Chromatographic Separations
Introduction & Basics
Read all of Skoog – Chapter 26.
Common analytical problem: identify and quantify >1 component
in a mixture.
Ideally
 Completely selective method to analyze each component
individually in the mixture
 In absence of such a method, separate the analyte(s) prior to
analysis to avoid selectivity issues
Separations Methods
 Distillation
 Extraction
 Chromatography
 Electrophoresis
Introduction to separations: liquid-liquid extraction
The solute = S is partitioned between 2 liquid phases Φ1 and Φ2
Equilibrium constant or
Partition coefficient or
Distribution constant K = [S]2/[S]1
1
So what gives a better separation of solute between the 2 phases –
1 large extraction or several small ones?
Solute A has K = 3 between toluene and water ([A] in toluene = 3x
[A] in water). Start with 100 mL of 0.01 M aqueous solution of A
and extract with toluene. Which procedure gives a better
extraction:
a) 1 extraction with 500 mL toluene
or
b) 5 extractions with 100 mL toluene/extraction
2
The more equilibria a mixture attains between 2 different phases
the greater the separation.
Instrumental separations methods (i.e. chromatography) designed
to give the maximum number of equilibria (theoretical plates).
Chromatography operates on the same principle as extraction, but
one phase is held in place (stationary phase) while the other moves
past it (mobile phase).
The interaction of the solute with the stationary phase to a large
extent dictates the distribution constant K. The nature of this
interaction is one way to generally categorize chromatographic
methods. For a solute A: K = [A]stat Φ/[A]mobile Φ
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The basics remain the same regardless of the type of interaction
dictating the distribution constant.
Note that your text in Table 26-1 also categorizes chromatographic
methods by the type of mobile phase:
 GC = gas chromatography, gaseous mobile phase
 LC = liquid chromatography, liquid mobile phase
 SFC = supercritical fluid chromatography, supercritical fluid
mobile phase
Below, 2 substances A and B are shown eluting down a column
packed with stationary phase. Mobile phase is continuously added
such that elution continues until the substances are eluted from the
end of the column.
If K = [A]stat Φ/[A]mobile Φ
 Then K for solute A < K for solute B
 As solute partitions between the stationary phase and fresh
mobile phase, bands from the 2 solutes begin to separate
from one another as a result of successive equilibria between
mobile and stationary phase
 Each equilibrium achieved between mobile and stationary
phase is a theoretical plate (holdover terminology from
distillation theory)
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 Since solute movement can occur only in the mobile phase,
the average rate at which a solute migrates down the column
depends on the fraction of time it spends in the mobile phase,
dictated by K for that solute
A chromatogram is a graph of detector response as a function of
elution time
2 factors affect column performance (separations)
1. As solutes elute down the column, band separation occurs
due to successive equilibria between phases (differences in
migration rates – good to maximize)
2. As solutes elute down the column, each solute band
inevitably broadens – good to minimize
Band (Zone) separation – An equilibrium treatment (Ch. 26
Section B)
The partition or distribution constant (K) is not readily measured,
but the retention time is, and it is directly related to K.
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Definitions:
 tM
 tR
 tR ’
 retention or capacity factor k or k’ =
 α (selectivity factor)
If:
Solute is in mobile phase all the time
Solute is in mobile phase 50% of the time and in stationary
phase 50% of the time
Solute is in mobile phase 25% of the time and in stationary
phase 75% of the time
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If the solute spends 3x as much time in the stationary phase
as the mobile phase, then 3x as many moles of solute are in
the stationary phase compared to the mobile phase.
If k’ < 1 then the solute elutes too quickly, near tM
If k’ > 20 then tR is too long causing various problems
Ideally k’ between 1 and 10, separation conditions are
adjusted to make that happen (discussed in Ch 26, Section D)
Now the last definition: selectivity factor. The point of
chromatography is to effect a separation, which is
fundamentally based on differences in partition coefficients
between solutes.
