Question

13.Explain each term in the Van Deempter Equation (Below). What major advantage is gained through open tubular GC in reference to this equation?

Answer 1

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

Where

• HETP = height equivalent to a theoretical plate, 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]

In open tubular capillaries, the A term will be zero as the lack of packing means channeling does not occur. In packed columns, however, multiple distinct routes ("channels") exist through the column packing, which results in band spreading. In the latter case, A will not be zero.

The form of the van Deemter equation is such that HETP achieves a minimum value at a particular flow velocity. At this flow rate, the resolving power of the column is maximized, although in practice, the elution time is likely to be impractical. Differentiating the van Deemter equation with respect to velocity, setting the resulting expression equal to zero, and solving for the optimum velocity yields the following:

The Van Deemter equation can be further expanded to:^[3]

Where:

• H is plate height
• λ is particle shape (with regard to the packing)
• d_p is particle diameter
• γ, ω, and R are constants
• D_m is the diffusion coefficient of the mobile phase
• d_c is the capillary diameter
• d_f is the film thickness
• D_s is the diffusion coefficient of the stationary phase.
• u is the linear velocity