Instrumental Methods of Analysis | Chemistry for EmSAT Achieve PDF Download

 Page 1


  
 
INSTRUMENTAL METHODS OF ANALYSIS 
 
 
 
 
 
3.1 INTRODUCTION 
 
Analytical instrumentation plays an important role in the production and evaluation of new 
products and in the protection of consumers and environment. It is used in checking the quality 
of raw materials such as substances used in integrated circuit chips, detection and estimation of 
impurities to assure safe foods, drugs, water and air, process optimization and control, quality 
check of finished products and research and development. Most of the modern instruments are 
microprocessor/computer controlled with user friendly software for collection of data, analysis 
and presentation. 
 
This chapter deals with the different types of analytical instrumental methods that find use in a 
variety of industries. These include molecular spectroscopic methods, thermal methods of 
analysis, X-ray diffraction, scanning electron microscope and sensors. 
 
3.2 SPECTROSCOPY 
 
It is the study of interaction of electromagnetic radiation with matter consisting of atoms and 
molecules. When a substance is irradiated with electromagnetic radiation, the energy of the 
incident photons may be transferred to atoms and molecules raising their energy from ground 
state level to excited state. This process is known as absorption and the resultant spectrum is 
known as absorption spectrum. The process of absorption can occur only when the energy 
difference between the two levels E is exactly matched by the energy of the incident photons as 
given by the equation 
 
E = h? = hc/? 
 
where h is Planck’s constant(6.63 x 10
-34
Js), ? is the frequency of incident radiation, c is the 
velocity of light and ? is the wavelength of the incident radiation. The excited state atoms and 
molecules then relax to the ground state by spontaneous emission of radiation. The frequency of  
the radiation emitted depends on E. 
 
The energy changes that occur in atoms and molecules during interaction with different regions 
of electromagnetic radiation are given below. 
 
Radiation 
absorbed 
Energy of the 
radiation 
(J/mole) 
Effect on the 
atoms/molecules 
Applications 
Introduction, absorption of radiation, UV-Visible Spectrophotometer: Instrumentation and 
application, IR Spectrophotometer: Instrumentation and application, Thermal methods of analysis- 
TGA, DTA, DSC, Sensors: Oxygen and Glucose sensor, Cyclic Voltammetry for redox system. 
 
Page 2


  
 
INSTRUMENTAL METHODS OF ANALYSIS 
 
 
 
 
 
3.1 INTRODUCTION 
 
Analytical instrumentation plays an important role in the production and evaluation of new 
products and in the protection of consumers and environment. It is used in checking the quality 
of raw materials such as substances used in integrated circuit chips, detection and estimation of 
impurities to assure safe foods, drugs, water and air, process optimization and control, quality 
check of finished products and research and development. Most of the modern instruments are 
microprocessor/computer controlled with user friendly software for collection of data, analysis 
and presentation. 
 
This chapter deals with the different types of analytical instrumental methods that find use in a 
variety of industries. These include molecular spectroscopic methods, thermal methods of 
analysis, X-ray diffraction, scanning electron microscope and sensors. 
 
3.2 SPECTROSCOPY 
 
It is the study of interaction of electromagnetic radiation with matter consisting of atoms and 
molecules. When a substance is irradiated with electromagnetic radiation, the energy of the 
incident photons may be transferred to atoms and molecules raising their energy from ground 
state level to excited state. This process is known as absorption and the resultant spectrum is 
known as absorption spectrum. The process of absorption can occur only when the energy 
difference between the two levels E is exactly matched by the energy of the incident photons as 
given by the equation 
 
E = h? = hc/? 
 
where h is Planck’s constant(6.63 x 10
-34
Js), ? is the frequency of incident radiation, c is the 
velocity of light and ? is the wavelength of the incident radiation. The excited state atoms and 
molecules then relax to the ground state by spontaneous emission of radiation. The frequency of  
the radiation emitted depends on E. 
 
The energy changes that occur in atoms and molecules during interaction with different regions 
of electromagnetic radiation are given below. 
 
Radiation 
absorbed 
Energy of the 
radiation 
(J/mole) 
Effect on the 
atoms/molecules 
Applications 
Introduction, absorption of radiation, UV-Visible Spectrophotometer: Instrumentation and 
application, IR Spectrophotometer: Instrumentation and application, Thermal methods of analysis- 
TGA, DTA, DSC, Sensors: Oxygen and Glucose sensor, Cyclic Voltammetry for redox system. 
 
