1. Colorimetry uses the measurement of light absorption to determine the concentration of colored compounds in solution. 2. Lambert's law and Beer's law describe the relationship between light absorption and characteristics of the absorbing medium like concentration and path length. 3. Beer's law states that absorbance remains constant when concentration and path length are changed in inverse proportion, allowing for determination of unknown concentrations.

1. Colorimetry Prof. Jadhav Swapnil S. (BMK)
Introduction: -
The term Colorimetry is originates from the times when the
measurements were done by comparing the colour of the components. In
analytical and physical chemistry, Colorimetry technique is used to determine
the concentration of coloured compounds in solution. Colorimetry analysis is
based on the variation of colour of a system with change in concentration of
some components.
Colorimetry is concerned with the determination of unknown
concentration of a substance by the measurement of relative absorption of the
light w.r.t. a known concentration of the substance. In visual Colorimetry,
white light is used as light source and device used is called colorimeter or
colour comparator. If the photoelectric cell is used to compare colour intensity,
the instrument is called photoelectric colorimeter. (Also called filter
photometer).
The chief advantage of colorimetric method is that they provide simple
means for determining very small quantity of sample. (1 or 2 %)
Theory of colorimetry: -
When a monochromatic or heterogeneous light is incident upon
homogeneous medium, a part of incident light is absorbed, a part is reflected
and remaining is transmitted.
If I0 = intensity of incident light Ia = intensity of absorbed light
Ir = intensity of reflected light It = intensity of transmitted light
Then we can write, I0 = Ia + Ir + It
For comparison cell, Ir is very small and is eliminated for air-glass interface
I0 = Ia + It

2. Lambert's Law:-
“When a beam of monochromatic light passes through a homogeneous
absorbing medium, then the rate of decrease of intensity of the incident light
with thickness of absorbing medium is directly proportional to the intensity of
the incident radiation.”
If, I = intensity of the incident light x = thickness of absorbing medium
dI = Small decrease of intensity of the incident radiation w.r.t small thickness
dx
Then
−𝑑𝐼
𝑑𝑥
α I
−𝑑𝐼
𝑑𝑥
= K.I
𝑑𝐼
𝐼
= -K .dx ----- (1) K= absorption coefficient.
Integrating the eq. (1) between the limits, I =I0 at x = 0 and I = I at x = x we get
I = intensity before interring absorbing medium (intensity of incident light)
I0 = intensity after interring absorbing medium (intensity of transmitted light)
∫
𝑑𝐼
𝐼
𝐼
I0
= -K ∫ 𝑑𝑥
𝑥
0
loge
𝐼
𝐼0
= - K. x
i.e.
𝐼
𝐼0
= e-k.x
I = I0 e-k.x --------- (2)
The Lamberts law is usually represented by eq. (2)
Lambert - Beer's Law: -
“When a beam of monochromatic light passes through a homogeneous
absorbing medium, then the rate of decrease of intensity of the incident light
with thickness of absorbing medium is directly proportional to the intensity of
the incident light as well as to the concentration of solution".
If, I = intensity of the incident light x = thickness of absorbing medium
C = concentration of solution. dI = Small decrease of intensity of the incident
radiation w.r.t small thickness dx
Then,
−𝒅𝑰
𝒅𝒙
α I.c i.e
−𝒅𝑰
𝒅𝒙
= K’.I.c
𝒅𝑰
𝑰
= -K’.c dx --------- (1) K’= molar absorption coefficient.

3. Integrating the eq. (1) between the limits, I =I0 at x = 0 and I = I at x = x we get
I = intensity before interring absorbing medium (intensity of incident light)
I0 = intensity after interring absorbing medium (intensity of transmitted light)
∫
𝑑𝐼
𝐼
𝐼
I0
= -K’ c ∫ 𝑑𝑥
𝑥
0
loge
𝐼
𝐼0
= - K’c x
i.e.
𝐼
𝐼0
= e-k.c.x
I = I0 e-k.c.x --------- (2)
also, loge
𝐼
𝐼0
= - K’c x i.e. 2.303 log10 =
𝐼
𝐼0
= - K’c x
log10
𝐼
𝐼0
=
− K’
2.303
c x i.e. log10
𝐼
𝐼0
= ε c x (
− K’
2.303
= ε )
i.e.
𝐼
𝐼0
= 10ε.c.x
----- (3) or I = I0 eε.c.x --------- (4)
ε = molar extinction coefficient or molar absorptivity or molar absorbance
index.
Note: - from eq. (3) & (4) Beer’s law may be stated as, “When a beam of
monochromatic light passes through a homogeneous absorbing medium, its
absorbance remains constant when the concentration(c) and the thickness (x)
of absorbing medium are changed in an inverse ratio."
Terms used in colorimetry: -
1. Transmittance or transmission (T): -
Transmittance is the fraction of incident light transmitted. Or the ratio of
intensity of transmitted light to the intensity of incident light is called
Transmittance.
T =
𝐼
𝐼0
2. Opacity: -
The reciprocal of transmittance is called opacity.
𝐼0
𝐼
or
1
𝑇
3. Optical density (D) or Extinction (E) or Absorbance (A): -
D = E = A = log
𝐼0
𝐼
= log
1
𝑇
= ε.c.x

