Chapter 4.4, Problem 11E

a)

Interpretation Introduction

Interpretation: Percentages of $n\text{-propylcyclohexane}$ and $n\text{-propylbenzene}$ in first few drops of distillate if $60\text{ mol \% }n\text{-propylcyclohexane}$ and $40\text{ mol \% }n\text{-propylbenzene}$ mixture is separated by simple distillation should be determined.

Concept introduction:Simple distillation is separation technique that is used to separate mixture of organic compounds with difference in their boiling points more than $40°\text{C}$ . In other words, this procedure is applied for removal of nonvolatile impurities from volatile solvents. If one of the compounds in organic mixture is volatile, its vapors will form first and are converted into liquid with help of condenser. This way all of volatile compound gets converted into liquid and therefore it is separated from nonvolatile component.

Explanation of Solution

The formula to calculate mole fraction of substance is as follows:

  $\text{Mole fraction of substance}=\frac{\text{Mole percent}}{\text{100 \%}}$ …… (1)

Substitute $60\text{ \%}$ for mole percent in equation (1) to calculate mole fraction of $n\text{-propylcyclohexane}$ .

  $\begin{array}{c}\text{Mole fraction of }n\text{-propylcyclohexane}=\frac{\text{60 \%}}{\text{100 \%}}\\ =0.6\end{array}$

Substitute $40\text{ \%}$ for mole percent in equation (1) to calculate mole fraction of $n\text{-propylbenzene}$ .

  $\begin{array}{c}\text{Mole fraction of }n\text{-propylbenzene}=\frac{\text{40 \%}}{\text{100 \%}}\\ =0.4\end{array}$

Raoult’s law describes relationship between composition of liquid mixture and vapor pressure. This law holds good only for ideal solutions. Mathematical expression of Raoult’s law is as follows:

$P_{\text{X}}=P_{\text{X}}^{°}{N}_{\text{X}}$ …… (2)

Where,

• $P_{\text{X}}$ is partial pressure of component $X$ .
• $P_{\text{X}}^{°}$ is partial pressure of pure component $X$ .
• $N_{\text{X}}$ is mole fraction of component $X$ .

Substitute 0.6 for $N_{\text{X}}$ and $769\text{ torr}$ for $P_{\text{X}}^{°}$ in equation (2) to calculate partial pressure of $n\text{-propylcyclohexane}$ .

  $\begin{array}{c}{P}_{n\text{-propylcyclohexane}}=\left(769\text{ torr}\right)\left(0.6\right)\\ =461.4\text{ torr}\end{array}$

Substitute 0.6 for $N_{\text{X}}$ and $725\text{ torr}$ for $P_{\text{X}}^{°}$ in equation (2) to calculate partial pressure of $n\text{-propylbenzene}$ .

  $\begin{array}{c}{P}_{n\text{-propylbenzene}}=\left(725\text{ torr}\right)\left(0.4\right)\\ =290\text{ torr}\end{array}$

Dalton’s law of partial pressures states that total pressure is defined as sum of partial pressure of all volatile components. Mathematical expression for Dalton’s law is as follows:

  $P_{\text{total}}=P_{\text{X}}+P_{\text{Y}}+P_{\text{Z}}+\mathrm{...}$ …… (3)

Where,

• $P_{\text{total}}$is total partial pressure of system.
• $P_{\text{X}}$ is partial pressure of component $X$ .
• $P_{\text{Y}}$ is partial pressure of component $Y$ .
• $P_{\text{Z}}$ is partial pressure of component $Z$ .

Since mixture comprises $n\text{-propylcyclohexane}$ and $n\text{-propylbenzene}$ , total pressure can be calculated by formula below.

  $P_{\text{total}}=P_{n\text{-propylcyclohexane}}+P_{n\text{-propylbenzene}}$ …… (4)

Substitute $461.4\text{ torr}$ for $P_{n\text{-propylcyclohexane}}$ and $290\text{ torr}$ for $P_{n\text{-propylbenzene}}$ in equation (4).

