Question

The “rule of three” states that the retention factor for a given solute decreases approximately threefold when the organic phase increases by10%.In figure $\mathbf{25}\mathbf{-}\mathbf{12}\mathbf{,}{\mathbf{t}}_{\mathbf{m}}\mathbf{=}\mathbf{2}\mathbf{.}\mathbf{7}$min. Find k for peak 5at 40%B .predict the retention time for peak at B and compare the observed and predicted times.

Short answer

The rule of three states that the retention factor for a given solute decreases.

$$\begin{gathered} \mathrm{K}=\frac{{\mathrm{t}}_{\mathrm{r}}-{\mathrm{t}}_{\mathrm{m}}}{{\mathrm{t}}_{\mathrm{m}}} \\ \mathrm{k}=\frac{\left(11-27\right)\min }{2.7\min } \\ {\mathrm{t}}_{\mathrm{r}}=27.81\min \end{gathered}$$

Step-by-step solution

Definition of retention

Retention implies the maintenance, possession, control, or retention of moisture.

According to the figure 25-12, we see that retention time for peak 5 is 11 min (for 50% B). So, the retention factor is

$$\begin{gathered} \mathrm{K}=\frac{{\mathrm{t}}_{\mathrm{r}}-{\mathrm{t}}_{\mathrm{m}}}{{\mathrm{t}}_{\mathrm{m}}} \\ \mathrm{k}=\frac{\left(11-27\right)\min }{2.7\min } \\ \mathrm{k}=3.1 \end{gathered}$$

Rule of three

Then, when B is 40%, k is (according to the rule of three) given by

$\mathrm{k}=3\cdot 3.1=9.3$

Retention time is

$$\begin{gathered} {\mathrm{t}}_{\mathrm{r}}=\mathrm{k}.{\mathrm{t}}_{\mathrm{m}}+{\mathrm{t}}_{\mathrm{m}} \\ {\mathrm{t}}_{\mathrm{r}}=9.3.2.7\min +2.7\min \\ {\mathrm{t}}_{\mathrm{r}}=27.81\min \end{gathered}$$

According to the figure 25-12, the observed retention time is 20.2 min.

Hence${\mathrm{t}}_{\mathrm{r}}=27.81\min$.