Question

In your own words explain what a theoretical plate is . What is the relationship between the number of theoretical plates and resolution? How is theoretical plate height related to resolution? Now quantitatively, answer the following question: How many theoretical plates, N, must a packed column have to achieve a resolution of 1.5 between 2 peaks that elute at 5.42 minutes and 5.63 minutes. At a resolution of 1.5 are these peaks considered resolved?

Answer 1

a)

A theoretical plate is a hypothetical stage or zone in which the liquid and vapour phases of a substance exist in equilibrium. The number of theoretical plates can be used to determine the performance and effectiveness of columns

b)

The relationship between number of theoretical plates (N) and the resolution (R) can be shown as,

Rs = (1/4) x (N)^1/2 x [(α - 1)/α] x [k/(1 + k)

Here, Rs is the resolution

N is the number of theoretical plates

α is the separation factor and k is the retention factor

The relation between theoretical plate height and the resolution:

c)

The height of theoretical plate can be calculated by H = L/N, where L = length of column used

This ratio gives information about the resolution.

d)

Here, By assuming t₀ = 0, α = (5.63-0)/(5.42-0) = 1.038

k = (5.63/5.42) – 1

=1.038 -1 = 0.038

By substituting the values,

1.5 = (1/4) x (N)^1/2 x [(1.038 - 1)/1.038] x [0.038/(1 + 0.038)

(N)^1/2 = 4471.9 ²

Therefore, N = 20042760.10

e)

A resolution of 1.5 is sufficient for the given peaks to be considered resolved.