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chapter two
Introduction to chromatographic
separation
Instrumental analysis lecture note by Dawit
A
1
• Historical background
• Chromatography means "to show with colors."
It was the Russian botanist Mikhail
Semyonovich (1872-1919) who invented the
first chromatography technique in 1900,
during his research on chlorophyll. He used a
liquid-adsorption column containing calcium
carbonate to separate plant pigments.
Instrumental analysis lecture note by Dawit
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• Chromatography -- what does it mean?
• to write with colors -- literally translated from
its Greek roots chroma and graphein.
Chromatography has since developed into a
laboratory tool for the separation and
identification of compounds.
• Although color usually no longer plays a role in
the process, the same principles of
chromatography still apply.
Instrumental analysis lecture note by Dawit
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• Why use chromatography? The key here is
separation. But what is the importance of
separation in the lab?
• Separation of chemical components is vital in
any type of chemical analysis.
• When trying to identify an unknown
substance, the sample must first be simplified
as much as possible into its constituent
compounds.
• The unknown can then be characterized by
individual identification of its parts.
Instrumental analysis lecture note by Dawit
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• This does not imply that the separated
chemical components are recovered after the
separation and analyzed.
• Separated compounds are compared to
known standards.
• As with most chemical exploration, it is
important to have an idea of what compounds
are being searched
Instrumental analysis lecture note by Dawit
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Components or terms of chromatography
Mobile phase is the phase which moves in a definite direction.
It may be a liquid (LC), a gas (GC), or a supercritical fluid
(supercritical-fluid chromatography, SFC).
The mobile phase consists of the sample being
separated/ analyzed and the solvent that moves the
sample through the column.
In the case of high performance liquid chromatography
(HPLC) the mobile phase consists of a non-polar solvent(s)
such as hexane in normal phase or polar solvents in
reverse phase chromatography and the sample being
separated.
The mobile phase moves through the chromatography
column (the stationary phase) where the sample
interacts with the stationary phase and is separated
Instrumental analysis lecture note by Dawit
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con
• Q? Which kind of phases can be used as mobile phase?
 Answer: gases and liquids, because gases and liquids are
fluids that can flow easily but solid is not fluid which can‟t be
used to transport sample.
• Stationary phase is the substance which is fixed in place for
the chromatography procedure. Examples include the silica
layer in thin layer chromatography.
• Q? Which kinds of phases can be used for stationary phase?
 Answer: liquid and solid. Liquid can be used as stationary
phase by immobilizing the liquid on a solid surface.
 Gases can‟t be used for stationary phase preparation
because it is difficult to fix the gas on fixed space.
Instrumental analysis lecture note by Dawit
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con
Note:
 In a chromatographic separation the mobile and stationary
phase must have low interaction.
 Always when we select a mobile phase we should consider the
following:
 The mobile phase must be the least eluted species.
 The mobile phase could not wash the stationary phase.
 Supporting medium: a solid surface on which the stationary
phase is bound or coated
 A chromatogram is the visual output of the chromatograph.
 In the case of an optimal separation, different peaks or
patterns on the chromatogram correspond to different
components of the separated mixture.
Instrumental analysis lecture note by Dawit
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2.2. Types (Classification) of Chromatography
 There are a number of different kinds of chromatography,
which differ in the mobile and the stationary phase used.
 Chromatography can be classified into groups based on
several properties. Here in this paper we will classify
chromatography based on three criteria
 1. Classification of chromatography based on the physical
means by which the stationary phase and mobile phase are
brought together.
 In this classification, chromatography is classified as:
A. Column Chromatography
 Column chromatography is a separation technique in which
the stationary phase is within a tube.
 The particles of the solid stationary phase or the support
coated with a liquid stationary phase may fill the whole inside
volume of the tube (packed column)
Instrumental analysis lecture note by Dawit
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 or be concentrated on or along the inside tube wall leaving an
open, unrestricted path for the mobile phase in the middle
part of the tube (open tubular column).
• Differences in rates of movement through the medium are
calculated to different retention times of the sample and the
mobile phase moves in the column either due to gravity or by
the force of pump.
B. Planar Chromatography
Planar chromatography is a separation technique in
which the stationary phase is present as or on a plane.
