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## Chapter 23

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### Chapter 23

Analytical Separations

We have looked briefly at distillation and more fully at extraction. How does this apply to chromatography?

Both separations were based on multiple equilibria.

For Distillation this was a evaporation / condensation step. (in a vertical column)

For extraction this was a solvent extraction step (in a piece of glassware).

What is ChromatographyEach step has enhanced purity of one of the compounds.

To improve this equilibrium step in distillation we force interaction between the vapor and liquid. This is done a variety of ways but one common way is to place plates in the column to collect the liquid.

This has become a key term in separations.

It now means a separation step.

ChromatographyPliny the Elder

Purification of water in antiquity.

Tswett Plant Physiologist - Russian 1906

Martin & Synge Nobel Prize

Craig

Van Deemter

Giddings

History1848 Way and Thompson: Recognized the phenomenon of ion exchange in solids.

1850-1900 Runge, Schoenbein, and Goeppelsroeder: Studied capillary analysis on paper.

1876 Lemberg: Illustrated the reversibility and stoichiometry of ion exchange in aluminum silicate minerals.

1892 Reed: First recorded column separation: tubes of kaolin used for separation of FeCI3 from CuSO4.

1903-1906 Tswett: Invented chromatography with use of pure solvent to develop the chromatogram; devised nomenclature; used mild adsorbents to resolve chloroplast pigments.

History1930-1932 Karrer, Kuhn, and Strain: Used activated lime, alumina and magnesia absorbents.

1935 Holmes and Adams: Synthesized synthetic organic ion exchange resins.

1938 Reichstein: Introduced the liquid or flowing chromatogram, thus extending application of chromatography to colorless substances.

1938 Izmailov and Schraiber: Discussed the use of a thin layer of unbound alumina spread on a glass plate.

1939 Brown: First use of circular paper chromatography.

History1940-1943 Tiselius: Devised frontal analysis and method of displacement development.

1941 Martin and Synge: Introduced column partition chromatography.

1944 Consden, Gordon, and Martin: First described paper partition chromatography.

1947-1950 Boyd, Tompkins, et al: Ion-exchange chromatography applied to various analytical problems.

1948 M. Lederer and Linstead: Applied paper chromatography to inorganic compounds.

History1951 Kirchner: Introduced thin-layer chromatography as it is practiced today.

1952 James and Martin: Developed gas chromatography.

1956 Sober and Peterson: Prepared first ion-exchange celluloses.

1956 Lathe and Ruthvan: Used natural and modified starch molecular sieves for molecular weight estimation.

1959 Porath and Flodin: Introduced cross-linked dextran for molecular sieving.

1964 J. C. Moore: Gel permeation chromatography developed as a practical method.

HistoryStationary Phase - The part of the system that does not move.

Mobile phase – The part of system that moves

Elution – Eluent (in), eluate (out)

Packed column

Open tube column.

TermsChromatogram - The instrumental output. A signal as a function of time (or volume)

Retention Time - How long a compound stays in the column. (tr) or could be expressed in terms of volume (Vr)

Dead volume Vm or could be expressed as a time(tm)

Volume to get through the system even without any interaction. A constant for a given column.

Adjusted retention time tr’

tr’ = tr - tm

Terms of Chromatography a alpha Relative Retention or Relative volatility, I will also refer to this as a separations factor.

a = (tr2’ / tr1’)

Capacity factor – measure of the amount of extra time a compound stays in the system beyond the tm. Will correlate with the equilibrium constant.

k’ = (tr – tm)/tm

TermsCapacity factor can be restated as the ratio of the time a compound is in the stationary phase over the time the compound is in the mobile phase.

This can be converted to moles. Thus the capacity factor is molesstat / molesmobile

This allows us to write k’ the following way

k’ = CsVs / CmVm

Retention time and partition coefficientRecall that K = Cs/Cm

So k’ = K (Vs/Vm) = (tr – tm) / tm = tm’ / tm

Relative Retention can also be expressed as

a = (tr2’/tr1’) = k2’/k1’ = K2/K1

To convert between volume and time one just needs the flow rate as a conversion factor.

RelationshipsFlow rate uv (ml/min)

Vr = tr * uv

Some types of chromatography will use volume and others time. However time is preferred.

TermsChromatography is known mostly as an analytical procedure. Separation of micrograms of material. The object of the game is to separate and quantify.

The system can be scaled up to separate at the gram scale.

Develop an analytical scale separation and then scale it up.

Scale UpScaling Rules (1)

- Keep column length the same.
- Cross-sectional area of column proportional to mass on column.

Scaling Rules (2)

- Maintain constant linear flow rate. (This will mean that the volume flow rate will change.)

Ideal chromatographic peaks are Gaussian in peak shape.

This comes directly from the Craig Model.

We know certain facts about Gaussian peaks.

The PeakFactors for Resolution

- Two
- The separation of the peaks
- The widths of the peaks
- Both separations are the same but the widths are wider for the bottom example.

Resolution

- Resolution = Dtr / wave = 0.589Dtr/w1/2ave

Diffusion

- A fundamental process. Leads to broadening of peaks in separation methods.
- Flux (mol/m2s) = J = -D(dc/dx)

Diffusion

- Broadening of band by diffusion.
- c concentration (mol/m3)
- t is time
- x distance along column
- Standard deviation of the band will be

Terms

Linear flow rate ux

Distance peak has traveled along the column x

Time on column then would be t = x / ux

s2 = 2Dt = 2D(x/ ux) = (2D/ ux)*x = Hx

2D/ux is the plate height giving us

H = s2 / x

Plate HeightThe longer a compound is in the column the wider the peak.

Narrow peaks will allow us to resolve peaks coming out at nearly the same time.

Different compounds passing through a column at different times might have different plate heights since they will generally have different diffusion coefficients.

Plate theory calls for constant plate height since diffusion is ignored in this model.

Plate Height is a Measure of Column EfficiencyPlates

- N = L/H = Lx/s2 = L2/s2 = 16L2/w2

We could potentially measure the width at half height and knowing it is a Gaussian peak derive the following.What if is difficult to measure the width of a baseline?

Factors Affecting Resolution

- Resolution can also be expressed with the following equation.

Band Spreading

- We have gone to a great deal of effort to separate our peaks. We can see that diffusion is working against us.
- We measure this spreading as the standard deviation squared (Variance). s2
- Variance comes from many sources but we can express it as a sum.

Outside the Column

- Injector, detector, tubing and tubing junctions.

Tells us the contribution to H of three sources.

Recall that we want a minimum number for H!

A Multiple paths B Longitudinal diffusion C Equilibration time

ux is the linear flow rate

Van Deemter EquationYou can see from the previous plot that that best flow rate for your system.

Where the H value is minimum

How do we find this point.

Run about 20 or more experiments at different flow rates, find H and then plot the resulting curve. Pick Hopt from this plot.

Optimum Flow RateOr ………

Make three injections, find the values of A, B and C.

Find the minimum point.

How?

Optimum Flow RateTake the derivative of the van Deempter equation.

At the minimum point the derivative will be zero so:

Optimum Flow RateOpen tube columns

Higher resolution

Shorter Analysis time

Increased sensitivity

Lower sample capacity

Comparison of open tubular and packed columns.Open Tubular Columns

- At a constant pressure
- Flow rate is proportional to cross sectional area
- Flow rate is inversely proportional to the column length

For open tubular column this means that we can get

Increased linear flow rate and/or a longer column

Decreased Plate height, which means improved better resolution

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