Chapter 23, Problem 23.28P

(a)

Interpretation Introduction

Interpretation:

From the columns given, the column with highest number of plates has to be identified.

Concept introduction:

Plates of column:

The relationship between $\text{N}\text{and}{\text{w}}_{\text{1/2}}$

$\begin{array}{l}\text{N}\text{=}\frac{\text{5}\text{.55}{\text{t}}_{\text{r}}{}^{\text{2}}}{{\text{w}}_{\text{1/2}}{}^{\text{2}}}\\ \text{Where,}\\ \text{N}\text{-}\text{number}\text{of}\text{plates}\text{on}\text{column}\\ {\text{t}}_{\text{r}}\text{-}\text{retention}\text{time}\\ {\text{w}}_{\text{1/2}}\text{-}\text{half-width}\end{array}$

Answer to Problem 23.28P

• The column with highest number of plates is $\text{Column}\text{2}\text{.}$

Explanation of Solution

Given information,

$\begin{array}{l}\text{Column}\text{1:}\text{N}\text{=}\text{1000}\text{;}{\text{k}}_{\text{2}}\text{=}\text{1}\text{.2}\text{;}\text{α}\text{=}\text{1}\text{.16}\text{;}\text{resolution}\text{=}\text{0}\text{.6}\\ \text{Column}\text{2:}\text{N}\text{=}\text{5000}\text{;}{\text{k}}_{\text{2}}\text{=}\text{3}\text{.9}\text{;}\text{α}\text{=}\text{1}\text{.06}\text{;}\text{resolution}\text{=}\text{0}\text{.8}\\ \text{Column}\text{3:}\text{N}\text{=}\text{500}\text{;}{\text{k}}_{\text{2}}\text{=}\text{4}\text{.7}\text{;}\text{α}\text{=}\text{1}\text{.31}\text{;}\text{resolution}\text{=}\text{1}\text{.1}\\ \text{Column}\text{4:}\text{N}\text{=}\text{2000}\text{;}{\text{k}}_{\text{2}}\text{=}\text{2}\text{.4}\text{;}\text{α}\text{=}\text{1}\text{.24}\text{;}\text{resolution}\text{=}\text{1}\text{.5}\end{array}$

Form the given columns, column 2 has the highest number of plates $\text{N}\text{=}\text{5000}\text{.}$

The column with highest number of plates is $\text{Column}\text{2}\text{.}$

(b)

Interpretation Introduction

Interpretation:

From the columns given, the column with greatest retention has to be identified.

Concept introduction:

Retention factor:

The retention factor $\left(\text{k}\right)$ is given by

$\begin{array}{l}\text{k}\text{=}\frac{{\text{t}}_{\text{r}}\text{-}{\text{t}}_{\text{m}}}{{\text{t}}_{\text{m}}}\\ \text{Where,}\\ \text{k}\text{-}\text{retention}\text{factor}\\ {\text{t}}_{\text{r}}\text{-}\text{time}\text{required}\text{to}\text{elute}\text{the}\text{peak}\\ {\text{t}}_{\text{m}}\text{-}\text{time}\text{required}\text{for}\text{mobile}\text{phase}\text{to}\text{pass}\text{through}\text{the}\text{column}\text{.}\end{array}$

Answer to Problem 23.28P

• The column with greatest retention is $\text{Column}\text{3}\text{.}$

Explanation of Solution

Given information,

$\begin{array}{l}\text{Column}\text{1:}\text{N}\text{=}\text{1000}\text{;}{\text{k}}_{\text{2}}\text{=}\text{1}\text{.2}\text{;}\text{α}\text{=}\text{1}\text{.16}\text{;}\text{resolution}\text{=}\text{0}\text{.6}\\ \text{Column}\text{2:}\text{N}\text{=}\text{5000}\text{;}{\text{k}}_{\text{2}}\text{=}\text{3}\text{.9}\text{;}\text{α}\text{=}\text{1}\text{.06}\text{;}\text{resolution}\text{=}\text{0}\text{.8}\\ \text{Column}\text{3:}\text{N}\text{=}\text{500}\text{;}{\text{k}}_{\text{2}}\text{=}\text{4}\text{.7}\text{;}\text{α}\text{=}\text{1}\text{.31}\text{;}\text{resolution}\text{=}\text{1}\text{.1}\\ \text{Column}\text{4:}\text{N}\text{=}\text{2000}\text{;}{\text{k}}_{\text{2}}\text{=}\text{2}\text{.4}\text{;}\text{α}\text{=}\text{1}\text{.24}\text{;}\text{resolution}\text{=}\text{1}\text{.5}\end{array}$

Form the given columns, column 3 has the greatest retention ${\text{k}}_{\text{2}}\text{=}\text{4}\text{.7}\text{.}$

The column with greatest retention is $\text{Column}\text{3}\text{.}$

(c)

Interpretation Introduction

Interpretation:

From the columns given, the column with highest relative retention has to be identified.