The plane can be a paper, serving as such or impregnated
by a substance as the stationary bed (paper
chromatography) or a layer of solid particles spread on a
support such as a glass plate (thin layer chromatography
Instrumental analysis lecture note by Dawit
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con
Different compounds in the sample mixture travel different
distances according to how strongly they interact with the
stationary phase as compared to the mobile phase. T
the specific Retention factor (Rf) of each chemical can be used
to aid in the identification of an unknown substance.
In this technique the mobile phase is transported across the
stationary phase by a capillary action.
This type of chromatography can be divided into:
Paper Chromatography
Paper chromatography is a technique that involves placing a
small dot or line of sample solution onto a strip of
chromatography paper
Instrumental analysis lecture note by Dawit
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 The paper is placed in a jar containing a shallow layer of
solvent and sealed.
 As the solvent rises through the paper, it meets the sample
mixture which starts to travel up the paper with the solvent.
This paper is made of cellulose, a polar substance, and the
compounds within the mixture travel farther if they are non-
polar.
 More polar substances bond with the cellulose paper more
quickly, and therefore do not travel as far.
Thin Layer Chromatography (TLC)
 Thin layer chromatography (TLC) is a widely employed
laboratory technique and is similar to paper chromatography
 However, instead of using a stationary phase of paper, it
involves a stationary phase of a thin layer of adsorbent like
silica gel, alumina, or cellulose on a flat, inert substrate.
Instrumental analysis lecture note by Dawit
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 Compared to paper, it has the advantage of faster runs, better
separations, and the choice between different adsorbents.
 For even better resolution and to allow for quantification,
high-performance TLC can be used
 Q? How you can identify if invisible spots could occur when
you do TLC?
 Answer: by applying Ultraviolet light or Iodine vapors to stain
spots.
 Q? Which types of mobile phases are used for column and
planar chromatography?
 Answer: for column chromatography a liquid and gas mobile
phase is used.
 For planar chromatography only liquid mobile phase is used.
Because in a planar stationary phase, a gas molecule could
not transport linearly and the transportation is not good.
Instrumental analysis lecture note by Dawit
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2. Classification of chromatography based on the type of mobile phase
and stationary phases
 In this case the classification is on the physical state of the mobile and
stationary phase.
 During naming using this classification the first latter represents the
type of the mobile phase while the second letter represents the
stationary phase used.
With these bases, chromatography can be divided in to three as major
part. These are liquid, gas and supercritical fluid chromatography
 Gas chromatography (GC) includes all chromatographic methods in
which gas is used as mobile phase. It uses only stationary phases either
coated or packed on a column.
 Liquid chromatography (LC) includes all chromatographic techniques in
which liquid is used as mobile phase. For LC a stationary phase is either
packed on a column or coated on a column or a planar plate can be
used.
 Supercritical fluid chromatography (SFC) includes chromatographic
techniques which uses supercritical fluid as mobile phase. For this
technique the stationary phase could be organic species bonded on a
solid surface. Instrumental analysis lecture note by Dawit
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Table 2.1. Classification of chromatography based on the type of
mobile phase and stationary phases
Instrumental analysis lecture note by Dawit
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3. Classification of chromatography based on the type of
interaction occur between the sample and stationary phase
• Table 2.2. Types of chromatography based on interaction
between sample and stationary phase
Instrumental analysis lecture note by Dawit
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 Note: Separation in chromatography is based on the elution of
the sample across the stationary phase by the mobile phase.
 Across the movement the components of the sample interacts
with the stationary phase differently.
 The solute which interacts strongly with the stationary phase
will be strongly retained.
 So the speed of this solute in the column or plane is very slow
and takes more time to be eluted.
 The solute, which interacts with the stationary phase weakly,
will be weakly retained. So the solute will be eluted easily.
Instrumental analysis lecture note by Dawit
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Instrumental analysis lecture note by Dawit
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• Figure 2.1. (a) Diagram showing the separation of a mixture of
components A and B by column elution chromatography. A -is a solute
which has a weak interaction with the stationary phase and weakly
retained. B –is a solute which has a strong interaction with the stationary
phase and strongly retained. (b) The detector signal at the various stages
of elution shown in (a).
Instrumental analysis lecture note by Dawit
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 Chromatogram is the plot (representation) of the variation
with time of the amount of the analyte in the mobile phase
exiting the chromatographic column.
 It is a curve that has a baseline which corresponds to the trace
obtained in the absence of a compound being eluted.
