# Ion Chromatography - Dispersion by Resistance to Mass Transfer in the Stationary Phase 2

All four molecules will continue down the column while molecules 5 and 6 diffuse to the surface. By the time molecules 5 and 6 enter the mobile phase the six molecules will have been smeared along the column and the band of six molecules will have been dispersed. Van Deemter derived and expression for the variance resulting from the resistance to mass transfer in the stationary phase (_{})which is as follows.

_{} (10)

where (**k')** is the capacity ratio of the solute,.

(**d**** _{f}**) is the effective film thickness of the stationary phase,

(**D**** _{S}**) is the Diffusivity of the solute in the stationary phase,

and the other symbols have the meaning previously ascribed to them.

Now all the expressions are for the variance contribution from each dispersion process to the total peak variance. Consequently, to obtain the overall variance of the peak eluted from the column the individual variances can be summed thus,

_{}

where (_{}) is the total variance per unit length of the eluted peak.

Replacing the expression for each varance term, s^{2}_{M ,} s^{2}_{L}, s^{2}_{MT(m)} and s^{2}_{(MT)s}

_{} (11)

The above equation was developed in 1956 and since that time a number of alternative equations have been put forward (see Chrom. Ed., Chromatography Theory) but the best fit to experimental data for liquid chromatography (including ion chromatography) remains that of Van Deemter Equation.

Now if (**s**** _{L}**) is the standard length deviation of a solute peak having passed through a column of length (

**L**) then by simple proportion,

_{}

or _{}

Now, from Chrom. Ed., Chromatography Theory)

_{}

and _{}

where, (**n**) is the number of theoretical plates in the column (**v**** _{m}**) is volume of mobile phase per plate,

(**v**** _{S}**) is the solume of stationary phaser per plate,

and (**K**) is the distribution coefficient of the solute between the phases.

_{}

or _{} (12)

It is now clear why equation (11) is called the HETP equation, (*i.e* the height of the Theoretical plate) equation as (L/n) is numerically the height of the theoretical plate and is equivalent to the variance per length of the column (_{} = H).

Placing the HETP equation in a simpler form ,

_{} (13)

where _{}