4. 4. Extinction coefficient (absorbance index) (a): -
Extinction coefficient is the optical density for unit path length.
Or Extinction coefficient is the reciprocal of thickness (x) required to reduce
the light to (1/10th
) of its intensity.
a = D/x or I = I0 10-a.x
5. Specific Extinction coefficient (absorbancy index) or (absorptivity)(Es):
Specific Extinction coefficient is the optical density per unit path length and
unit concentration.
Es = D/c.x or I = I0 10-Es.c.x
6. Molar Extinction coefficient (molar absorptivity index) or (absorptivity)(ε): -
Molar Extinction coefficient is the Specific Extinction coefficient for unit path
length and unit concentration.
ε = D/c.x
Application of Beer’s law: -
1. C1 & C2 are concentrations of two sample having thickness x1 & x2
respectively and same colour intensity. We can write
I1 = I2 => I0 10-ε.c1.x1 = I0 10-ε.c2.x2 i.e. C1 x1 = C2 x2 (system is optically balanced)
From this ,
i) we investigate the validity of Beer’s law by varying C1 & C2.
ii) we can determine an unknown concentration C2 comparing with known
concentration C1 .
2. When spectrophotometer is used, I/I0 is found directly at known x. By
varying x and c verify Lambert’s-Beer’s law and ε may be calculated. Thus
unknown concentration cx is calculated as
cx =
log(𝐼/𝐼0)
𝜀.𝑥
3. Beer’s law is used to determine the concentration of substance in a solution
by making use of absorbance of the substance.

5. Deviation from Beer’s law: -
Beer’s law may not holds good under following condition.
i. large amount of electrolyte may affect the absorption and extinction
coefficient.
ii. Discrepancies are observed when colour solutes dissociates or associates in
the solution.
iii. Discrepancies are observed when monochromatic light is not used.
iv. Discrepancies are observed when temperature is not kept constant.
v. when the coloured compounds are kept long time, their colour decomposes
and discrepancies are observed.
vi. Scattering of light due to particles in the sample.
vii. Fluorescence or phosphorescence of the sample.
viii. Chemical reactions caused by absorption of light. (E.g. photolysis,
dimerization.)
ix. Shift in chemical equilibrium and change in PH
as a function of
concentration.
x. Stray light.
Classification of methods of colour measurement or comparison: -
There are several methods for colour measurement. Standard series
method, Duplication method, Dilution method, Balancing method,
Photoelectric photometer method, Spectrophotometer method
Photoelectric photometer method (single photoelectric colorimeter):
Photoelectric colorimeter divided into two classes i.e. one cell and two
cell instrument.
* One cell photoelectric colorimeter:-
Essential parts- i) A light source ii) A light filter iii) A container for the
solution. iv) Photocell (Barrier-layer photocell) v) Galvanometer.
i) A light source: -

6. 2-6 volt lamp operated by battery or A.C. main is used as light source.
(sun light, arc light, mercury vapour lamp or discharge tube can also be used.)
ii) A light filter: - (monochromator)
Monochromator give light of suitable wavelength. It consist of filter or
prism. Filter is coloured glass or coloured gelatine coated glass. The best filter
is one which gives maximum absorption for given concentration of solution.
Now a day’s interference filters are used. These filters are composed of two
highly reflecting but partially transmitting films of metal like silver.
iii) A container for the solution (Cuvete): -
The cells or cuvettes are rectangular or cylindrical vessels with accurate
dimensions.
For visible light, glass vessels are used. For UV light, quartz vessels are used.
iv) A Barrier-layer photocell (photovoltaic or photronic cell): -
i. It consists of an iron metal base plate (A) on which a thin layer of selenium
(B) is deposited.
ii. Selenium layer is covered by a transparent gold metal layer (D) except
mechanically strengthened portion (E)called collecting ring.
iii. The underside of the metal base plate is covered by a non-oxidizing metal.
iv. When light passing through the gold metal layer fall upon the selenium
layer. Electrons are released from selenium which penetrates a hypothetical
barrier layer (C) giving negative charge to gold metal layer (D). I.e. collecting
ring acquires negative polarity while metal base plate acquires positive polarity.
Hence this formed cell is connected to a galvanometer.

7. v. Photovoltaic cells operate without the use of battery. They are highly
sensitive, portable and cheap. They have considerable temperature coefficient.
V) Galvanometer: -
The response from the photocell is measured b means of galvanometer.
* Schematic representation of a single cell photoelectric colorimeter: -
Here a light from the source is passes through collimating lens for
getting a parallel beam which is then passes through a suitable filter to give a
light of particular wavelength. This light is passes through a solvent is received
by the photocell which produces a deflection in galvanometer.
To determine the unknown concentration, series of reading of standards
are taken. These reading are then plotted against concentration and from the
graph unknown concentration can be determined.

8. B) Spectrophotometer method (single beam direct reading
Spectrophotometer): -
Essential parts of Spectrophotometer are- i. Light source. ii. Monochromator.
iii. Cuvette. iv. Galvanometer.
Instrumental Layout: -
Working: -
1. The light source is focused on entrance slit (D) by condensing mirror (B) and
diagonal mirror (C).
2. The light is then following n prism (F) through collimating mirror (E).
3. Prism (monochromator) divides light into its different wavelength and
reflects towards slit (D) through collimating mirror (E).
4. The light with selected wavelength is passed through cuvette (G) and
photocell (H), which is connected to meter (M).
5. For visible & near UV region, source is Tungsten-halogen lamp. Far UV
region, source is deuterium lamp. In modern instrument prism (F) is replaced
by diffraction greeting.
Determination of unknown concentration by using concentration-
absorption plot: -
The response of photocell is measured by
micro-ammeter in terms of % absorbance
or % transmittance. But for quantitative
measurement, % absorbance is more convenient.
Hence, we plot a graph of % absorbance vs.
concentration and determine the unknown
concentration.