 The separation is complete when the chromatogram shows as
many chromatographic peaks as there are components in the
mixture to be analyzed (
Instrumental analysis lecture note by Dawit
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Figure 2.2. A typical Chromatogram
 Where : tM = retention time of mobile phase (dead time)
 tR = retention time of analyte (solute)
 tS = time the solute spent in stationary phase (adjusted
retention time)
Instrumental analysis lecture note by Dawit
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 A chromatogram is a plot of the detector signal as a function of
time taken for the resolution.
 It is useful for qualitative and quantitative analysis.
 The position of the peaks on the time axis (retention time) may
serve to identify the components of the sample.
 The area under each peak provides the quantitative measure of
the amount of each component
Note:
 During elution weakly retained species elute first and reach the
detector first and detected first while strongly retained species
elute late to reach the detector.
Instrumental analysis lecture note by Dawit
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2.3. Efficiency of Separation (Column Resolution, Rs)
 The resolution of a column tells us how far apart two bands or
peaks are relative to their widths.
 The goal of chromatography is to separate a sample into a series of
chromatographic peaks, each representing a single component of
the sample.
 The resolution provides a quantitative measure of the ability of the
column to separate two analytes, like A and B. The resolution of
each column is defined as:
Instrumental analysis lecture note by Dawit
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Figure 2.3. A chromatogram of separation of two solutes, A and B
Based on the above equation to increase the resolution:
A) We have to increase the difference in the retention time of the strongly retained
species B and the weakly retained species A, i.e. and Z
B) We have to decrease base line width of species A and B.
Instrumental analysis lecture note by Dawit
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 1, increasing z is done by adjusting the migration rate of the
two species.
 That is by increasing retention time of the strongly retained
species, solute B and by decreasing the retention time of
weakly retained species, solute A.
 2, decreasing the sum of A W and B W is done by decreasing
the line broadening.
Instrumental analysis lecture note by Dawit
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Figure 2.4. Chromatogram with: a) poor resolution b) More separation and c) Less
band spread (High resolution
Instrumental analysis lecture note by Dawit
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 Example: In chromatographic analysis of lemon oil, a peak
for limonene has a retention time of 8.36 min with a
baseline width of 0.96 min. g-Terpinene elutes at 9.54 min,
with a baseline width of 0.64 min. what is the resolution
between the two peaks?
• SOLUTION: b y APPLYING THE FORMULA
 2X(9.8-8.36)/0.96+0.64=1.48
Instrumental analysis lecture note by Dawit
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2.4. Migration Rates of Solutes
 The effectiveness of a chromatographic column in separating
two solutes depends in part on the relative rates at which
the two species are eluted.
 These rates in turn are determined by the ratios of the solute
concentrations in each of the two phases.
 The separation is enhanced by altering the relative flow rate
of solutes. i.e. by increasing the flow rate of weakly retained
species and decreasing the flow rate of strongly retained
species.
Instrumental analysis lecture note by Dawit
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 The rate of elution of a solute is determined by the magnitude
of the equilibrium constant for the reaction by which the
solutes distribute themselves between the mobile phase and
the stationary phase.
The following are those factors which affect the migration rates
of a solute
2.4.1. Distribution Constant, K or D
 All chromatographic separations are based on differences in
the extent to which solutes are distributed between the
mobile and stationary phases.
 The distribution constant for a solute in chromatography is
equal to the ratio of its molar concentration in the stationary
phase to its molar concentration in the mobile phase.
 For the solute species A, the equilibrium involved is described
by the equation
A in mobile phase= A in stationary phase
Instrumental analysis lecture note by Dawit
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Instrumental analysis lecture note by Dawit
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2.4.2. Retention time
 The retention time (tR) is the time between injection of a
sample and the appearance of a solute peak at the detector of
a chromatographic column.
 The dead time (void time) (tM) is the time it takes for an
unretained species to pass through a chromatographic
column.
 All components spend this amount of time in the mobile
phase.
 Separations are based on the different times tS that
components spend in the stationary phase.
