Question

A chromatogram gives an ideal Gaussian peak with tr = 9.70 min and w1/2 = 0.23 min.

How many theoretical plates does the column have?

What is the plate height (in mm) of the column if the column is 12.2 cm long?

Answer 1

Given retention time t_r=9.70 min and width w_1/2=0.23 min

The formula for number of theoretical plates

N=16(t_r/w)²=5.5416(t_r/w_1/2)²

where t_r is the component retention time;

w is the chromatography peak width at the baseline;

w1/2 is the peak width at half height.

Now substitue given values in the above equation,

N=5.54 (9.70/0.23)²=9852.659 plates.

The number of theoretical plates, N,

N=L/H

where L is the column’s length and H is the height of a theoretical plate.

Given L=12.2 cm =122 mm.

height H=L/N=122 mm/9852.659 plates=0.0124 mm

Plate height H=0.0124 mm.