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 TheoryQuestions 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) Solid3. 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 FAlso, 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 TheoryWhat 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 TheoryWhat 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 TheoryShape 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)

2

21

exp2

1xx

y

2σ

Inflection lines

wb

Height

Half Height

wh

Chromatographic TheoryMeasures 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

Chromatographic TheoryMeasures 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 TheoryNon-ideal Peak Shapes

40

45

50

55

60

65

70

75

80

85

13.00 13.20 13.40 13.60 13.80 14.00

time

Res

po

nse

Tailing Peak (actually slow detector)

Tailing Factor = TF = b/a > 1 (tailing peak)

a b

Fronting Peak (TF < 1)

Chromatographic TheoryDefinitions - 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

where d = (tR)B – (tR)A

and ave w = [(wb)A + (wb)B]/2

bS w

dR

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 minRS = 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 = = ratio of distribution constants = KB/KA = kB/kA = (t’R)B/(t’R)A

Where (tR)B > (tR)A so that > 1• Smaller (closer to 1) means more difficult separation• In example chromatogram, (1st 2 peaks)

= (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 > 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)

Chromatographic TheoryQuestions 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 TheoryQuestions on Definitions

4. List 3 main components of chromatographs.5. 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?

6. 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, .

Chromatographic TheoryQuestions 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 TheoryQuestions 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 ; 1st 2 peaks on top)?

– Should be able to calculate k, N, RS, and α

min0 2.5 5 7.5 10 12.5 15 17.5

mV

0

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600

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1000

ADC1 A, ADC1 CHANNEL A (LILLIAN\102507000009.D)

0.9

26

7.1

73

8.4

44

12.

821

14.

242

15.

436

VWD1 A, Wavelength=210 nm (LILLIAN\102507000009.D)

0.8

41 1

.201

1.4

70 1

.613

2.6

96

8.3

09

14.

103

ADC1 A, ADC1 CHANNEL A (LILLIAN\102507000006.D)

0.9

24 1

.042

12.

754

VWD1 A, Wavelength=210 nm (LILLIAN\102507000006.D)

0.8

45 1

.204

1.4

73 1

.616

2.6

95

Unretained pk

min0 1 2 3 4 5 6 7 8

mV

50

100

150

200

250

ADC1 A, ADC1 CHANNEL A (MONIQUE\062608000004.D)

2.2

08

2.5

99

5.7

56

6.6

59

7.8

72

ADC1 B, ADC1 CHANNEL B (MONIQUE\062608000004.D) VWD1 A, Wavelength=205 nm (MONIQUE\062608000004.D)

2.8

42