Chapter 24, Problem 24.15P

a)

Interpretation Introduction

Interpretation:

The adjusted retention time and retention factor has to be calculated.

Concept Introduction:

Adjusted retention time:

The extra time that is required to travel the length of the column beyond which is required by the solvent is called as adjusted retention time. The adjusted retention time is calculated using the equation,

${\text{t}}_{\text{r}}{}^{\text{'}}{\text{=t}}_{\text{r}}{\text{-t}}_{\text{m}}$

Where, ${\text{t}}_{\text{r}}{}^{\text{'}}$ = adjusted retention time

${\text{t}}_{\text{r}}$ = retention time

${\text{t}}_{\text{m}}$ = minimum possible time for the travel of unretained solute through the column.

Retention factor:

The time that is necessary to elute that peak minus the minimum possible time for the travel of unretained solute through the column is called as retention factor. The retention factor is calculated using the equation,

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

Where,

${\text{t}}_{\text{r}}$ = retention time

${\text{t}}_{\text{m}}$ = minimum possible time for the travel of unretained solute through the column.

To calculate the adjusted retention time and retention factor

Answer to Problem 24.15P

The adjusted retention time is $\text{4}\text{.7}\text{min}$ .

The retention factor is $\text{1}\text{.3}$.

Explanation of Solution

Given,

${\text{t}}_{\text{r}}$= $\text{8}\text{.4}\text{min}$

${\text{t}}_{\text{m}}$= $\text{3}\text{.7}\text{min}$

The adjusted retention time is calculated as,

${\text{t}}_{\text{r}}{}^{\text{'}}{\text{=t}}_{\text{r}}{\text{-t}}_{\text{m}}$

${\text{t}}_{\text{r}}{}^{\text{'}}\text{=8}\text{.4}\text{min-3}\text{.7}\text{min}$

${\text{t}}_{\text{r}}{}^{\text{'}}\text{=4}\text{.7}\text{min}$

The adjusted retention time = $\text{4}\text{.7}\text{min}$

The retention factor is calculated as,

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

$\begin{array}{l}\text{k=}\frac{\text{8}\text{.4-3}\text{.7}}{3.7}\\ \\ \text{k=1}\text{.3}\end{array}$

The retention factor = $\text{1}\text{.3}$

b)

Interpretation Introduction

Interpretation:

The phase ratio $\text{β}$ has to be calculated.

Concept Introduction:

Phase ratio $\beta$:

The volume of mobile phase divided by the volume of the stationary phase is called as dimensionless phase ratio. The phase ratio is calculated as,

$\text{β=}\frac{\text{r}}{{\text{2d}}_{\text{f}}}$

Where, $\text{β}$ = phase ratio

$\text{r}$ = radius of column

${\text{d}}_{\text{f}}$ = thickness of stationary phase time

Increase in thickness of stationary phase, decreases in $\text{β}$, that increases the retention time and capacity of sample.

To calculate the phase ratio $\text{β}$

Answer to Problem 24.15P

The phase ratio $\text{β}$ is found to be $\text{80}$.

Explanation of Solution

Given,

$\text{d=0}\text{.32}\text{mm}$

${\text{d}}_{\text{f}}\text{=1}\text{.0μm}$

The phase ratio is calculated as,

$\text{β=}\frac{\text{r}}{{\text{2d}}_{\text{f}}}$

$\begin{array}{l}\text{β=}\frac{\text{0}\text{.16}\text{mm}}{\text{2×1}\text{.0}\text{μm}}\\ \\ \text{β=}\frac{\text{0}\text{.16}\text{mm}}{\text{0}\text{.002}\text{mm}}\\ \\ \text{β=80}\end{array}$

The phase ratio $\text{β}$= $\text{80}$

c)

Interpretation Introduction

Interpretation:

The partition coefficient for the analyte has to be calculated.

Concept Introduction:

Partition coefficient:

The partition coefficient for the analyte is calculated using the formula of retention factor,

$\text{k=}\frac{\text{K}}{\text{β}}$

Here, $\text{k}$ = retention factor

$\text{K}$ =partition coefficient

$\text{β}$ = phase ratio

The formula for calculating the partition coefficient for the analyte is,

$\text{K=k×β}$

To calculate the partition coefficient for the analyte

Answer to Problem 24.15P

The partition coefficient for the analyte is $\text{104}$ .

Explanation of Solution

Given,

Retention factor = $\text{1}\text{.3}$

Phase ratio $\text{β}$= $\text{80}$

The partition coefficient for the analyte is calculated as,

$\text{K=k×β}$

$\begin{array}{l}\text{K=80×1}\text{.3}\\ \\ \text{K=104}\end{array}$

The partition coefficient for the analyte = $\text{104}$

d)

Interpretation Introduction

Interpretation:

The retention time for the given length and thickness has to be calculated.

Concept Introduction:

Retention factor:

The time that is necessary to elute that peak minus the minimum possible time for the travel of unretained solute through the column is called as retention factor. The retention factor is calculated using the equation,

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

Where,

${\text{t}}_{\text{r}}$ = retention time

${\text{t}}_{\text{m}}$ = minimum possible time for the travel of unretained solute through the column.

The retention time can be calculated using the formula of retention factor,

$\text{k=}\frac{\text{K}}{\text{β}}$

Here, $\text{k}$ = retention factor

$\text{K}$ =partition coefficient

$\text{β}$ = phase ratio

Phase ratio:

The volume of mobile phase divided by the volume of the stationary phase is called as dimensionless phase ratio. The phase ratio is calculated as,

$\text{β=}\frac{\text{r}}{{\text{2d}}_{\text{f}}}$

Where, $\text{β}$ = phase ratio

$\text{r}$ = radius of column

${\text{d}}_{\text{f}}$ = thickness of stationary phase time

Increase in thickness of stationary phase, decreases in $\text{β}$, that increases the retention time and capacity of sample.

To calculate the retention time

Answer to Problem 24.15P

The retention time is calculated to be $\text{6}\text{.1}\text{min}$.

Explanation of Solution

Given,

The partition coefficient for the analyte = $\text{104}$

$\text{d=0}\text{.32}\text{mm}$

${\text{d}}_{\text{f}}\text{=0}\text{.5μm}$

The phase ratio is calculated as,

$\text{β=}\frac{\text{r}}{{\text{2d}}_{\text{f}}}$

$\begin{array}{l}\text{β=}\frac{\text{0}\text{.16}\text{mm}}{\text{2×}\text{.05}\text{μm}}\\ \\ \text{β=}\frac{\text{0}\text{.16}\text{mm}}{\text{2}\times \text{0}\text{.005mm}}\\ \\ \text{β=160}\end{array}$

The phase ratio $\text{β}$= $160$

The retention time is calculated as,

$\begin{array}{l}\text{k=}\frac{\text{K}}{\text{β}}\\ \\ \frac{{\text{t}}_{\text{r}}{\text{-t}}_{\text{m}}}{{\text{t}}_{\text{m}}}\text{=}\frac{\text{K}}{\text{β}}\\ \\ \frac{{\text{t}}_{\text{r}}\text{-3}\text{.7}}{\text{3}\text{.7}}\text{=}\frac{\text{104}}{\text{160}}\\ \\ {\text{t}}_{\text{r}}\text{-3}\text{.7=0}\text{.65×3}\text{.7}\\ \\ {\text{t}}_{\text{r}}\text{-3}\text{.7=2}\text{.405=2}\text{.405+3}\text{.7}\\ \\ {\text{t}}_{\text{r}}\text{=6}\text{.105}\text{min}\end{array}$

The retention time = $\text{6}\text{.1}\text{min}$