?-radiation 
> 10
9
 
Change in nuclear 
configuration 
Used for cancer radiotherapy. 
X- radiation 
10
7
- 10
9
 
Change in core electron 
distribution 
Chemical crystallography, 
qualitative and quantitative 
analysis. 
Ultraviolet 
and Visible 
radiation 
10
5
-10
7
 
Change in valence shell 
electron distribution. 
In qualitative and quantitative 
analysis. 
Infra red rays 
10
3
-10
5 
Change in the vibrational 
and rotational energy 
levels  
Detection of functional groups in 
compounds, calculation of force 
constant, bond length, etc., and in 
quantitative analysis 
Microwave 
radiation 
10-10
3
 
Change in rotational 
energy levels 
Calculation of force constant, 
bond length , bond angle, etc. 
Radio 
frequency 
10
-3
 - 10 
Changes in nuclear and 
electron spin in the 
presence of external 
magnetic field. 
Detection of proton environment 
and paramagnetic ions. 
  
3.2.1 UV-Visible spectroscopy 
 
The UV –Visible spectroscopy is also known as electronic absorption spectroscopy as molecules 
absorb radiation resulting in transitions between electronic energy levels. Absorption of radiation 
in the UV (wavelength range 190-400nm) and visible (wavelength 400–800nm) regions result in 
transitions between electronic energy levels. The principle of electronic transitions and the 
instruments required to record electronic transitions are common for both the regions. The 
electronic transition occurs based on Franck Condon principle which states that electronic 
transition takes place so rapidly that a vibrating molecule does not change its inter-nuclear 
distance appreciably during the transition. 
 
Polyatomic organic molecules, according to molecular orbital theory, have valence shell 
electronic energy structure as shown in Fig 3.1. 
 
 
 
 
 
 
 
Page 3


  
 
INSTRUMENTAL METHODS OF ANALYSIS 
 
 
 
 
 
3.1 INTRODUCTION 
 
Analytical instrumentation plays an important role in the production and evaluation of new 
products and in the protection of consumers and environment. It is used in checking the quality 
of raw materials such as substances used in integrated circuit chips, detection and estimation of 
impurities to assure safe foods, drugs, water and air, process optimization and control, quality 
check of finished products and research and development. Most of the modern instruments are 
microprocessor/computer controlled with user friendly software for collection of data, analysis 
and presentation. 
 
This chapter deals with the different types of analytical instrumental methods that find use in a 
variety of industries. These include molecular spectroscopic methods, thermal methods of 
analysis, X-ray diffraction, scanning electron microscope and sensors. 
 
3.2 SPECTROSCOPY 
 
It is the study of interaction of electromagnetic radiation with matter consisting of atoms and 
molecules. When a substance is irradiated with electromagnetic radiation, the energy of the 
incident photons may be transferred to atoms and molecules raising their energy from ground 
state level to excited state. This process is known as absorption and the resultant spectrum is 
known as absorption spectrum. The process of absorption can occur only when the energy 
difference between the two levels E is exactly matched by the energy of the incident photons as 
given by the equation 
 
E = h? = hc/? 
 
where h is Planck’s constant(6.63 x 10
-34
Js), ? is the frequency of incident radiation, c is the 
velocity of light and ? is the wavelength of the incident radiation. The excited state atoms and 
molecules then relax to the ground state by spontaneous emission of radiation. The frequency of  
the radiation emitted depends on E. 
 
The energy changes that occur in atoms and molecules during interaction with different regions 
of electromagnetic radiation are given below. 
 
Radiation 
absorbed 
Energy of the 
radiation 
(J/mole) 
Effect on the 
atoms/molecules 
Applications 
Introduction, absorption of radiation, UV-Visible Spectrophotometer: Instrumentation and 
application, IR Spectrophotometer: Instrumentation and application, Thermal methods of analysis- 
TGA, DTA, DSC, Sensors: Oxygen and Glucose sensor, Cyclic Voltammetry for redox system. 
 