  $\begin{array}{c}{P}_{\text{total}}=461.4\text{ torr}+290\text{ torr}\\ =\text{751}\text{.4 torr}\end{array}$

The formula to calculate percentage composition of substance is as follows:

  $\text{\% composition of substance}=\left(\frac{\text{Pressure of substance}}{\text{Total pressure}}\right)\left(100\text{ \%}\right)$ …… (5)

Substitute $461.4\text{ torr}$ for pressure of substance and $751.4\text{ torr}$ for total pressure in equation (5) to calculate $\%$ composition of $n\text{-propylcyclohexane}$ .

  $\begin{array}{c}\text{\% composition of }n\text{-propylcyclohexane}=\left(\frac{\text{461}\text{.4 torr}}{\text{751}\text{.4 torr}}\right)\left(100\text{ \%}\right)\\ =61\text{ \%}\end{array}$

Substitute $290\text{ torr}$ for pressure of substance and $751.4\text{ torr}$ for total pressure in equation (5) to calculate $\%$ composition of $n\text{-propylbenzene}$ .

  $\begin{array}{c}\text{\% composition of }n\text{-propylbenzene}=\left(\frac{290\text{ torr}}{\text{751}\text{.4 torr}}\right)\left(100\text{ \%}\right)\\ =39\text{ \%}\end{array}$

Hence percentage composition of $n\text{-propylcyclohexane}$ is $61\text{ \%}$ while that of $n\text{-propylbenzene}$ is $39\text{ \%}$ .

b)

Interpretation Introduction

Interpretation:Distillation temperature and percentage composition of first few drops of distillatein mixture of $50\text{ mol \% benzene}$ and $50\text{ mol \% toluene}$ should be determined.

Concept introduction:Simple distillation is separation technique that is used to separate mixture of organic compounds with difference in their boiling points more than $40°\text{C}$ . In other words, this procedure is applied for removal of nonvolatile impurities from volatile solvents. If one of the compounds in organic mixture is volatile, its vapors will form first and are converted into liquid with help of condenser. This way all of volatile compound gets converted into liquid and therefore it is separated from nonvolatile component.

Explanation of Solution

Temperature-composition diagram for binary mixture of benzene and toluene is as follows:

  

Composition of mixture is $50\text{ mol \% benzene}$ and $50\text{ mol \% toluene}$ so temperature that corresponds to this composition is $93°\text{C}$ that can be determined as follows:

  

Since distillation temperature comes out to be $93°\text{C}$ , composition of distillate in first few drops can also be determined with help of above diagram. Composition that corresponds to first few drops of distillate comes out to be $25\text{ mol \% toluene}$ and $75\text{ mol \% benzene}$ .

c)

Interpretation Introduction

Interpretation:Distillation results in mixture of $n\text{-propylcyclohexane}$ and $n\text{-propylbenzene}$ and that of benzene and toluene should be compared. Also,whether mixture of $n\text{-propylcyclohexane}$ and $n\text{-propylbenzene}$ or that of benzene and toluene require more efficient fractional distillation column for separation of components should be explained.

Concept introduction:Fractional distillation is separation technique that separates various fractions of components in mixture. This process is based on vaporization of one or more fractions or parts of mixture. It is used to separate components of mixture that have difference in boiling points less than $25°\text{C}$ .

Explanation of Solution

Boiling points of $n\text{-propylcyclohexane}$ and $n\text{-propylbenzene}$ are $156°\text{C}$ and $159°\text{C}$ respectively while those of benzene and toluene are $80°\text{C}$ and $111°\text{C}$ respectively. Since difference in boiling points of $n\text{-propylcyclohexane}$ and $n\text{-propylbenzene}$ is lower as compared to that between benzene and toluene, this mixture is more likely to need more efficient fractional distillation.