Concept introduction:

Relative retention:

The ratio of the adjusted retention time of two components is given by relative retention $\text{α}$

$\begin{array}{l}\text{α}\text{=}\frac{{\text{t}}_{\text{r}}^{\text{'}}{}_{\text{2}}}{{\text{t}}_{\text{r}}^{\text{'}}{}_{\text{1}}}\\ \text{Where,}\\ \text{α}\text{-}\text{relative}\text{retention}\left(\text{also}\text{called}\text{separation}\text{factor}\right)\\ {\text{t}}_{\text{r}}^{\text{'}}{}_{\text{2}}\text{-}\text{adjusted}\text{retention}\text{time}\text{of}\text{component}\text{2}\\ {\text{t}}_{\text{r}}^{\text{'}}{}_{\text{1}}\text{-}\text{adjusted}\text{retention}\text{time}\text{of}\text{component}\text{1}\\ \text{The}\text{separation}\text{between}\text{the}\text{two}\text{component}\text{will}\text{be}\text{higher}\text{when}{\text{t}}_{\text{r}}^{\text{'}}{}_{\text{2}}\text{>}{\text{t}}_{\text{r}}^{\text{'}}{}_{\text{1}}\text{,}\text{so}\text{α}\text{>}\text{1}\end{array}$

Answer to Problem 23.28P

• The column with highest relative retention is $\text{Column}\text{3}\text{.}$

Explanation of Solution

Given information,

$\begin{array}{l}\text{Column}\text{1:}\text{N}\text{=}\text{1000}\text{;}{\text{k}}_{\text{2}}\text{=}\text{1}\text{.2}\text{;}\text{α}\text{=}\text{1}\text{.16}\text{;}\text{resolution}\text{=}\text{0}\text{.6}\\ \text{Column}\text{2:}\text{N}\text{=}\text{5000}\text{;}{\text{k}}_{\text{2}}\text{=}\text{3}\text{.9}\text{;}\text{α}\text{=}\text{1}\text{.06}\text{;}\text{resolution}\text{=}\text{0}\text{.8}\\ \text{Column}\text{3:}\text{N}\text{=}\text{500}\text{;}{\text{k}}_{\text{2}}\text{=}\text{4}\text{.7}\text{;}\text{α}\text{=}\text{1}\text{.31}\text{;}\text{resolution}\text{=}\text{1}\text{.1}\\ \text{Column}\text{4:}\text{N}\text{=}\text{2000}\text{;}{\text{k}}_{\text{2}}\text{=}\text{2}\text{.4}\text{;}\text{α}\text{=}\text{1}\text{.24}\text{;}\text{resolution}\text{=}\text{1}\text{.5}\end{array}$

Form the given columns, column 3 has the highest relative retention $\text{α}\text{=}\text{1}\text{.31}\text{.}$

The column with highest relative retention is $\text{Column}\text{3}\text{.}$

(d)

Interpretation Introduction

Interpretation:

From the columns given, the column with best separation has to be identified.

Concept introduction:

Purnell equation:

The relationship between $\text{H}\text{and}\text{α}$ is given by Purnell equation,

$\begin{array}{l}\text{Resolution}\text{=}\frac{\sqrt{\text{N}}}{\text{4}}\frac{\left(\text{α}\text{-}\text{1}\right)}{\text{α}}\left(\frac{{\text{k}}_{\text{2}}}{\text{1}\text{+}\text{}{\text{k}}_{\text{2}}}\right)\\ \text{Where,}\\ \text{N}\text{-}\text{number}\text{of}\text{theoretical}\text{plates}\\ \text{α}\text{-}\text{relative}\text{retention}\text{of}\text{the}\text{two}\text{peaks}\\ {\text{k}}_{\text{2}}\text{-}\text{retention}\text{factor}\text{of}\text{the}\text{more}\text{retained}\text{component}\end{array}$

Answer to Problem 23.28P

• The column with best separation is $\text{Column}4.$

Explanation of Solution

Given information,

$\begin{array}{l}\text{Column}\text{1:}\text{N}\text{=}\text{1000}\text{;}{\text{k}}_{\text{2}}\text{=}\text{1}\text{.2}\text{;}\text{α}\text{=}\text{1}\text{.16}\text{;}\text{resolution}\text{=}\text{0}\text{.6}\\ \text{Column}\text{2:}\text{N}\text{=}\text{5000}\text{;}{\text{k}}_{\text{2}}\text{=}\text{3}\text{.9}\text{;}\text{α}\text{=}\text{1}\text{.06}\text{;}\text{resolution}\text{=}\text{0}\text{.8}\\ \text{Column}\text{3:}\text{N}\text{=}\text{500}\text{;}{\text{k}}_{\text{2}}\text{=}\text{4}\text{.7}\text{;}\text{α}\text{=}\text{1}\text{.31}\text{;}\text{resolution}\text{=}\text{1}\text{.1}\\ \text{Column}\text{4:}\text{N}\text{=}\text{2000}\text{;}{\text{k}}_{\text{2}}\text{=}\text{2}\text{.4}\text{;}\text{α}\text{=}\text{1}\text{.24}\text{;}\text{resolution}\text{=}\text{1}\text{.5}\end{array}$

Form the given columns, column 4 has the best separation $\text{Resolution}\text{=}\text{1}\text{.5}\text{.}$

The column with best separation is $\text{Column}4.$