Chapter 17, Problem 54E

(a)

Interpretation Introduction

Interpretation:

Whether the solution of water and propanol are ideal or not needs to be determined.

Concept Introduction:

Vapor pressure being a colligative property is directly proportional to amount of solute in solution. If a solute is present in solvent, the vapor pressure is lowered as there is less number of solvent molecules. Vapor pressure is due to evaporation of liquid.

Answer to Problem 54E

The solution of water and propanol is not ideal.

Explanation of Solution

Given is the vapor pressure of solution of propanol with water at different composition.

${{\rm X}}_{H_{2}O}$	Vapor pressure	${{\rm X}}_{proponal}$
0	74.0	1
0.15	77.3	0.85
0.37	80.2	0.63
0.54	81.6	0.54
0.69	80.6	0.31
0.83	78.2	0.17
1.00	71.9	0

We know that vapor pressure of solution is $({{\rm X}}_{H_{2}O}{\text{ x P}}_{H_{2}O})\text{ + }({{\rm X}}_{proponal}{\text{ x P}}_{proponal})$

Where P is the vapor pressure

Mole fraction of propanol = 1 − mile fraction of water

The calculation for the vapor pressure using Raoult’s Law is

  $\begin{array}{l}{\text{P}}_{solution}=\text{(0}\text{.85 x 74 torr) + (0}\text{.15 x 71}\text{.9 torr)= 73}\text{.68 torr}\\ {\text{P}}_{solution}=\text{(0}\text{.63 x 74 torr) + (0}\text{.37 x 71}\text{.9 torr)= 73}\text{.22 torr}\\ {\text{P}}_{solution}=\text{(0}\text{.46 x 74 torr) + (0}\text{.54 x 71}\text{.9 torr)= 72}\text{.86 torr}\\ {\text{P}}_{solution}=\text{(0}\text{.31 x 74 torr) + (0}\text{.69 x 71}\text{.9 torr)= 72}\text{.55 torr}\\ {\text{P}}_{solution}=\text{(0}\text{.17 x 74 torr) + (0}\text{.83 x 71}\text{.9 torr)= 72}\text{.25 torr}\end{array}$

The values obtained are not equal to the values that are depicted in the table. Hence, the solution of propanol and water is not ideal.

(b)

Interpretation Introduction

Interpretation:

The sign of $\Delta H_{solution}$ for water-propane solution needs to be determined.

Concept Introduction:

The intermolecular forces in a solute can be broken down by new interactions from the solution as each solute particle will be surrounded by solvent particles in a solution. This can happen when there is disruption between the solute -solute and solvent-solvent interaction.

The formation of solution involves enthalpy changes which is depicted as $\Delta H_{so\ln }=\Delta H_1+\Delta H_2+\Delta H_3$

Answer to Problem 54E

As there is positive deviation from Raoult’s law, the value of $\Delta H_{solution}$ is positive.

Explanation of Solution

The vapor pressures of solutions are compared with those from the table given. From Results law the vapor pressure is

  $\begin{array}{l}{\text{P}}_{solution}=\text{(0}\text{.85 x 74 torr) + (0}\text{.15 x 71}\text{.9 torr)= 73}\text{.68 torr}\\ {\text{P}}_{solution}=\text{(0}\text{.63 x 74 torr) + (0}\text{.37 x 71}\text{.9 torr)= 73}\text{.22 torr}\\ {\text{P}}_{solution}=\text{(0}\text{.46 x 74 torr) + (0}\text{.54 x 71}\text{.9 torr)= 72}\text{.86 torr}\\ {\text{P}}_{solution}=\text{(0}\text{.31 x 74 torr) + (0}\text{.69 x 71}\text{.9 torr)= 72}\text{.55 torr}\\ {\text{P}}_{solution}=\text{(0}\text{.17 x 74 torr) + (0}\text{.83 x 71}\text{.9 torr)= 72}\text{.25 torr}\end{array}$

The values obtained are not equal and are higher than individual components. This indicates that the deviation from Raoult’s law is positive. If there is a positive deviation from Raoult’s law, the value of

  $\Delta H_{solution}$ is positive.

(c)

Interpretation Introduction

Interpretation:

Whether the interactive forces between propanol and water molecules are weaker, stronger or equal needs to be determined.

Concept Introduction:

Raoult’s law indicates that the vapor pressure of solution is dependent on mole fraction of solute that is present in solution. There could be negative or positive deviations from Raoult’s law. If the deviation is positive, then it means the vapor pressure is higher than expected of the solution. If the deviation is negative, and then it means that the vapor pressure is lower than expected of the solution.

Answer to Problem 54E

The interactive forces between propanol and water are weaker as the there is a positive deviation from Raoult’s law.

Explanation of Solution

The vapor pressure of propanol is computed as follows:

  $\begin{array}{l}{\text{P}}_{solution}=\text{(0}\text{.85 x 74 torr) + (0}\text{.15 x 71}\text{.9 torr)= 73}\text{.68 torr}\\ {\text{P}}_{solution}=\text{(0}\text{.63 x 74 torr) + (0}\text{.37 x 71}\text{.9 torr)= 73}\text{.22 torr}\\ {\text{P}}_{solution}=\text{(0}\text{.46 x 74 torr) + (0}\text{.54 x 71}\text{.9 torr)= 72}\text{.86 torr}\\ {\text{P}}_{solution}=\text{(0}\text{.31 x 74 torr) + (0}\text{.69 x 71}\text{.9 torr)= 72}\text{.55 torr}\\ {\text{P}}_{solution}=\text{(0}\text{.17 x 74 torr) + (0}\text{.83 x 71}\text{.9 torr)= 72}\text{.25 torr}\end{array}$

When comparing with the data on the table, there is a deviation of the values obtained. As the deviation from Raoult’s law is positive, it indicates that interaction between propanol and water molecules are weaker than the interaction between the pure substances.

(d)

Interpretation Introduction

Interpretation:

The solution from the table having lowest boiling point needs to be determined.

Concept Introduction:

When the vapor pressure of the liquid becomes equal to that of atmosphere then the liquid is said to boil. The liquid is said to high vapor pressure if the intermolecular forces are small. To separate the molecules more heat is required and hence the boiling point is high.

Answer to Problem 54E

The solution with mole fraction of 0.54 has the lowest boiling point.

Explanation of Solution

It is known that if a solution has highest vapor pressure, its boing point is low.

Observing the table,

${{\rm X}}_{H_{2}O}$	Vapor pressure
0	74.0
0.15	77.3
0.37	80.2
0.54	81.6
0.69	80.6
0.83	78.2
1.00	71.9

It can be seen that solution having a mole fraction of 0.54 depicts the highest vapor pressure. Hence, this solution of 0.54 mole fraction will have low boiling point.