Chem. 230 – 9/23 Lecture
Announcements
• Exam 1 today – first 40 min.
• Second Homework Set will be online soon
• Today’s Topics – Chromatographic Theory
– Basic definitions (flow – time relationship, distribution
constant, retention factor, velocities, plate number,
plate height, asymmetry factor, resolution, separation
factor)
– How to read chromatograms
– Meaning of parameters (more when we cover
optimization)
Chromatographic Theory
Questions on Definitions
1. When is chromatographic separation needed
vs. only simple separations?
2. An analyte interacts with a stationary phase
via adsorption. The stationary phase is most
likely:
a) Liquid b) Liquid-like c) Solid
3. What are the required two phases in
chromatography called?
4. What are advantages and disadvantages with
the three common stationary phases (liquid,
liquid-like, and solid)?
Chromatographic Theory
Definition Section – Flow – Volume Relation
• Relationship between volume (used with
gravity columns) and time (most common
with more modern instruments):
V = t·F
V = volume passing through column part in
time t at flow rate F
Also, VR = tR·F where R refers to retention
time/volume (time it takes component to go
through column or volume of solvent needed
to elute compound)
Chromatographic Theory
Definition Section – More on Volume
• Hold-up volume = VM = volume occupied
by mobile phase in column
• Stationary phase volume = VS
• Calculation of VM:
VM = Vcolumn – Vpacking material – VS
VM = tM·F, where tM = time needed for
unretained compounds to elute from column
Chromatographic Theory
Definition Section – Partition and Retention
• Distribution Constant (= Partition Coefficient
from LLE) = KC = [X]S/[X]M
• KC is constant if T and/or solvent remain
constant
• Retention Factor (= Capacity Factor = Partition
Ratio) = k = (moles X)S/(moles X)M = KC/(VM/VS)
• k = KC/β where β = VM/VS
• Retention Factor is more commonly used
because of ease in measuring, and since β =
constant, k = constant·KC (for a given column)
• Note: kColumn1 ≠ kColumn2 (because β changes)
Chromatographic Theory
Definition Section – Partition and Retention
• Since the fraction of time a solute molecule
spends in a given phase is proportional to the
fraction of moles in that phase,
k = (time in stationary phase)/(time in mobile
phase)
• Experimentally, k = (tR – tM)/tM
• The same equations can be made with volumes
instead: k = (VR – VM)/VM
• Note: t’R = tR – tM = adjusted retention time
Chromatographic Theory
Reading Chromatograms
•
•
•
•
•
Determination of parameters from reading chromatogram (HPLC example)
tM = 2.37 min. (normally determined by finding 1st peak for unretained
compounds – contaminant below)
VM = F·tM = (1.0 mL/min)(2.37 min) = 2.37 mL (Note: 4.6 x 250 mm column,
so total vol. = (π/4)(0.46 cm)2(25 cm)(1 mL/cm3) = 4.15 mL
Vol. of packing material + stationary phase = 4.15 mL – 2.37 mL = 1.78 mL
(note only VS is useful)
1st peak, tR = 5.93 min.; k = (5.93 -2.37)/2.37 = 1.50
Chromatographic Theory
What do all these Parameters Mean?
• KC is just like KP in liquid – liquid extractions for HPLC or
KH (Henry’s law constant) for GC
• Large KC value means analyte prefers stationary phase
• In GC:
– KC value will depend on volatility and polarity (analyte vs
stationary phase)
– KC value adjusted by changing T (most common)
– The mobile phase or carrier gas (e.g. He vs. N2) has no effect on
KC
• In HPLC
– KC value will depend on analyte vs. mobile phase and stationary
phase polarity
– KC value adjusted by changing mobile phase polarity
Chromatographic Theory
What do all these Parameters Mean? II
• Retention Factor is a more useful measure of
partitioning because value is related to elution
time
• Compounds with larger KC, will have larger k,
and will elute later
• Practical k values
–
–
–
–
~0.5 to ~10
Small k values → usually poor selectivity
Large k values → must wait long time
Higher k values are more practical for complicated
samples while low k values are desired for simpler
samples to save time
Chromatographic Theory
Definition Section – Velocity
• Mobile phase velocity (u) and analyte
average speed (v) can be useful quantities
• u = L/tM (L = column length)
• v = L/tR
• R = retardation factor = v/u (similar to RL
used in TLC based on distance migrated)
Chromatographic Theory
Reading Chromatogram – cont.