?-radiation 
> 10
9
 
Change in nuclear 
configuration 
Used for cancer radiotherapy. 
X- radiation 
10
7
- 10
9
 
Change in core electron 
distribution 
Chemical crystallography, 
qualitative and quantitative 
analysis. 
Ultraviolet 
and Visible 
radiation 
10
5
-10
7
 
Change in valence shell 
electron distribution. 
In qualitative and quantitative 
analysis. 
Infra red rays 
10
3
-10
5 
Change in the vibrational 
and rotational energy 
levels  
Detection of functional groups in 
compounds, calculation of force 
constant, bond length, etc., and in 
quantitative analysis 
Microwave 
radiation 
10-10
3
 
Change in rotational 
energy levels 
Calculation of force constant, 
bond length , bond angle, etc. 
Radio 
frequency 
10
-3
 - 10 
Changes in nuclear and 
electron spin in the 
presence of external 
magnetic field. 
Detection of proton environment 
and paramagnetic ions. 
  
3.2.1 UV-Visible spectroscopy 
 
The UV –Visible spectroscopy is also known as electronic absorption spectroscopy as molecules 
absorb radiation resulting in transitions between electronic energy levels. Absorption of radiation 
in the UV (wavelength range 190-400nm) and visible (wavelength 400–800nm) regions result in 
transitions between electronic energy levels. The principle of electronic transitions and the 
instruments required to record electronic transitions are common for both the regions. The 
electronic transition occurs based on Franck Condon principle which states that electronic 
transition takes place so rapidly that a vibrating molecule does not change its inter-nuclear 
distance appreciably during the transition. 
 
Polyatomic organic molecules, according to molecular orbital theory, have valence shell 
electronic energy structure as shown in Fig 3.1. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Fig.3.1 Valence shell electronic structure of polyatomic molecules and possible electronic 
transitions 
 
In most of the organic molecules, the bonding and non-bonding molecular orbitals are filled, and 
the anti-bonding orbitals are vacant. The various electronic transitions that can take place include 
(i) s-s
*
 (ii) n-s
* 
(iii) p-p
*
and (iv) n-p
*
. The relative energy changes involved in these transitions 
are in the increasing order n-p
*
< p-p
*
~ n-s
*
<< s-s
*
.  
 
n-p
*
, p-p
*
and
 
n-s
*
 transitions account for the absorption in 200 – 800 nm region of the 
electromagnetic spectrum. On the other hand, s-s
*
 transition occur in vacuum UV region below 
200 nm. 
 
3.2.2 Laws of Absorption 
 
The fraction of the photons absorbed by the molecule at a given frequency depends on 
 
1. The nature of the absorbing molecules 
2. The concentration of the molecules (C). The higher the molar concentration, the higher is the 
absorption of photons. 
3. The length of the path of the radiation through the substance or the thickness of the absorbing 
medium. Larger the path length (in cm), larger is the number of molecules exposed and 
greater is the probability of photons being absorbed. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Page 4


  
 
INSTRUMENTAL METHODS OF ANALYSIS 
 
 
 
 
 
3.1 INTRODUCTION 
 
Analytical instrumentation plays an important role in the production and evaluation of new 
products and in the protection of consumers and environment. It is used in checking the quality 
of raw materials such as substances used in integrated circuit chips, detection and estimation of 
impurities to assure safe foods, drugs, water and air, process optimization and control, quality 
check of finished products and research and development. Most of the modern instruments are 
microprocessor/computer controlled with user friendly software for collection of data, analysis 
and presentation. 
 
This chapter deals with the different types of analytical instrumental methods that find use in a 
variety of industries. These include molecular spectroscopic methods, thermal methods of 
analysis, X-ray diffraction, scanning electron microscope and sensors. 
 
3.2 SPECTROSCOPY 
 
It is the study of interaction of electromagnetic radiation with matter consisting of atoms and 
molecules. When a substance is irradiated with electromagnetic radiation, the energy of the 
incident photons may be transferred to atoms and molecules raising their energy from ground 
state level to excited state. This process is known as absorption and the resultant spectrum is 
known as absorption spectrum. The process of absorption can occur only when the energy 
difference between the two levels E is exactly matched by the energy of the incident photons as 
given by the equation 
 
E = h? = hc/? 
 
where h is Planck’s constant(6.63 x 10
-34
Js), ? is the frequency of incident radiation, c is the 
velocity of light and ? is the wavelength of the incident radiation. The excited state atoms and 
molecules then relax to the ground state by spontaneous emission of radiation. The frequency of  
the radiation emitted depends on E. 
 
The energy changes that occur in atoms and molecules during interaction with different regions 
of electromagnetic radiation are given below. 
 
