 2.303 are
t
combined to the single constant ‘a’ which is known as absorptivity. The value of ‘a’ as well as
its name depend on units of concentration. When ‘c’ is in moles litre –1 , ‘a’ is called molar
absorptivity, formerly known as molar extinction coefficient (ε)
then the equation takes the form:
A = ε.b.c.
When the absorbance is measured for 1% (w/v) solution in a 1 cm cell, then the equation
takes the form
1%
A = A 1cm.b.c.
1%
A 1cm is known as specific absorbance.
Colorimetric analysis is also based on Beer–Lambert’s law. Here the light used is
visible one and coloured samples are analysed.
Infrared Spectroscopy
When infrared light is passed through a sample of an organic compound, some of the
frequencies are transmitted through the sample without being absorbed. If we plot the percent
absorbance or percent transmittance against frequency the result is infrared (IR) spectrum.
Molecular vibration
At ordinary temperatures organic molecules are in a constant state of vibration each
bond having its characteristic stretching and bending frequency and being capable of absorbing
light of that frequency. The vibrations of two atoms joined together by a chemical bond can be
compared to the vibrations of two balls joined by a spring, using this analogy we can justify
several frequencies of infrared spectrum.