• u = L/tM = 250 mm/2.37 min = 105 mm/min
• v(1st peak) = L/tR = 250 mm/5.93 min = 42.2 mm/min
• R = 42.2/105 = 0.40
Chromatographic Theory
Shape of Chromatographic Peak
• Gaussian Distribution
 1  x  x 2 
1
y 
exp  
 
2

 2

 

Gaussian Shape (Supposedly)
• Normal Distribution Area =
1
• Widths
– σ (std deviation)
Height
– wb (baseline width) = 4σ
– wh (peak width at half height)
= 2.35σ
– w’ = Area/ymax = 2.51σ (often
given by integrators)
Inflection lines
2σ
Half
Height
wh
wb
Chromatographic Theory
Measures of Chromatographic Efficiency
• Plate Number = N (originally number of
theoretical plates – similar to number of liquidliquid extractions or distillations)
• N = (tR/σ)2 (= 16(tR/wb)2 )
• N is an absolute measure of column efficiency
but depends on length
• Plate Height = H = length of column needed to
get N of 1
• H = L/N, but H is constant under specific
conditions, while N is proportional to L
Chromatographic Theory
Measures of Chromatographic Efficiency
• Measuring N and H is valid under isocratic conditions
• Later eluting peaks normally used to avoid effects from
extra-column broadening
• Example: N = 16(14.6/0.9)2 = 4200 (vs. ~3000 for pk 3)
• H = L/N = 250 mm/4200 = 0.06 mm
Wb ~ 0.9 min
Chromatographic Theory
Non-ideal Peak Shapes
Tailing Peak (actually slow detector)
85
80
Response
75
70
65
60
55
50
45
40
13.00
13.20
13.40
13.60
time
a
b
Tailing Factor = TF = b/a >
1 (tailing peak)
13.80
14.00
Fronting Peak (TF < 1)
Chromatographic Theory
Definitions - More on Peak Shapes
• A Gaussian peak shape is assumed for
many of the calculations given previously
(e.g. peak width and N)
• For non-Gaussian peaks, the equations
relating specific widths to σ are no longer
valid.
• New equations are required for equations
that have width in them
Chromatographic Theory
Definitions - Resolution
• Resolution is a measure of the ability to
separate two peaks from each other
• Resolution = RS
d
RS 
wb
where d = (tR)B – (tR)A
and ave w = [(wb)A + (wb)B]/2
Chromatographic Theory
Definitions - Resolution
• Resolution indicates the amount of overlap
between peaks
• RS < 1, means significant overlap
• RS = 1.5, means about minimum for
“baseline resolution” (at least for two
peaks of equal height)
• RS > 2 often needed if it is important to
integrate a small peak near a large peak
Chromatographic Theory
Definitions - Resolution
• RS calculation examples:
– 1st two peaks:
• tR(1st pk) = 4.956 min., w (integrator) = w’ = 0.238 min, so wb =
0.238·(4/2.5) = 0.38 min.
• tR(2nd pk) = 5.757 min., wb = 0.44 min
RS = 0.801/0.410 = 1.95 (neglecting non-Gaussian peak shape)
– Last two peaks, RS = 3.0
Chromatographic Theory
Definitions - Resolution
• Higher resolution values
are needed to quantify
small peaks next to large
peaks
• RS = 1.61 (assuming wb
1st peak equals 2nd peak)
• RS is not sufficient for
accurate integration of 1st
peak (but o.k. for
integration of 2nd peak)
Expansion of above box
Large integration error on 1st pk
Chromatographic Theory
Definitions - Peak Capacity
• Peak Capacity is the theoretical maximum number of peaks that can
be separated with RS = 1.0 within a given time period.
