Question

Understand and be able to explain each of the terms in the Purnell equation (N, α, and k) and the van Deemter equation (A, B, C, μx). Know how changing these factors will affect the separation (broader/narrower peaks, longer time, shorter time, separation between peaks)

Answer 1

What is Purnell Equation?

In the Analytical Chemistry division, Purnell equation is employed for the purpose of calculating the resolution R_s, among the two peaks in the Chromotagram.

The Equation is

R = N₂ / 4 (   - 1 /   ) (  '₂  / 1 +  '₂  )

R_s  = Resolution among the two Peaks

N₂ = Number of Plates in the Second Peak

= Factor of Separation among the two peaks

'_{2 =}  Retention factor of the Second Peak

The Separation gets enhanced, by the larger resolution.

Van Deemter Equation

The analysis of Broadbanding in Chromatography method leads to the derivation called Van Deemter Equation. The Equation correlates the height similar to the theoretical plate and the experimental parameters such as

a. rate of flow regarding the mobile phase.

b. The Diameter of the particles which are in the Staionary phase.

c. Diffusion Coefficients of the Solute phases in the stationary as well as mobile

The Expression of Van Deemter Equation which is beneficial in the enhancement of chromatographic accomplishment is

HETP = 2d_p + 2vd_g  / u + 8 /²  K / (1 + K)² d_f² / d_l x u

= Constant value which signifies the packing of Column

d_p   = Diameter of the Particle

v = Factor of Blockage

d_{g =}  Diffusion Coefficient of the Solute molecules which is present in the carrier gas in cm² / sec

u = Carrier gas Velocity

8 /²  = Number value belongs to the consistency of the liquid film thickness which is present on the particles.

K = Volume Factor

d_f  = Liquid Phase film thickness

d_l  = Difficient Cofficient of the Solute which is in the liquid phase in cm² / sec

In this Equation, the Velocity of the Carrier Gas 'u' is the variable one, whereas all the terms are constant. The reduced form of the equation is

HETP = A + B / u + Cu

HETP = Height of the Plate

A = Multiple path Coefficient of Eddy's Diffusion

B = Term of Longitudinal Diffusion

C = Hindrance to the coefficient of Mass Transfer

u = Carrier Gas Velocity

Effects of Changing these factors in Separation

a.The overall change due to the alteration of Eddy's Diffusion term results in band broadening.

b. Longitudinal diffusion is evident for low flow rates

c. Change in the Mass Transfer results in the enlargement of the portion associated with mobile phase.