Question

Solvent passes through a column in 3minbut solute requires9min (a) Calculate the retention factor,k.(b) What fraction of time is the solute in the mobile phase in the column? (c) The volume of stationary phase is$\frac{\mathbf{1}}{\mathbf{10}}$of the volume of the mobile phase in the column${\mathbf{V}}_{\mathbf{S}}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{10}{\mathbf{V}}_{\mathbf{M}}$. Find the partition coefficient, K, for this system.

Short answer

$$\begin{gathered} \mathrm{a})\mathrm{k}=2 \\ \mathrm{b})\mathrm{fraction}=0.33 \\ \mathrm{c})\mathrm{K}=20 \end{gathered}$$

Step-by-step solution

Given Information:

${\mathrm{t}}_{\mathrm{r}}=9\min ,{\mathrm{t}}_{\mathrm{m}}=3\min ,{\mathrm{V}}_{\mathrm{S}}=0.10{\mathrm{V}}_{\mathrm{m}}$

To find the Retention factor:

Retention factor can be expressed as

$\mathrm{k}=\frac{{\mathrm{t}}_{\mathrm{r}}-{\mathrm{t}}_{\mathrm{m}}}{{\mathrm{t}}_{\mathrm{m}}}$

Substitute the given values are

$$\begin{gathered} \mathrm{k}=\frac{9\min -3\min }{3\min } \\ \mathrm{k}=2 \end{gathered}$$

To find the fraction of time of the solute in the mobile phase:

$$\begin{gathered} \mathrm{fraction}=\frac{{\mathrm{t}}_{\mathrm{m}}}{{\mathrm{t}}_{\mathrm{r}}} \\ \mathrm{fraction}=\frac{3\min }{9\min } \\ \mathrm{fraction}=0.33 \end{gathered}$$

To find the Partition coefficient in the stationary phase:

$$\begin{gathered} \mathrm{K}=\mathrm{k}\times \frac{{\mathrm{V}}_{\mathrm{m}}}{{\mathrm{V}}_{\mathrm{s}}} \\ \mathrm{K}=2\times \frac{{\mathrm{V}}_{\mathrm{m}}}{0.10{\mathrm{V}}_{\mathrm{m}}} \\ \mathrm{K}=2\times \frac{{\mathrm{V}}_{\mathrm{m}}}{0.10{\mathrm{V}}_{\mathrm{m}}} \\ \mathrm{K}=2\times \frac{1}{0.10} \\ \mathrm{K}=20 \end{gathered}$$