1. Separation Techniques
Extraction and Chromatography

2. Extraction
Simple liquid-liquid extraction in analytical work is generally done for one of two reasons:
Purification, i.e., separating the analyte from interferents, or
Concentration, i.e., getting the analyte into a smaller volume
If the analyte is a metal ion, the extracting medium will often include a complexing agent.

3. Partition Coefficient, or Distribution Ratio
When a solute distributes itself between two immiscible phases, typically aqueous and organic, equilibrium may be established
Saq ↔ Sorg
and the resulting equilibrium expression is
KD = [Sorg]/[Saq]
where KD is the partition coefficient.

4. D = [HA]org / {[HA]aq + [A-]aq}
Distribution Ratio
Some solutes may appear in more than one form in a solvent, e.g., when an acid dissociates, HA ↔ H+ + A-.
If such dissociation occurs in the aqueous phase but not the organic phase, then we can define the distribution ratio as
D = [HA]org / {[HA]aq + [A-]aq}

5. Extraction Efficiency
If we define the fraction of solute extracted in a single step extraction, Ei, and the fraction remaining behind unextracted as, Ui, it can be shown (see your handout) that
E1 = KD/ [(V1/V2)+KD], and
U1 = V1/ [V1 + V2KD] *
Further, Ui = (U1)i
*(same as equation 7.24 in your text with different symbols)

6. Chromatography
Chromatography can be thought of as a method involving continuous extraction in very small increments of clean extracting solvent.
Chromatography always has two phases, just as in extraction, but they are called the mobile phase and the stationary phase.
The movement of the solute through the column is called elution.
The phase distribution of the solute(s) in chromatography can occur by any of several equilibria, not just solubility, as in extraction.

7. Types of Equilibria Applied to Chromatography
Adsorption – the stationary phase is a solid on which the solutes adsorb.
Solubility – the stationary phase is a liquid into which the solutes dissolve.
Ion-exchange – the stationary phase is composed of ion exchange beads which attract cations or anions
Size-exclusion – the stationary phase is porous beads which temporarily trap solutes based on their particle size.

9. A way of visualizing what
happens in chromatography
by thinking of it as taking
place in a series of many
small steps.
This diagram simulates what
happens when two solutes
are separated. As the caption
says, the A component has a
KD of 1 and the B component
has a KD of 3.

11. General Chromatogram

12. Chromatographic Terms
Retention time, tr,A, the time it takes com-ponent A to exit the column past the detector.
Void time, tm, the time it takes a non-retained component (air in GC) to exit.
Adjusted retention time, tr’ = tr – tm.
Baseline width, Wb, measured at inter-section of tangents with sides and baseline.

13. Resolution

14. Different Resolutions

15. The Chromatographic Challenge
Looking at the resolution curves, it can be seen that resolution can be increased by increasing the time between the peaks or by decreasing the width of the peaks.
The challenge for the chromatographer is to accomplish optimal resolution within a reasonable amount of time. Thus, simply increasing the time by some means is not necessarily the best way to go.
Let us consider what causes band broadening and see if we can figure ways to decrease it.

16. Capacity Factor
Capacity factor, k’ (also known as retention factor), takes into account the relative volumes of the mobile and stationary phases,
k’ = D (Vs/Vm)
It turns out that it can also be related rather simply to retention times,
k’ = tr’/tm

17. Column Selectivity Factor
The selectivity factor, α, relates to the ability of a column to separate two solutes,
α = kB’ / kA’
It will be equal to one when the two components have the same retention times.

18. Plate Theory of Band Broadening
Early on, theorists drew parallels between the behavior of chromatographic columns and fractional distillation columns with plates separating temperature regions.
Chromatography can be thought of as behaving like a fractional distillation column with many plates.
Each time the solute enters the stationary phase essentially constitutes a ‘theoretical plate.’

19. Calculating Column ‘Plates’
The distance a solute travels, on average, between stops in or on the stationary phase determines, in part, how wide a peak gets.
Further, the longer the solute stays in the column, the wider the peak gets.
Thus the height equivalent to a ‘theoretical plate,’ HETP or just H, can be related to peak width and retention time
H = Lw2/16tr2

20. Calculating Column ‘Plates’
The number of times on average the solute stops in or on the stationary phase is essentially the number ‘theoretical plates’ a column behaves as though it has.
N = (4tr/w)2
It is also equal to the column length divided by H.

21. Band Broadening
Van Deemter gave an equation which relates the number of theoretical plates in a column to the flow rate, u, of the mobile phase and three parameters
H = A + B/u + Cu

22. Van Deemter Parameters
A, eddy diffusion,is related to the size and uniformity of the stationary phase particles.
B, longitudinal diffusion, is the inevitable diffusion of a fluid in all directions.
C, mass transfer, is complexly related to the geometry of the stationary phase, the distribution coefficient, and diffusion rates in the mobile and stationary phases

24. So, with all that, how do I increase resolution?
Increase Δtr by
Increasing L
Increase amount of stationary phase
Get a better selectivity factor, α
Decrease temperature
Get a better stationary phase
Get a better liquid phase (in liquid chromatograpy)
(more)

25. More resolution improvement
Decrease band width, w, by
Using more uniform packing
Using smaller packing
Use no packing, use SCOT column (for GC)
Optimize flow rate
Reduce sample size
Reduce dead space in column
Decrease diameter of column