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Some days ago, I tried for the first time a chromatography machine. The data I collected are the following:

$$ \begin{array}{lrrr} \hline \text{Compound} & t_\mathrm{R}/\pu{min} & w/\pu{min} & N \\ \hline \text{Benzene} & 2.325 & 0.047 & 39153 \\ \text{Toluene} & 2.712 & 0.067 & 26214 \\ \text{Chlorobenzene} & 3.690 & 0.099 & 22228 \\ \textit{p}\text{-Chlorotoluene} & 4.332 & 0.106 & 26723 \\ \hline \end{array} $$

I know the relationship between retention time $t_\mathrm{R},$ peak width $w$ and theoretical plates $N.$

Known the different properties, boiling points, polarities, or shapes of the molecules involved, is there a way to predict which molecule will yield an higher number of theoretical plates?

Which characteristics of the molecules affect the different number of plates for each molecule?

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The number of theoretical plates can be calculated as:

$\mathrm{N_t = \frac {H}{HETP}}$

$\mathrm{N_t =}$ number of theoretical plates
$\mathrm{H =}$ total height (or usually length) of the column [$\mathrm{m}$]
$\mathrm{HETP =}$ Height Equivalent to a Theoretical Plate [$\mathrm{m}$]

Where $\mathrm{HETP =}$ can be calculated from the Van Deemter equation:

$\mathrm{HETP = A + \frac {B}{u} + (C_s + C_m) * u}$

$\mathrm{A =}$ Eddy-diffusion parameter, related to channeling through a non-ideal packing [$\mathrm{m}$]
$\mathrm{B =}$ diffusion coefficient of the eluting particles in the longitudinal direction, resulting in dispersion [$\mathrm{m^2 s^{−1}}$]
$\mathrm{C =}$ Resistance to mass transfer coefficient of the analyte between mobile and stationary phase [$\mathrm{s}$]
$\mathrm{u =}$ Linear Velocity [$\mathrm{m s^{−1}}$]

So, the characteristics specific to the analyte molecule that determine the number of theoretical plates are B and, unfortunately from the standpoint of developing an ab initio model, C.

Various models have been developed, however. Below is a list of references to some articles of interest in this field.

[ 1 (abstract)]"The problem of plate modeling: Theoretical and computational results", Computer Methods in Applied Mechanics and Engineering, Volume 100, Issue 2, October 1992, Pages 249–273

[ 2 ]"Plate Models in Chromatography: Analysis and Implication for Scale Up", Chromatograpy,Springer-Verlag

[ 3 (abstract)]"Neural Network Modeling of Structured Packing Height Equivalent to a Theoretical Plate", Ind. Eng. Chem. Res., 2000, 39 (5), pp 1520–1525

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  • $\begingroup$ I think it may be worth noting explicitly in this answer that the column chemistry is a primary determinant of it HETP and of N. GC usually uses nonpolar stationary phases such that vapor pressure is a primary determinant of these parameters. Would the same be true if an e.g. an aqueous stationary phase was used to analyze ammonia gas? $\endgroup$
    – Curt F.
    Dec 28 '20 at 17:10

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