Instrumental analysis lecture note by Dawit
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Figure 2.5. Measurement of the column‟s void time tM, and the retention
time tR
Instrumental analysis lecture note by Dawit
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Instrumental analysis lecture note by Dawit
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The Relationship between Migration Rate and Distribution Constant
Instrumental analysis lecture note by Dawit
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chapter 2 instrumental analysis.pdf

  • 1. chapter two Introduction to chromatographic separation Instrumental analysis lecture note by Dawit A 1
  • 2. • Historical background • Chromatography means "to show with colors." It was the Russian botanist Mikhail Semyonovich (1872-1919) who invented the first chromatography technique in 1900, during his research on chlorophyll. He used a liquid-adsorption column containing calcium carbonate to separate plant pigments. Instrumental analysis lecture note by Dawit A 2
  • 3. • Chromatography -- what does it mean? • to write with colors -- literally translated from its Greek roots chroma and graphein. Chromatography has since developed into a laboratory tool for the separation and identification of compounds. • Although color usually no longer plays a role in the process, the same principles of chromatography still apply. Instrumental analysis lecture note by Dawit A 3
  • 4. • Why use chromatography? The key here is separation. But what is the importance of separation in the lab? • Separation of chemical components is vital in any type of chemical analysis. • When trying to identify an unknown substance, the sample must first be simplified as much as possible into its constituent compounds. • The unknown can then be characterized by individual identification of its parts. Instrumental analysis lecture note by Dawit A 4
  • 5. • This does not imply that the separated chemical components are recovered after the separation and analyzed. • Separated compounds are compared to known standards. • As with most chemical exploration, it is important to have an idea of what compounds are being searched Instrumental analysis lecture note by Dawit A 5
  • 6. Components or terms of chromatography Mobile phase is the phase which moves in a definite direction. It may be a liquid (LC), a gas (GC), or a supercritical fluid (supercritical-fluid chromatography, SFC). The mobile phase consists of the sample being separated/ analyzed and the solvent that moves the sample through the column. In the case of high performance liquid chromatography (HPLC) the mobile phase consists of a non-polar solvent(s) such as hexane in normal phase or polar solvents in reverse phase chromatography and the sample being separated. The mobile phase moves through the chromatography column (the stationary phase) where the sample interacts with the stationary phase and is separated Instrumental analysis lecture note by Dawit A 6
  • 7. con • Q? Which kind of phases can be used as mobile phase?  Answer: gases and liquids, because gases and liquids are fluids that can flow easily but solid is not fluid which can‟t be used to transport sample. • Stationary phase is the substance which is fixed in place for the chromatography procedure. Examples include the silica layer in thin layer chromatography. • Q? Which kinds of phases can be used for stationary phase?  Answer: liquid and solid. Liquid can be used as stationary phase by immobilizing the liquid on a solid surface.  Gases can‟t be used for stationary phase preparation because it is difficult to fix the gas on fixed space. Instrumental analysis lecture note by Dawit A 7
  • 8. con Note:  In a chromatographic separation the mobile and stationary phase must have low interaction.  Always when we select a mobile phase we should consider the following:  The mobile phase must be the least eluted species.  The mobile phase could not wash the stationary phase.  Supporting medium: a solid surface on which the stationary phase is bound or coated  A chromatogram is the visual output of the chromatograph.  In the case of an optimal separation, different peaks or patterns on the chromatogram correspond to different components of the separated mixture. Instrumental analysis lecture note by Dawit A 8
  • 9. 2.2. Types (Classification) of Chromatography  There are a number of different kinds of chromatography, which differ in the mobile and the stationary phase used.  Chromatography can be classified into groups based on several properties. Here in this paper we will classify chromatography based on three criteria  1. Classification of chromatography based on the physical means by which the stationary phase and mobile phase are brought together.  In this classification, chromatography is classified as: A. Column Chromatography  Column chromatography is a separation technique in which the stationary phase is within a tube.  The particles of the solid stationary phase or the support coated with a liquid stationary phase may fill the whole inside volume of the tube (packed column) Instrumental analysis lecture note by Dawit A 9