Radiation 
absorbed 
Energy of the 
radiation 
(J/mole) 
Effect on the 
atoms/molecules 
Applications 
Introduction, absorption of radiation, UV-Visible Spectrophotometer: Instrumentation and 
application, IR Spectrophotometer: Instrumentation and application, Thermal methods of analysis- 
TGA, DTA, DSC, Sensors: Oxygen and Glucose sensor, Cyclic Voltammetry for redox system. 
 
?-radiation 
> 10
9
 
Change in nuclear 
configuration 
Used for cancer radiotherapy. 
X- radiation 
10
7
- 10
9
 
Change in core electron 
distribution 
Chemical crystallography, 
qualitative and quantitative 
analysis. 
Ultraviolet 
and Visible 
radiation 
10
5
-10
7
 
Change in valence shell 
electron distribution. 
In qualitative and quantitative 
analysis. 
Infra red rays 
10
3
-10
5 
Change in the vibrational 
and rotational energy 
levels  
Detection of functional groups in 
compounds, calculation of force 
constant, bond length, etc., and in 
quantitative analysis 
Microwave 
radiation 
10-10
3
 
Change in rotational 
energy levels 
Calculation of force constant, 
bond length , bond angle, etc. 
Radio 
frequency 
10
-3
 - 10 
Changes in nuclear and 
electron spin in the 
presence of external 
magnetic field. 
Detection of proton environment 
and paramagnetic ions. 
  
3.2.1 UV-Visible spectroscopy 
 
The UV –Visible spectroscopy is also known as electronic absorption spectroscopy as molecules 
absorb radiation resulting in transitions between electronic energy levels. Absorption of radiation 
in the UV (wavelength range 190-400nm) and visible (wavelength 400–800nm) regions result in 
transitions between electronic energy levels. The principle of electronic transitions and the 
instruments required to record electronic transitions are common for both the regions. The 
electronic transition occurs based on Franck Condon principle which states that electronic 
transition takes place so rapidly that a vibrating molecule does not change its inter-nuclear 
distance appreciably during the transition. 
 
Polyatomic organic molecules, according to molecular orbital theory, have valence shell 
electronic energy structure as shown in Fig 3.1. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Fig.3.1 Valence shell electronic structure of polyatomic molecules and possible electronic 
transitions 
 
In most of the organic molecules, the bonding and non-bonding molecular orbitals are filled, and 
the anti-bonding orbitals are vacant. The various electronic transitions that can take place include 
(i) s-s
*
 (ii) n-s
* 
(iii) p-p
*
and (iv) n-p
*
. The relative energy changes involved in these transitions 
are in the increasing order n-p
*
< p-p
*
~ n-s
*
<< s-s
*
.  
 
n-p
*
, p-p
*
and
 
n-s
*
 transitions account for the absorption in 200 – 800 nm region of the 
electromagnetic spectrum. On the other hand, s-s
*
 transition occur in vacuum UV region below 
200 nm. 
 
3.2.2 Laws of Absorption 
 
The fraction of the photons absorbed by the molecule at a given frequency depends on 
 
1. The nature of the absorbing molecules 
2. The concentration of the molecules (C). The higher the molar concentration, the higher is the 
absorption of photons. 
3. The length of the path of the radiation through the substance or the thickness of the absorbing 
medium. Larger the path length (in cm), larger is the number of molecules exposed and 
greater is the probability of photons being absorbed. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Lambert’s law 
 
When a monochromatic beam of radiation passes through an absorbing medium, the intensity of 
the transmitted radiation decreases exponentially with the thickness of the absorbing medium. 
The law is expressed as  
 
I
t
 = I
o
10 
–kx
                                                 (1) 
 
I
t
  and I
o
 are the intensities of the transmitted and incident beams of radiations, x is the thickness 
of the absorbing medium and k is a constant. 
 
 
 
Beer’s law 
 
When a monochromatic beam of radiation passes through an absorbing medium, the intensity of 
the transmitted radiation decreases exponentially with the concentration of the absorbing 
substance. The law is expressed as  
 
I
t
 = I
o
10 
– k’C                             
                          (2) 
 
where C is the molar concentration of the absorbing substance and k’ is another constant. 
 
Beer-Lambert’s law 
 
When a beam of monochromatic radiation is passed through a transparent absorbing medium, the 
decrease in the intensity of radiation is directly proportional to the concentration of the absorbing 
substance and the thickness of the absorbing medium. 
 
