1. Chem. 230 – 9/23 Lecture

2. 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)

3. Chromatographic Theory Questions on Definitions
When is chromatographic separation needed vs. only simple separations?
An analyte interacts with a stationary phase via adsorption. The stationary phase is most likely:
a) Liquid b) Liquid-like c) Solid
What are the required two phases in chromatography called?
What are advantages and disadvantages with the three common stationary phases (liquid, liquid-like, and solid)?

4. 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)

5. 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

6. 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)

7. 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

8. 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 = ( )/2.37 = 1.50

9. 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

10. 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

11. 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)

12. 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 = mm/min
R = 42.2/105 = 0.40

13. Chromatographic Theory Shape of Chromatographic Peak
Gaussian Distribution
Normal Distribution Area = 1
Widths
σ (std deviation)
wb (baseline width) = 4σ
wh (peak width at half height) = 2.35σ
w’ = Area/ymax = 2.51σ (often given by integrators)
Gaussian Shape (Supposedly)
Inflection lines
Height 2σ
Half Height wh wb

14. Chromatographic Theory Measures of Chromatographic Efficiency
Plate Number = N (originally number of theoretical plates – similar to number of liquid-liquid 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

15. 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

16. Chromatographic Theory Non-ideal Peak Shapes
Fronting Peak (TF < 1)
Tailing Peak (actually slow detector) a b
Tailing Factor = TF = b/a > 1 (tailing peak)

17. 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

18. Chromatographic Theory Definitions - Resolution
Resolution is a measure of the ability to separate two peaks from each other
Resolution = RS
where d = (tR)B – (tR)A
and ave w = [(wb)A + (wb)B]/2

19. 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

20. Chromatographic Theory Definitions - Resolution
RS calculation examples:
1st two peaks:
tR(1st pk) = min., w (integrator) = w’ = min, so wb = 0.238·(4/2.5) = 0.38 min.
tR(2nd pk) = min., wb = 0.44 min
RS = 0.801/0.410 = (neglecting non-Gaussian peak shape)
Last two peaks, RS = 3.0

21. 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

22. 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).

23. 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

24. 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 non-Gaussian peak shapes (leads to additional band broadening plus need for new equations)

25. Chromatographic Theory Questions on Definitions
List two ways in which a stationary phase is “attached” to a column?
What column component is present in packed columns but not open-tubular columns?
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 > Explain this.

26. Chromatographic Theory Questions on Definitions
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.

27. Chromatographic Theory Questions on Definitions
What “easy” change can be made to increase KC in GC? In HPLC?
A GC is operated close to the maximum column temperature and for a desired analyte, k = 10. Is this good?
If a new column for problem 8 could be purchased, what would be changed?
In reversed-phase HPLC, the mobile phase is 90% H2O, 10% ACN and k = 10, is this good?
Column A is 100 mm long with H = mm. Column B is 250 mm long with H = mm. Which column will give more efficient separations (under conditions for determining H)?

28. Chromatographic Theory Questions on Definitions
Given the two chromatograms to the right:
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
Unretained pk