  • 10.  or be concentrated on or along the inside tube wall leaving an open, unrestricted path for the mobile phase in the middle part of the tube (open tubular column). • Differences in rates of movement through the medium are calculated to different retention times of the sample and the mobile phase moves in the column either due to gravity or by the force of pump. B. Planar Chromatography Planar chromatography is a separation technique in which the stationary phase is present as or on a plane. The plane can be a paper, serving as such or impregnated by a substance as the stationary bed (paper chromatography) or a layer of solid particles spread on a support such as a glass plate (thin layer chromatography Instrumental analysis lecture note by Dawit A 10
  • 11. con Different compounds in the sample mixture travel different distances according to how strongly they interact with the stationary phase as compared to the mobile phase. T the specific Retention factor (Rf) of each chemical can be used to aid in the identification of an unknown substance. In this technique the mobile phase is transported across the stationary phase by a capillary action. This type of chromatography can be divided into: Paper Chromatography Paper chromatography is a technique that involves placing a small dot or line of sample solution onto a strip of chromatography paper Instrumental analysis lecture note by Dawit A 11
  • 12.  The paper is placed in a jar containing a shallow layer of solvent and sealed.  As the solvent rises through the paper, it meets the sample mixture which starts to travel up the paper with the solvent. This paper is made of cellulose, a polar substance, and the compounds within the mixture travel farther if they are non- polar.  More polar substances bond with the cellulose paper more quickly, and therefore do not travel as far. Thin Layer Chromatography (TLC)  Thin layer chromatography (TLC) is a widely employed laboratory technique and is similar to paper chromatography  However, instead of using a stationary phase of paper, it involves a stationary phase of a thin layer of adsorbent like silica gel, alumina, or cellulose on a flat, inert substrate. Instrumental analysis lecture note by Dawit A 12
  • 13.  Compared to paper, it has the advantage of faster runs, better separations, and the choice between different adsorbents.  For even better resolution and to allow for quantification, high-performance TLC can be used  Q? How you can identify if invisible spots could occur when you do TLC?  Answer: by applying Ultraviolet light or Iodine vapors to stain spots.  Q? Which types of mobile phases are used for column and planar chromatography?  Answer: for column chromatography a liquid and gas mobile phase is used.  For planar chromatography only liquid mobile phase is used. Because in a planar stationary phase, a gas molecule could not transport linearly and the transportation is not good. Instrumental analysis lecture note by Dawit A 13
  • 14. 2. Classification of chromatography based on the type of mobile phase and stationary phases  In this case the classification is on the physical state of the mobile and stationary phase.  During naming using this classification the first latter represents the type of the mobile phase while the second letter represents the stationary phase used. With these bases, chromatography can be divided in to three as major part. These are liquid, gas and supercritical fluid chromatography  Gas chromatography (GC) includes all chromatographic methods in which gas is used as mobile phase. It uses only stationary phases either coated or packed on a column.  Liquid chromatography (LC) includes all chromatographic techniques in which liquid is used as mobile phase. For LC a stationary phase is either packed on a column or coated on a column or a planar plate can be used.  Supercritical fluid chromatography (SFC) includes chromatographic techniques which uses supercritical fluid as mobile phase. For this technique the stationary phase could be organic species bonded on a solid surface. Instrumental analysis lecture note by Dawit A 14
  • 15. Table 2.1. Classification of chromatography based on the type of mobile phase and stationary phases Instrumental analysis lecture note by Dawit A 15
  • 16. 3. Classification of chromatography based on the type of interaction occur between the sample and stationary phase • Table 2.2. Types of chromatography based on interaction between sample and stationary phase Instrumental analysis lecture note by Dawit A 16
  • 17.  Note: Separation in chromatography is based on the elution of the sample across the stationary phase by the mobile phase.  Across the movement the components of the sample interacts with the stationary phase differently.  The solute which interacts strongly with the stationary phase will be strongly retained.  So the speed of this solute in the column or plane is very slow and takes more time to be eluted.  The solute, which interacts with the stationary phase weakly, will be weakly retained. So the solute will be eluted easily. Instrumental analysis lecture note by Dawit A 17
  • 18. Instrumental analysis lecture note by Dawit A 18
  • 19. • Figure 2.1. (a) Diagram showing the separation of a mixture of components A and B by column elution chromatography. A -is a solute which has a weak interaction with the stationary phase and weakly retained. B –is a solute which has a strong interaction with the stationary phase and strongly retained. (b) The detector signal at the various stages of elution shown in (a). Instrumental analysis lecture note by Dawit A 19
