A peak with a retention time of 407 s has a width at half-height (w1/2) of 7.6 s. A neighboring peak is eluted 17 s later with a w1/2 of 9.4 s. A compound that is known not to be retained was eluted in 2.5 s. The peaks are not baseline resolved. How many theoretical plates would be needed to achieve a resolution of 1.5?

2.46 x 104

Explanation:

Solution

Recall that:

The retention time of a peak = 407 s

with a width at half-height of = 7.6 s

A compound is retained in 2.5 s.

resolution to be achieved = 1.5

Thus,

The number of plates (theoretical)= 16(tr2 / w2)

The R Resolution R= 0.589 Δtr / w1/2av = 0.589(17s) / 1/2(7.6s + 9.4s) = 1.18

Supposed that applied column contains 10,000 theoretical plates and the resolution of two peaks is 1.18

So if the column is replaced to obtain 1.5 resolution, the number of theoretical plates is needed is  stated below;

width at the base = 9.4 - 7.6 = 1.8; tr = 0.786

N = 5.55tr2 / w21/2 = 5.55 (0.7862/ 1.182) x 104

= 2.46 x 104

Therefore, required theoretical plates to achieve a resolution of 1.5 is 2.46 x 104