-dI = kC dx 
                                                         I 
 
where I is the intensity of radiation, C is the molar concentration of the absorbing species, x is 
the thickness of the absorbing medium and k is the proportionality constant. If I
o
 is the intensity 
of incident radiation and I is the intensity of transmitted radiation, after passing through a path 
length (thickness) of l cm in the solution, and upon integrating the above equation, between the 
limits I = I
o
 when x= 0 and I= I at x= l, we get, 
?
  
 
 
 
  
   ?  
 
 
 
         
     ln 
 
  
 = - kCl   
 
2.303 log
 
  
  = -kCl 
 
Page 5


  
 
INSTRUMENTAL METHODS OF ANALYSIS 
 
 
 
 
 
3.1 INTRODUCTION 
 
Analytical instrumentation plays an important role in the production and evaluation of new 
products and in the protection of consumers and environment. It is used in checking the quality 
of raw materials such as substances used in integrated circuit chips, detection and estimation of 
impurities to assure safe foods, drugs, water and air, process optimization and control, quality 
check of finished products and research and development. Most of the modern instruments are 
microprocessor/computer controlled with user friendly software for collection of data, analysis 
and presentation. 
 
This chapter deals with the different types of analytical instrumental methods that find use in a 
variety of industries. These include molecular spectroscopic methods, thermal methods of 
analysis, X-ray diffraction, scanning electron microscope and sensors. 
 
3.2 SPECTROSCOPY 
 
It is the study of interaction of electromagnetic radiation with matter consisting of atoms and 
molecules. When a substance is irradiated with electromagnetic radiation, the energy of the 
incident photons may be transferred to atoms and molecules raising their energy from ground 
state level to excited state. This process is known as absorption and the resultant spectrum is 
known as absorption spectrum. The process of absorption can occur only when the energy 
difference between the two levels E is exactly matched by the energy of the incident photons as 
given by the equation 
 
E = h? = hc/? 
 
where h is Planck’s constant(6.63 x 10
-34
Js), ? is the frequency of incident radiation, c is the 
velocity of light and ? is the wavelength of the incident radiation. The excited state atoms and 
molecules then relax to the ground state by spontaneous emission of radiation. The frequency of  
the radiation emitted depends on E. 
 
The energy changes that occur in atoms and molecules during interaction with different regions 
of electromagnetic radiation are given below. 
 
Radiation 
absorbed 
Energy of the 
radiation 
(J/mole) 
Effect on the 
atoms/molecules 
Applications 
Introduction, absorption of radiation, UV-Visible Spectrophotometer: Instrumentation and 
application, IR Spectrophotometer: Instrumentation and application, Thermal methods of analysis- 
TGA, DTA, DSC, Sensors: Oxygen and Glucose sensor, Cyclic Voltammetry for redox system. 
 
?-radiation 
> 10
9
 
Change in nuclear 
configuration 
Used for cancer radiotherapy. 
X- radiation 
10
7
- 10
9
 
Change in core electron 
distribution 
Chemical crystallography, 
qualitative and quantitative 
analysis. 
Ultraviolet 
and Visible 
radiation 
10
5
-10
7
 
Change in valence shell 
electron distribution. 
In qualitative and quantitative 
analysis. 
Infra red rays 
10
3
-10
5 
Change in the vibrational 
and rotational energy 
levels  
Detection of functional groups in 
compounds, calculation of force 
constant, bond length, etc., and in 
quantitative analysis 
Microwave 
radiation 
10-10
3
 
Change in rotational 
energy levels 
Calculation of force constant, 
bond length , bond angle, etc. 
Radio 
frequency 
10
-3
 - 10 
Changes in nuclear and 
electron spin in the 
presence of external 
magnetic field. 
Detection of proton environment 
and paramagnetic ions. 
  
3.2.1 UV-Visible spectroscopy 
 
The UV –Visible spectroscopy is also known as electronic absorption spectroscopy as molecules 
absorb radiation resulting in transitions between electronic energy levels. Absorption of radiation 
in the UV (wavelength range 190-400nm) and visible (wavelength 400–800nm) regions result in 
transitions between electronic energy levels. The principle of electronic transitions and the 
instruments required to record electronic transitions are common for both the regions. The 
electronic transition occurs based on Franck Condon principle which states that electronic 
transition takes place so rapidly that a vibrating molecule does not change its inter-nuclear 
distance appreciably during the transition. 
 