• We won’t cover calculation, but for example, about 2X more peaks
could be possible between 5 and 13 min.
• Peak capacity 2.3 to 20 min. would be ~27 peaks.
• Greater peak capacity is typical with temperature/gradient programs
(like in example).
Chromatographic Theory
Definitions - Separation Factor
• Separation Factor = a = ratio of distribution constants
 a = KB/KA = kB/kA = (t’R)B/(t’R)A
Where (tR)B > (tR)A so that a > 1
• Smaller a (closer to 1) means more difficult separation
• In example chromatogram, (1st 2 peaks)
a = (5.77 – 2.37)/(4.96 – 2.37) = 1.31
Chromatographic Theory
Definitions - Overview
• The “good” part of chromatography is
separation, which results from differences in KC
values giving rise to a > 1
• The “bad” part of chromatography is band
broadening or dispersion, leading to decreased
efficiency (and also reducing sensitivity)
• The “ugly” part of chromatography is nonGaussian peak shapes (leads to additional band
broadening plus need for new equations)
Chromatographic Theory
Questions on Definitions
1. List two ways in which a stationary phase is
“attached” to a column?
2. What column component is present in packed
columns but not open-tubular columns?
3. In HPLC, typical packing material consist of μm
diameter spherical particles. Even though
tightly packing the spheres should lead to >
50% of the column being sphere volume, the
ratio of VM/Column Volume > 0.5. Explain
this.
Chromatographic Theory
Questions on Definitions
4.
5.
6.
List 3 main components of chromatographs.
A chemist perform trial runs on a 4.6 mm diameter
column with a flow rate of 1.4 mL/min. She then
wants to scale up to a 15 mm diameter column (to
isolate large quantities of compounds) of same length.
What should be the flow rate to keep u (mobile phase
velocity) constant?
A chemist purchases a new open tubular GC column
that is identical to the old GC column except for having
a greater film thickness of stationary phase. Which
parameters will be affected: KC, k, tM, tR(component
X), β, a.
Chromatographic Theory
Questions on Definitions
7. What “easy” change can be made to increase
KC in GC? In HPLC?
8. A GC is operated close to the maximum
column temperature and for a desired analyte,
k = 10. Is this good?
9. If a new column for problem 8 could be
purchased, what would be changed?
10. In reversed-phase HPLC, the mobile phase is
90% H2O, 10% ACN and k = 10, is this good?
11. Column A is 100 mm long with H = 0.024 mm.
Column B is 250 mm long with H = 0.090 mm.
Which column will give more efficient
separations (under conditions for determining
H)?
Chromatographic Theory
Questions on Definitions
5.756
6.659
250
7.872
200
150
2.208
2.842
50
2.599
100
0
1
2
3
4
5
6
7
8
min
17.5
min
ADC1 A, ADC1 CHANNEL A (LILLIAN\102507000009.D)
VWD1 A, Wavelength=210 nm (LILLIAN\102507000009.D)
ADC1 A, ADC1 CHANNEL A (LILLIAN\102507000006.D)
VWD1 A, Wavelength=210 nm (LILLIAN\102507000006.D)
12.754
mV
1000
Unretained pk
1.204
1.201
14.242
800
600
400
0
2.5
5
7.5
12.5
15.436
12.821
8.309
8.444
10
14.103
0
7.173
200
2.696
2.695
– Which column shows a
larger N value?
– Which shows better
resolution (1st 2 peaks top
chromatogram)?
– Which shows better
selectivity (larger a; 1st 2
peaks on top)?
– Should be able to calculate
k, N, RS, and α
mV
0.841
0.845
0.926
0.924
1.042
1.470
1.473
1.613
1.616
• Given the two
chromatograms to the
right:
ADC1 A, ADC1 CHANNEL A (MONIQUE\062608000004.D)
ADC1 B, ADC1 CHANNEL B (MONIQUE\062608000004.D)
VWD1 A, Wavelength=205 nm (MONIQUE\062608000004.D)
15