Question

The van Deemter plot (a) Sketch and fully label a van Deemter plot for gas chromatography. (b) Sketch and fully label a van Deemter plot for liquid chromatography. (c) Point out the important differences between the two graphs in (a) and (b). (d) The shape of the plots in (a) and (b) are often described based on four variables. Describe these variables and their contribution to the van Deemter curve. (e) One of the variables is negligible or non-existent for open-tubular columns. Which variable and why?

Answer 1

A. A van Deemter plot for gas chromatography can be seen below. A, B and C are constants and v is the linear velocity, the carrier gas flow rate. The A term is independent of velocity and represents "eddy" mixing. It is the smallest when the packed column particles are small and uniform. The B term represents axial diffusion or the natural diffusion tendency of molecules. This effect is diminished at high flow rates and so this term is divided by v. The C term is due to kinetic resistance to equilibrium in the separation process. The kinetic resistance is the time lag involved in moving from the gas phase to the packing stationary phase and back again. The greater the flow of gas, the more a molecule on the packing tends to lag behind molecules in the mobile phase. Thus this term is proportional to v.

HETP-A+B/v+Cv 0.6 Cv I 0.4 B/v 0.2 0.0 30 50 40 80 0 20 60 70 Linear velocity (cm/s)

B. The van Deemter equation relates height equivalent to a theoretical plate (HETP) of a chromatographic column to the various flow and kinetic parameters which cause peak broadening, as follows:

${\displaystyle HETP=A+{\frac {B}{u}}+(C_{s}+C_{m})\cdot u}$

-van Deemter equation multiple paths term mass transfer term longitudinal diffusion term B/u A=1.5 mm 8-25 mm C, + Cm 0.025 mm sis 100 20 40 80 60 Flow Rate (mL/min)

C. the linear velocity can be taken as the ratio of the column length to the dead time. If the mobile phase is a gas, then the pressure correction must be applied. The variance per unit length of the column is taken as the ratio of the column length to the column efficiency in theoretical plates.  

D. Where

• HETP = a measure of the resolving power of the column [m]
• A = Eddy-diffusion parameter, related to channeling through a non-ideal packing [m]
• B = diffusion coefficient of the eluting particles in the longitudinal direction, resulting in dispersion [m² s⁻¹]
• C = Resistance to mass transfer coefficient of the analyte between mobile and stationary phase [s]
• u = Linear Velocity [m s⁻¹]