Polyatomic organic molecules, according to molecular orbital theory, have valence shell 
electronic energy structure as shown in Fig 3.1. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Fig.3.1 Valence shell electronic structure of polyatomic molecules and possible electronic 
transitions 
 
In most of the organic molecules, the bonding and non-bonding molecular orbitals are filled, and 
the anti-bonding orbitals are vacant. The various electronic transitions that can take place include 
(i) s-s
*
 (ii) n-s
* 
(iii) p-p
*
and (iv) n-p
*
. The relative energy changes involved in these transitions 
are in the increasing order n-p
*
< p-p
*
~ n-s
*
<< s-s
*
.  
 
n-p
*
, p-p
*
and
 
n-s
*
 transitions account for the absorption in 200 – 800 nm region of the 
electromagnetic spectrum. On the other hand, s-s
*
 transition occur in vacuum UV region below 
200 nm. 
 
3.2.2 Laws of Absorption 
 
The fraction of the photons absorbed by the molecule at a given frequency depends on 
 
1. The nature of the absorbing molecules 
2. The concentration of the molecules (C). The higher the molar concentration, the higher is the 
absorption of photons. 
3. The length of the path of the radiation through the substance or the thickness of the absorbing 
medium. Larger the path length (in cm), larger is the number of molecules exposed and 
greater is the probability of photons being absorbed. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Lambert’s law 
 
When a monochromatic beam of radiation passes through an absorbing medium, the intensity of 
the transmitted radiation decreases exponentially with the thickness of the absorbing medium. 
The law is expressed as  
 
I
t
 = I
o
10 
–kx
                                                 (1) 
 
I
t
  and I
o
 are the intensities of the transmitted and incident beams of radiations, x is the thickness 
of the absorbing medium and k is a constant. 
 
 
 
Beer’s law 
 
When a monochromatic beam of radiation passes through an absorbing medium, the intensity of 
the transmitted radiation decreases exponentially with the concentration of the absorbing 
substance. The law is expressed as  
 
I
t
 = I
o
10 
– k’C                             
                          (2) 
 
where C is the molar concentration of the absorbing substance and k’ is another constant. 
 
Beer-Lambert’s law 
 
When a beam of monochromatic radiation is passed through a transparent absorbing medium, the 
decrease in the intensity of radiation is directly proportional to the concentration of the absorbing 
substance and the thickness of the absorbing medium. 
 
-dI = kC dx 
                                                         I 
 
where I is the intensity of radiation, C is the molar concentration of the absorbing species, x is 
the thickness of the absorbing medium and k is the proportionality constant. If I
o
 is the intensity 
of incident radiation and I is the intensity of transmitted radiation, after passing through a path 
length (thickness) of l cm in the solution, and upon integrating the above equation, between the 
limits I = I
o
 when x= 0 and I= I at x= l, we get, 
?
  
 
 
 
  
   ?  
 
 
 
         
     ln 
 
  
 = - kCl   
 
2.303 log
 
  
  = -kCl 
 
                                                            log  
  
 
 = 
    
     
   or 
 
                                                            log  
  
 
 
 =  e Cl  (where e = k/2.303) 
 
e is the molar absorptivity or molar extinction coefficient, and logI /I
o 
 = A which is known as 
the absorbance of the material. 
 
A = e C l                                (3) 
 
Thus absorbance A, also known as optical density, is directly proportional to (i) the 
concentration C of the absorbing species and (ii) the path length l and has no units. Eq. (3) is the 
mathematical expression for Lambert’s Beer law. 
 
e is defined as the absorbance of the solution of unit molar concentration (1M) placed in a cell of 
path length one cm. If C is expressed in mol dm
-3
, then the unit for e is dm
3
 mol
-1
 cm
-1
.  
 
Limitations of Beer –Lambert’s law 
 
Beer-Lambert’s law is strictly valid only in dilute solutions. For dilute solutions, a linear 
relationship is exhibited by a plot of absorbance (A) as a function of concentration of the 
absorbing substance (C), as shown in Fig 3.2. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Fig 3.2 Plot of Absorbance versus Concentration 
 
(i) Real deviations occur at higher concentration of the absorbing species. At higher 
concentrations (>10
-3
M), there is a change in the refractive index of the solution.  
(ii) Chemical deviations occur when there is more than one absorbing species present in the 
solution. When the absorbing molecules associate or dissociate in the solution, there is a 
change in the number of absorbing species.   
(iii)Instrumental deviation occurs due to changes in absorptivity of the species as a function of 
instrumental bandwidth. 
 
Transmittance T