α = KA/KB = selectivity factor
(α > 1 by definition)
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Two factors contribute to how well compounds are separated:
1. Difference in elution times between peaks: (already)
explained by equilibrium theory. Larger difference in K, the
better the separation.
2. The wider the peaks, the poorer the separation. Now to be
treated by rate theory.
Band broadening and column efficiency: Rate theory Section 26C
Chromatography peaks are Gaussian.
Overall uncertainty = ∑ many random uncertainties
Most common result = mean
Width defined by standard deviation
In previous section we looked at the average result (mean = tR)
In this section better to think at the molecular level
and remember…
A solute can only move down the column while in the mobile
phase
A single solute molecule may get “hung up” in the stationary phase
and lag behind,
Or
A single solute molecule may spend an inordinate amount of time
in the mobile phase and race ahead.
The result: band broadening.
8
Early on chromatography and band spreading was treated as an
equilibrium process using distillation theory. Terminology, which
can cause confusion, unfortunately remains.
Theoretical Plate – where a solute undergoes equilibrium between
mobile and stationary phase.
Number of theoretical plates = N
Plate Height = H
If N = L/H and H = s2/L
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w2 = 16s2; s2 = w2/16
At a given mobile phase flow rate L is proportional to tR for a
given solute so:
A solute with a retention time of 407s has a width at the base of
13s, on a 12.2m long column. Find N and H.
Column separation efficiency increases as N increases, and
increases as H decreases.
Compare N and H only for the same compound.
Chromatography:
N = 100 – 10,000
H = 0.1 – 0.001 cm
Capillary electrophoresis: N ~ 106
H ~ 10-3 cm
So far, column efficiency discussed by plate or equilibrium theory,
which cannot explain the following experimental data:
10
The above van Deemter plot shows that there is an optimum flow
rate, and that plate height is very much a function of mobile phase
flow velocity.
What are the mechanisms for zone broadening?
H = A + B/u + Cu
van Deemter equation
The multipath (A) term
11
The longitudinal diffusion (B/u) term
Mobile and stationary phase mass transfer (Cu) term
Breaking the van Deemter plot into individual contributors:
12
Comparison of van Deemter plots for gas chromatography (GC)
and liquid chromatography (LC)
 At low flow rates plate height decreases with increasing flow
rates from longitudinal diffusion term. Larger effect in GC
 For same reason plate heights smaller in LC than GC.
The multipath A term:
13
A = 0 for no packing (common in GC, not LC)
Summary
 Addressed migration rates and distribution constants (26B)
 Addressed zone broadening (26C)
Now – optimization of column performance (26D) by either
 Altering relative migration rates, or
 reducing zone broadening
The goal is to resolve 2 or more solutes in a mixture – dependent
on differences in retention time and zone width.
Resolution Rs = ΔtR/Wav
14
A little algebra to derive relationships relating resolution, retention
times (i.e. retention and selectivity factors), and zone broadening
(i.e. theoretical plates).
15
Note that the above equation can be rearranged to find N for a
desired resolution:
In practical terms, resolution is only important when KA≈KB
Example 26-1 on p. 777 reviews many concepts.
The fundamental parameters of selectivity (α), retention factor (k)
and theoretical plates (N,H) can all be varied to achieve a
separation.
Selectivity:
Theoretical Plates/Plate Height:
Retention factor: easiest way to improve resolution
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A more general discussion…
Gradient Elution in liquid chromatography – a systematic variation
of mobile phase composition to optimize k for a wide range of
solutes.
Temperature programming in gas chromatography – a systematic
variation of temperature to optimize k for a wide range of solutes.
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General applications of chromatography (Section 26F)
Qualitative analysis
 tR only qualitative information. No structural information.
Strong indicator of presence of analyte, unequivocal proof of
analyte absence.
 Useful for separation prior to acquiring structural information
using another technique which would not be useful for a
mixture.
Quantitative analysis
 Peak areas
 Reproducible injection volumes (calibrations)
End of Chapter 26 questions/problems:
1-3, 6-15, 17-19, 21
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