Advanced Separations

Question 1

Draw a schematic of the apparatus used in chromatography.

Answer 1

Question 2

What is the principle basis of chromatography?

Answer 2

The principle basis of chromatography is that the partitioning of the analytes between the mobile and stationary phases gives rise to separation.

Question 3

Draw a simple sketch of a chromatogram, defining the term t_m.

Answer 3

The dead time or void time, t_m, is the amount of time that it takes for an analyte that doesn’t interact with the stationary phase to elute (e.g. the amount of time it takes for the mobile phase to elute).

Question 4

What is the equation for resolution, R_s?

Answer 4

Where t_R is the retention time and W is the peak width at the base.

Question 5

What is the value of R_s for baseline resolution?

Answer 5

For baseline resolution, R_s > 1.5.

Question 6

What is the equation for the capacity factor, k’?

Answer 6

Question 7

What is the capacity factor, k’?

Answer 7

The capacity factor is an experimental parameter used to compare migration rates of solutes in columns (i.e. the amount of time the solute spends in the stationary phase relative to the amount of time the solute spends in the mobile phase). The ideal range is 1-5, but in reality it is 0.5-20. The larger the retention time, the greater the capacity factor.

Question 8

What is the selectivity factor, α?

Answer 8

The selectivity factor is the ratio of the capacity factors of two analytes. For separation to occur, the analytes must have different capacity factors.

Question 9

What is the equation for the selectivity factor, α?

Answer 9

If analyte 1 is eluted first then k’2 > k’1 and α > 1.

Question 10

How is the capacity factor, k’, related to the equilibrium constant, K?

Answer 10

Where c is the concentration, n is the amount in moles, and V is the volume. If the column is run slowly enough to be at equilibrium, C_s/C_m is the equilibrium constant, K. Because the ratio of the phase volumes is constant for a given column and mobile phase, the capacity factor for any analyte is directly proportional to its partition equilibrium constant.

Question 11

How is the equation for the capacity factor, k’, derived from migration velocity?

Answer 11

The migration velocity depends on the distribution of the analyte between the mobile and stationary phases, where UM is the velocity of the mobile species and UR is the velocity of the retained species.

Question 12

How does the band shape of a chromatographic peak change with time?

Answer 12

The total area under the peak remains the same.

Question 13

What is the rate theory of chromatography?

Answer 13

It is a random walk in one dimension. There is a symmetrical spread of velocities around a mean value.

Question 14

What is variance?

Answer 14

Where σ is the standard deviation in length units and τ is the standard deviation in time units (τ = W / 4). 68 % of the peak area is in the range t_R ± τ and 95 % is in the range t_R ± 2τ.

Question 15

What is the diffusion coefficient, D, and how is it related to variance?

Answer 15

The diffusion coefficient, D, measures the rate at which a substance moves randomly from a region of high concentration to a region of low concentration. Where σ² is the variance and t is the time.

Question 16

What causes asymmetric band shapes?

Answer 16

Skewing occurs when the partition equilibrium constant, K, is dependent on the concentration. Fronting occurs from the overloading of too much solvent, and it can be corrected by using smaller or dilute samples. Tailing occurs when small quantities of solute are retained more strongly than large quantities. It can be corrected by masking the strong adsorption sites on the stationary phase.

Question 17

What is plate height, H?

Answer 17

Plate height is the constant of proportionality between the variance of the band and the distance is has travelled. It can be thought of as approximately the length of column required for one equilibration of the solute between the mobile and stationary phases. It is a measure of variance per unit length (H = σ² / L). It is also known as the “height equivalent to a theoretical plate” - HETP.

Question 18

What is the equation for plate height, H, and how is it derived?

Answer 18

If a solute has travelled a distance, x, at linear flow rate, U_x, then the time it has been on the column is:

Question 19

What is the plate model?

Answer 19

The plate model states that the column contains a large number of separate layers (theoretical plates). The analyte moves down the column by the transfer of equilibrates mobile phase from one plate to the next.

Question 20

What is the equation for efficiency, N?

Answer 20

Efficiency, N, is the theoretical number of plates or the plate count. It is dimensionless and can range from 100-100,000.

Question 21

What can you use to describe column performance?

Answer 21

Plate height, efficiency, peak asymmetry and the capacity factor can be used to describe column performance.

Question 22

How is the resolution, R_s, related to the efficiency, N, and the difference in retention time, Δt_r?

