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11.2.4 Plate height and resolution

Plate height

Chromatography columns are considered to consist of a number of adjacent zones

in each of which there is sufficient space for an analyte to completely equilibrate

between the two phases. Each zone is called atheoretical plate(of which there are

Nin total in the column). The length of column containing one theoretical plate is

referred to as theplate height,H, which has units of length normally in micro-

metres. The smaller the value ofHand the greater the value ofN,the more efficient

is the column in separating a mixture of analytes. The numerical value of both

NandHfor a particular column is expressed by reference to a particular analyte.

Plate height is simply related to the width of the analyte peak, expressed in terms of

its standard deviations(Fig. 11.1), and the distance it travelled within the column,x.

Specifically:

H¼

^2

x ð^11 :^7 Þ

For symmetrical Gaussian peaks, the base width is equal to 4sand the peak width

at the point of inflection,wi, is equal to 2s. Hence the value ofHcan be calculated

from the chromatogram by measuring the peak width. The number of theoretical

plates in the whole column of lengthLis equal toLdivided by the plate height:

N¼L

H

¼Lx

^2

ð 11 : 8 Þ

If the position of a peak emerging from the column is such thatx¼L,from knowledge

of the fact that the width of the peak at its base,w, obtained from tangents drawn

to the two steepest parts of the peak, is equal to 4s(this is a basic property of all

Gaussian peaks) hences¼w/4 and equation 11.8 can therefore be converted to:

N¼

L^2

^2

¼

16 L^2

w^2

ð 11 : 9 Þ

If bothLandware measured in units of time rather than length, then equation 11.9

becomes:

N¼ 16 ðtR=wÞ^2 ð 11 :10aÞ

Rather than expressingNin terms of the peak base width, it is possible to express it in

terms of the peak width at half height (w1/2) and this has the practical advantage that

this is more easily measured:

N¼ 5 : 54 ðtR=w 1 = 2 Þ^2 ð 11 :10bÞ

Equations 11.9 and 11.10 represent alternative ways to calculate the column

efficiencyin theoretical plates. The value ofN, which has no units, can be as high

as 50 000 to 100 000 per metre for efficient columns and the corresponding value ofH

can be as little as a few micrometres. The smaller the plate height (the larger the value

ofN), the narrower is the analyte peak (Fig. 11.2).

438 Chromatographic techniques