26.5: Summary of Important Relationships for Chromatography

In this chapter we have introduced many chromatographic variables, some directly measured from the chromatogram, provided by the manufacturer, or from the operating conditions, and some derived from these variables. The following two tables summarize these variables.

Table \(\PageIndex{1}\). Chromatographic Variables Directly Measured From Chromatogram, Provided by Manufacturer, or From Operating Conditions

variable	name	source
\(t_r\)	retention time for solute	chromatogram
\(t_m\)	retention time for non-retained solute	chromatogram
\(w\)	peak width	chromatogram
\(u\)	mobile phase flow rate	operating conditions
\(L\)	length of column's stationary phase	manufacturer
\(d_c\)	diameter of column	manufacturer
\(d_p\)	diameter of packing material	manufacturer
\(d_f\)	thickness of stationary phase	manufacturer
\(V_s\)	volume of stationary phase	operating conditions

Table \(\PageIndex{2}\). Derived Chromatographic Variables

variable	name	equation to derive value
\(V_m\)	volume of mobile phase	\(V_m = t_m u\)
\(k\)	retention factor	\(k = \frac{t_r - t_m}{t_m}\)
\(t_r^{\prime}\)	adjusted retention time	\(t_r^{\prime} = t_r - t_m\)
\(D\)	distribution ratio	\(D = k \times \frac{V_s}{V_m}\)
\(\alpha\)	selectivity factor	\(\alpha = \frac{k_B}{k_A}\)
\(R_{AB}\)	resolution	\(R_{AB} = \frac{\sqrt{N_B}}{4} \times \frac{\alpha - 1}{\alpha} \times \frac{k_B}{1 + k_B}\)
\(N\)	number of theoretical plates	\(N = 16 \left(\frac{t_r}{w} \right)^2\)
\(H\)	height of theoretical plates	\(H = \frac{Lw^2}{16 t_r^2} = \frac{L}{N}\)
\(H_p\)	height due to multiple paths	\(H_p = 2 \lambda d_p\)
\(H_d\)	height due to longitudinal diffusion	\(H_d = \frac{2 \gamma D_m}{u}\)
\(H_s\)	height due to mass transfer in stationary phase	\(H_s = \frac{qkd_f^2}{(1 + k)^2 D_s}u\)
\(H_m\)	height due to mass transfer in mobile phase	\(H_m = \frac{fn(d_p^2, d_c^2)}{D_m}u\)

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