91Ó°ÊÓ

The retention factor, also known as the capacity factor (k), in column chromatography is defined as the ratio of time an analyte is retained in the stationary phase to time the analyte is retained in the mobile phase.

${\mathrm{m}}_1=4\mathrm{mg},\mathrm{I}=40\mathrm{cm},{\mathrm{d}}_1=0.85\mathrm{cm}$

To compare the size of the two columns are

$$\begin{gathered} \frac{{\mathrm{m}}_2}{{\mathrm{m}}_1}={\left(\frac{{\mathrm{d}}_2}{{\mathrm{d}}_1}\right)}^2 \\ \frac{100\mathrm{mg}}{4\mathrm{mg}}={\left(\frac{{\mathrm{d}}_2}{0.85\mathrm{cm}}\right)}^2 \\ 25=\frac{{\mathrm{d}}_2^2}{0.7225{\mathrm{cm}}^2} \\ {\mathrm{d}}_2^2=18.06{\mathrm{cm}}^2 \\ {\mathrm{d}}_2^2=\sqrt{18.06{\mathrm{cm}}^2} \\ {\mathrm{d}}_2=4.25\mathrm{cm} \end{gathered}$$

The size of the column would be 40cmwith a diameter of 4.25cm

If the volume flow is 0.22mL /min on the smaller column, to determine the volume flow rate should be used on the larger column

$$\begin{gathered} \frac{{\mathrm{m}}_2}{{\mathrm{m}}_1}=\frac{{\mathrm{u}}_2}{{\mathrm{u}}_1} \\ \frac{100\mathrm{mg}}{4\mathrm{mg}}=\frac{{\mathrm{u}}_2}{0.22\mathrm{mL}/\min } \\ 25=\frac{{\mathrm{u}}_2}{0.22\mathrm{mL}/\min } \\ 25×0.22\mathrm{mL}/\min ={\mathrm{u}}_2 \\ 5.5\mathrm{mL}/\min ={\mathrm{u}}_2 \end{gathered}$$

To find the volume of a small column as

$$\begin{gathered} {\mathrm{V}}_1={\mathrm{ττ}}^2×\mathrm{I} \\ {\mathrm{V}}_1=\mathrm{ττ}×{\left(0.85/2\mathrm{cm}\right)}^2×40\mathrm{cm} \\ {\mathrm{V}}_1=22.7\mathrm{mL} \end{gathered}$$

Volume of a mobile phase as

$$\begin{gathered} {\mathrm{V}}_{\mathrm{m}}=0.35×22.7\mathrm{mL} \\ {\mathrm{V}}_{\mathrm{m}}=7.94\mathrm{mL} \end{gathered}$$

To calculate the linear flow

$$\begin{gathered} {\mathrm{u}}_{\mathrm{x}}=\frac{\mathrm{I}}{{\mathrm{V}}_{\mathrm{m}}×{\mathrm{u}}_1} \\ {\mathrm{u}}_{\mathrm{x}}=\frac{40\mathrm{cm}}{7.94\mathrm{mL}×0.22\mathrm{mL}/\min } \\ {\mathrm{u}}_{\mathrm{x}}=1.11\mathrm{cm}/\min \end{gathered}$$