Answer 22

Therefore, R_s is proportional to the square root of N.

Question 23

What is the van Deemter equation?

Answer 23

Where A is the contribution from multiple flow paths, B is the contribution from longitudinal diffusion and C is the contribution from mass transfer or equilibrium time. For packed columns, all three terms contribute. For open tubular columns, A is zero. For capillary electrophoresis, A and C are zero.

Question 24

How can the different terms in the van Deemter equation be reduced?

Answer 24

A is the contribution from multiple flow paths. If an analyte has a short path, it will emerge from the column faster. This effect is reduced by using smaller stationary phase particles. B is the contribution from longitudinal diffusion. The longer an analyte is in the column, the more diffusion will occur and the wider the band width will be. This effect can be reduced by using a faster linear flow. C is the contribution from mass transfer or equilibrium time. There is a finite time for the analyte to equilibrate between the mobile and stationary phases. This effect can be reduced by decreasing the stationary phase thickness or column radius, or increasing the temperature.

Question 25

How does plate height vary with flow rate?

Answer 25

Question 26

How does the order of elution occur in GC?

Answer 26

Within a compound class, analytes elute in the order of their boiling points. Molecules within different compound classes are more strongly retained is they have a greater similarity to the stationary phase.

Question 27

What is the relationship between the capacity factor, k’, and the boiling point, T_bp?

Answer 27

Question 28

How can you elute analytes with a wide range of boiling points?

Answer 28

You can control the retention time by varying the temperature (i.e. increase the temperature with time to elute analytes with high boiling points faster).

Question 29

Compare open tubular and packed GC columns.

Answer 29

Packed columns have a high flow resistance, short length, high phase ratio and low efficiency; overloading is not a problem. Open tubular columns have a low flow resistance, long length, low phase ratio and high efficiency; overloading is a problem if too much analyte is injected.

Question 30

How does the order of elution occur in HPLC?

Answer 30

The analytes elute in the order of their hydrophobicity (i.e. the most hydrophobic last) if the stationary phase is non-polar.

Question 31

What is eluent strength, ε°?

Answer 31

Eluent strength, ε°, is the solvent adsorption energy, which is defined as zero for pentane on bare silica. As ε° increases, the solute elutes more rapidly. In reverse phase HPLC, a less polar solvent has a higher ε°.

Question 32

How can the capacity factor, k’, be controlled using an organic modifier?

Answer 32

Where Φ is the volume fraction of organic modifier in the mobile phase and k’_w is the capacity factor in water.

log(k’) decreases linearly with Φ.

We can change the type of organic modifier (OM) because different OMs have different values of S or we can vary the volume fraction of the OM (i.e. the mobile phase composition). Changing the solvent composition during a HPLC run is analogous to changing the temperature in GC. Most HPLC runs use gradient elution.

Question 33

How can the capacity factor, k’, be controlled using porous or non-porous silica?

Answer 33

Non-porous silica has a much lower phase ratio (V_s/V_m) and can decrease the capacity factor by a factor of 10-100.

Question 34

Compare the plate heights in LC and GC.

Answer 34

The plate height is much smaller in LC because transverse diffusion is slower in a liquid; therefore, the B term in the van Deemter equation is smaller.

Question 35

How does plate height change with particle diameter?

Answer 35

The A term in the van Deemter equation increases with particle diameter because there is a less uniform flow through the column. The C term increases with particle diameter because it takes longer to diffuse through the inner pores. Therefore, the plate height increases with particle diameter.

Question 36

What is UHPLC?

Answer 36

UHPLC is ultra-high pressure liquid chromatography. As the particle size decreases to < 2.5 μm, there is an increase in efficiency that does not significantly decrease at higher flow rates. However, this requires an investment in new systems, and the transfer of methods is not straightforward.

Question 37

Compare efficiencies in LC and GC.

Answer 37

The efficiency is higher in capillary GC due to the very long column length.

Question 38

How should you optimise efficiency in LC?

Answer 38

Use a packed column with a particle diameter as small as possible that is consistent with the pressure limitations. Also, minimise any extra band broadening effects. The distance to the detector is critical so use UV or MS.

Question 39

Compare the selectivity in LC and GC.

Answer 39

A 4% difference in retention time is needed in LC, but only a 1% difference is needed in GC; therefore, GC has a lower minimum selectivity requirement for baseline separation.