This document discusses gas chromatography (GC), which separates compounds that can be vaporized without decomposing. It has two types depending on the stationary phase: gas-solid chromatography (GSC) and gas-liquid chromatography (GLC). The distribution of analytes between phases is expressed by the distribution constant K. Plate theory and rate theory, including the Van Deemter equation, are presented to describe column efficiency and factors influencing peak broadening such as eddy diffusion, longitudinal diffusion, and mass transfer under non-equilibrium conditions.

1. Presented by: Anvita Jadhav
M.Pharm (IP)

2. Gas Chromatography
 Gas chromatography is a common type of
chromatography used in analytical chemistry for
separating and analyzing the compounds that can be
vaporized without decomposition.
 It has two types
• Mobile Phase : Gas
• Stationary Phase: SolidGSC
• Mobile Phase : Gas
• Stationary Phase : LiquidGLC

3.  The distribution of an analyte between stationary and mobile
phase is expressed by the distribution constant K.
K = Cs/Cm
Cs = concentration of a component in the stationary phase
Cm = concentration of a component in the mobile phase
 In case of GSC, the interaction of solutes with the stationary
phase is in the form of their adsorption on it & this adsorption is
non-linear.
 This does not keep the ratio of the concentration of a solute in
the stationary phase (Cs) to that in the mobile phase (Cm)
constant.
 In case of the GLC ratio of the concentration of a solute in the
stationary phase (Cs) to that in the mobile phase (Cm) constant.

4. Isotherm for Linear-Nonideal
GLC
Isotherm for Nonlinear-Nonideal
GSC
The isotherm is a graphical representation of the distribution
constant K
CS = concentration in stationary phase;
CG = concentration in mobile phase at equilibrium.

5. Plate Theory
 The theory assumes that the column is divided into a
number of zones called theoretical plates.
 At each plate equilibrium of the solute between the
mobile phase & the stationary is assumed to take place.
 The partitioning of a solute between the phases takes
plate at each theoretical plate.
 Thus, the number theoretical plates in the column is
used as a measure of efficiency of the column to
separate the components from each other

6.  The number of theoretical plates can be determined
by
where, n = no. of theoretical plates
VR = retention time
W = base width of the peak

7.  HETP value can be determined by,
 Plate theory disregards the kinetics of mass transfer;
therefore, it reveals little about the factors influencing
HETP values.
 The resulting behavior of the plate column is calculated on
the assumption that the distribution coefficient remains
unaffected by the presence of other solutes and that the
distribution isotherm is linear.
 The diffusion of solute in the mobile phase from one plate
to another is also neglected.

8. Plate
Theory
Discrete
Flow Model
Continuous
Flow Model

9. Discrete-Flow Model
 The assumptions in this model are
(a)
• All the mobile phase moves from one segment to
the next segment at the end of a discrete interval
(b)
• The sample molecules are always in equilibrium
with the mobile and stationary phases

10. Continuous-Flow Model
 The assumptions in this model are
(a)
• The mobile and stationary phases remain in
equilibrium throughout the separation
(b)
• The mobile phase flows from one segment to the next
segment at a constant rate
(c)
• Perfect mixing takes place in all segments

11. Rate Theory
 It was introduced by Van Deemter.
 It describes the effect of an elution band as well as its
time of elution.
 Van Deemter equation describes the relation of the
height of a theoretical plate H and the average linear
velocity of the mobile phase.

12. Van Deemter Equation
 H = height of a theoretical plate
 u = average linear velocity of the mobile phase
 A = eddy diffusion term
 B = longitudinal or ordinary diffusion term
 C = nonequilibrium or resistance to mass transfer term

13. Eddy Diffusion
 The A term refers to band broadening caused by
dispersion (multi-pathway) effects (Eddy diffusion)
A = 2λdp
 λ = correction factor for the irregularity of the column
packing
 dp = average particle diameter.

14.  In this case the spaces along the column are not uniform.
 When a sample migrates down the column, each molecule “sees”
different paths and each path is of a different length.
 Some molecules take the longer paths and others take the
shorter paths.
 There are also variations in the velocities of the mobile phase
within these pathways.
 The overall result is that some molecules lag behind the center of
the zone, whereas others move ahead of the zone.

15. Longitudinal Diffusion
 The B term represents band broadening by
longitudinal diffusion, the molecular diffusion both in
and against the flow direction:
B = 2γDG
 γ = labyrinth factor of the pore channels (0<γ <1)
 DG = diffusion coefficient of the analyte in the gas
phase

16.  This process results when there exists a region of high
concentration and a region of low concentration.
 The migration is from the higher to the lower
concentration region in the axial direction of the column.
 Diffusion occurs on the molecular level, resulting from
movement of molecules after collision
 The diffusion is about 100–1,000-fold faster in gases than in
liquids, therefore B terms shows higher impact in GC than
in LC.

17. Mass transfer under non equilibrium
 The C terms refers to the mass transfer between stationary and
mobile phase.
 As the zone of solute continues to migrate down the column, it is
constantly bringing an ever-changing concentration profile in
contact with the next part of the column. This effect results in
different rates of equilibration along the column.
 Thus theoretical plate in the column is constantly attempting to
equilibrate with a variable concentration zone in the mobile phase.
 At one time the zone attempts to equilibrate with a low
concentration in the mobile phase, and then at another time with a
high concentration.
 These overall processes result in nonequilibrium at each theoretical
plate.

18.  The rapid mass transfer depends on the factors originating from
the stationary phase as well as the mobile phase The term ‘C’ in
Van Deemter equation is therefore, the sum of Cs & CM.
 The stationary phase contribution (Cs) to the plate height H, due
to the mass transfer under nonequilibrium condition, is given by,
 q = configuration factor
 r = a constant dependent upon the relative rate of migration of a
solute & the mobile phase,
 d = thickness of the stationary phase
 Ds = diffusion coefficient of a solute in the stationary phase.

19.  The mobile phase contribution (CM) to the plate
height H, due to the mass transfer under
nonequilibrium conditions, is given by,
 DG = diffusion coefficient in the gas phase
 dp = average particle diameter
 ω = obstruction factor for packed bed

20. Van Deemter Plot
The term ‘A’ is independent
of flow rate of the mobile
phase
The term B/u decreases
drastically in the beginning
with increase in the flow rate
of mobile phase. Increase in
the flow rate beyond
particular value, leads to slow
decrease in the value of B/u.
The term Cu increases with
increse in the flow rate