25-1 What should be the volume flow rate and injected volume for a 1.5-mm-diameter column?

Interpretation:

The volume flow rate and the injected volume, if the solute is injected in a column with 1.5 mm diameter has to be calculated.

Concept Introduction:

The efficiency of the chromatography increases when the rate at which the solute particles equilibrate between mobile phase and stationary phase is increased. The column volume of the HPLC is directly proportional to square of the diameter of column.

The volume flow rate is 0.32 mL/min.

The injected volume is$2.1\mathrm{\mu L}$

As we know that the column volume is proportional to square of diameter of the column, when the diameter is changed from 4.6 mm to 1.5 mm, the volume factor also gets reduced. This is shown as:

Reduction in volume $$\begin{gathered} ={\left(1.5/4.6\right)}^2 \\ ={\left(0.326\right)}^2 \\ =0.106 \end{gathered}$$

Hence, uV has to be reduced by a factor of 0.106.

From the above volume reduced factor, we can calculate the volume flow rate in the given column.

$$\begin{gathered} {\mathrm{Uv}}_{\mathrm{v}}\left(\mathrm{small}\mathrm{column}\right)=0.106\times {\mathrm{uv}}^{\left(\mathrm{largecolumn}\right)} \\ =0.106\times 3.0\mathrm{mL}/\min \\ =0.318/\min \\ =0.32\mathrm{mL}/\min \end{gathered}$$

The volume flow rate is calculated as 0.32 mL / min.

The injected volume of the solute can be calculated as shown below.

$=0.106\times 20\mathrm{\mu L}$

Injection volume in small column$$\begin{gathered} =2.12\mathrm{\mu L} \\ =2.1\mathrm{\mu L} \end{gathered}$$

The injected volume in the given column is calculated as$=2.1\mathrm{\mu L}$.