  • 20.  Chromatogram is the plot (representation) of the variation with time of the amount of the analyte in the mobile phase exiting the chromatographic column.  It is a curve that has a baseline which corresponds to the trace obtained in the absence of a compound being eluted.  The separation is complete when the chromatogram shows as many chromatographic peaks as there are components in the mixture to be analyzed ( Instrumental analysis lecture note by Dawit A 20
  • 21. Figure 2.2. A typical Chromatogram  Where : tM = retention time of mobile phase (dead time)  tR = retention time of analyte (solute)  tS = time the solute spent in stationary phase (adjusted retention time) Instrumental analysis lecture note by Dawit A 21
  • 22.  A chromatogram is a plot of the detector signal as a function of time taken for the resolution.  It is useful for qualitative and quantitative analysis.  The position of the peaks on the time axis (retention time) may serve to identify the components of the sample.  The area under each peak provides the quantitative measure of the amount of each component Note:  During elution weakly retained species elute first and reach the detector first and detected first while strongly retained species elute late to reach the detector. Instrumental analysis lecture note by Dawit A 22
  • 23. 2.3. Efficiency of Separation (Column Resolution, Rs)  The resolution of a column tells us how far apart two bands or peaks are relative to their widths.  The goal of chromatography is to separate a sample into a series of chromatographic peaks, each representing a single component of the sample.  The resolution provides a quantitative measure of the ability of the column to separate two analytes, like A and B. The resolution of each column is defined as: Instrumental analysis lecture note by Dawit A 23
  • 24. Figure 2.3. A chromatogram of separation of two solutes, A and B Based on the above equation to increase the resolution: A) We have to increase the difference in the retention time of the strongly retained species B and the weakly retained species A, i.e. and Z B) We have to decrease base line width of species A and B. Instrumental analysis lecture note by Dawit A 24
  • 25.  1, increasing z is done by adjusting the migration rate of the two species.  That is by increasing retention time of the strongly retained species, solute B and by decreasing the retention time of weakly retained species, solute A.  2, decreasing the sum of A W and B W is done by decreasing the line broadening. Instrumental analysis lecture note by Dawit A 25
  • 26. Figure 2.4. Chromatogram with: a) poor resolution b) More separation and c) Less band spread (High resolution Instrumental analysis lecture note by Dawit A 26
  • 27.  Example: In chromatographic analysis of lemon oil, a peak for limonene has a retention time of 8.36 min with a baseline width of 0.96 min. g-Terpinene elutes at 9.54 min, with a baseline width of 0.64 min. what is the resolution between the two peaks? • SOLUTION: b y APPLYING THE FORMULA  2X(9.8-8.36)/0.96+0.64=1.48 Instrumental analysis lecture note by Dawit A 27
  • 28. 2.4. Migration Rates of Solutes  The effectiveness of a chromatographic column in separating two solutes depends in part on the relative rates at which the two species are eluted.  These rates in turn are determined by the ratios of the solute concentrations in each of the two phases.  The separation is enhanced by altering the relative flow rate of solutes. i.e. by increasing the flow rate of weakly retained species and decreasing the flow rate of strongly retained species. Instrumental analysis lecture note by Dawit A 28
  • 29.  The rate of elution of a solute is determined by the magnitude of the equilibrium constant for the reaction by which the solutes distribute themselves between the mobile phase and the stationary phase. The following are those factors which affect the migration rates of a solute 2.4.1. Distribution Constant, K or D  All chromatographic separations are based on differences in the extent to which solutes are distributed between the mobile and stationary phases.  The distribution constant for a solute in chromatography is equal to the ratio of its molar concentration in the stationary phase to its molar concentration in the mobile phase.  For the solute species A, the equilibrium involved is described by the equation A in mobile phase= A in stationary phase Instrumental analysis lecture note by Dawit A 29
  • 30. Instrumental analysis lecture note by Dawit A 30
  • 31. 2.4.2. Retention time  The retention time (tR) is the time between injection of a sample and the appearance of a solute peak at the detector of a chromatographic column.  The dead time (void time) (tM) is the time it takes for an unretained species to pass through a chromatographic column.  All components spend this amount of time in the mobile phase.  Separations are based on the different times tS that components spend in the stationary phase. Instrumental analysis lecture note by Dawit A 31
  • 32. Figure 2.5. Measurement of the column‟s void time tM, and the retention time tR Instrumental analysis lecture note by Dawit A 32
  • 33. Instrumental analysis lecture note by Dawit A 33
  • 34. The Relationship between Migration Rate and Distribution Constant Instrumental analysis lecture note by Dawit A 34
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  • 38. Instrumental analysis lecture note by Dawit A 38