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Making Sense of Band Broadening, Column Efficiency and Resolution


You might already noticed that chromatographic peaks have a ‘normal distribution curve’ appearance. In the figure below,  you will see the distribution of solute molecules along the column at the time when the analyte peak reaches the end of packing.

Relationship between Plate Height and Peak Area

In this figure above, band broadening is proportional to the chromatographic term plate height (H) which intern is inversely proportional to column efficiency. The other related quantitative measure of column efficiency is number of theoretical plates (N) and described as:

N = L/H

Details of the theoretical model of plate theory of chromatography are discussed during the lecture!

Now can you guess the relationship between column efficiency and plate numbers?

A further understanding of band broadening of chromatographic peaks can be achieved by reviewing the rate theory of chromatography which mainly relate to rate of elution. Here we consider The Eddy diffusion (A), Longitudinal diffusion (B) and Resistance to mass transfer (C). The relationship between these elution and band broadening parameters with pate height is shown by the equation:

H = A + B / u + C u      where u is average velocity of mobile phase.

The resulting relationship between flow rate and plate height is shown in the Van Deemter plot below.

 Van Deemter Plot

Can you predict the effect of the following conditions on band broadening or column efficiency?

1.      Flow rate of mobile phase

2.      Diffusion coefficient of solutes ((a) gas, (b) liquid mobile phase)

3.      Relationship between the above two conditions (1, and 2)

The relationship between plate numbers and retention time and peak broadening can be shown mathematically as:

N = 16 (tR/W)2   where W = width of the peak at the base

The ability to separate analytes is called resolution Rs and for two components A and B analytes in a mixture, Rs can be defined as:

Have you noticed the difference between selectivity factor and resolution?

From the equation below, one could further see the relationship between resolution and number of plates, selectivity factor and capacity factor.

 

Problem - A student tried to increase the resolution of his chromatogram by doubling the length of his column.  It didn't work! Explain why and give alternatives approaches to achieve the goal.

From the above resolution equation, you can see that there would be no resolution if selectivity factor is reduced to unity! Suggest possible ways of increasing selectivity?

Are you ready to further review your study on column efficiency, selectivity and resolution? Sketch a typical chromatogram for two compounds under the following conditions:

1.    Poor resolution and efficiency; adequate selectivity

2.      Good resolution, selectivity and efficiency

3.      Poor resolution, efficiency and selectivity

4.      Good resolution and selectivity, long analysis time and, poor efficiency

5.      Good efficiency and selectivity, poor resolution

 

Further summary and exercise

1.      I  expect you to know the definition of the following:

a)     Elution

b)     Mobile and stationary phase

c)      Partition ratio

d)     Retention time

e)     Capacity factor

f)        Selectivity factor

g)     Plate height and number of plates

h)      Resolution

2.      Based on the data below, calculate for each compound

a)     Capacity factor

b)     Partition coefficient

c)      Resolution

d)     Selectivity

e)     Number of plates

f)        Plate height

Length of column       30 cm

Flow rate                    1 ml/min

VM                               6 ml

VS                                0.5 ml

 

Retention time

Peak width (W), min.

Solvent

4 min

-

Compound A

7 min

0.5

Compound B

22 min

1.5

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