Chapter 12, Problem 12.129QP

(a)

Interpretation Introduction

Interpretation:

The Lewis structure for given acetone and carbon disulfide molecules should be determined and the deviation from ideal behavior should be explained using intermolecular forces.

Concept Introduction:

• The Lewis structure is based on the concept of the octet rule so that the electrons shared in each atom should have 8 electrons in its outer shell.
• Sometimes the chemical bonding of a molecule cannot be represented using a single Lewis structure. In these cases, the chemical bonding are described by delocalization of electrons and is known as resonance.

Lewis structure for any molecule is drawn by using the following steps,

First the skeletal structure for the given molecule is drawn then the total number of valence electrons for all atoms present in the molecule is determined

The next step is to subtract the electrons present in the total number of bonds present in the skeletal structure of the molecule with the total valence electrons such that considering each bond contains two electrons with it.

Finally, the electrons which got after subtractions have to be equally distributed such that each atom contains eight electrons in its valence shell.

Intermolecular force: The attractive force that withholds two molecules is called as intermolecular force. The influence of intermolecular forces depends on molar mass and the functional group present in the molecule.

Types and strength of intermolecular forces in decreasing order:

$\text{ionic >hydrogen bonding>dipole-dipole interaction>Vander Waals dispersion force}$

Polar molecule: Polar molecules have large dipole moments.

Non-Polar molecules: Non-polar molecules have bonded atoms with similar electronegativity results to have zero dipole moments.

Explanation of Solution

The Lewis structures are as follows,

The given molecule acetone is polar whereas the molecule carbon disulfide is nonpolar molecule.

According to Like dissolves like principle, the attraction between acetone and $C{S}_2$ is weaker since one is polar and other is non polar. Hence, the interaction between acetone molecules and carbon disulfide molecules are stronger.

Due to weak attractions the molecules will leave the solution that result in increased vapor pressure of the solution than the sum of vapor pressures by Raoutl’s law.

(b)

Interpretation Introduction

Interpretation:

The vapor pressure of the solution under ideal condition should be determined.

Concept Introduction:

Raoult’s law: Raoult’s law states that solvent partial pressure over a solution is equal to vapor pressure of pure solvent multiplied with mole fraction of the solvent.

${\text{P}}_{\text{1}}{\text{= χ}}_{\text{1}}{\text{P}}^{\text{°}}{}_{\text{1}}$

Where, ${\text{P}}_{\text{1}}=$ Partial pressure of solvent

${\text{P}}_{\text{1}}^{\circ }=$ Partial pressure of its pure solvent

${\text{χ}}_{\text{1}}=$ Mole fraction of the solvent

The solution that obeys Raoult’s law is defined as ideal solution.

Explanation of Solution

$\begin{array}{c}A\Rightarrow acetone\\ B\Rightarrow carbondisulfide\end{array}$

The ideal solution should obey Raoult’s law.

$\begin{array}{c}{\text{P}}_{\text{A}}{\text{= χ}}_{\text{A}}{\text{P}}^{\text{°}}{}_{\text{A}}\\ {\text{P}}_{\text{B}}{\text{= χ}}_{\text{B}}{\text{P}}^{\text{°}}{}_{\text{B}}\\ {\text{P}}_{\text{Total}}{\text{= P}}_{\text{A}}{\text{+ P}}_{\text{B}}\end{array}$

Partial pressure for A is as follows,

$\begin{array}{c}{\text{P}}_{\text{A}}{\text{= χ}}_{\text{A}}{\text{P}}^{\text{°}}{}_{\text{A}}\\ \text{=}\left(\text{0}\text{.60}\right)\left(\text{349 mmHg}\right)\\ \text{=209}\text{.4 mmHg}\end{array}$

Partial pressure for B is as follows,

$\begin{array}{c}{\text{P}}_{\text{B}}{\text{= χ}}_{\text{B}}{\text{P}}^{\text{°}}{}_{\text{B}}\\ \text{=}\left(\text{0}\text{.40}\right)\left(\text{501 mmHg}\right)\\ \text{=200}\text{.4 mmHg}\end{array}$

$\begin{array}{c}{\text{P}}_{\text{Total}}{\text{= P}}_{\text{A}}{\text{+ P}}_{\text{B}}\\ \text{=}\left(\text{209}\text{.4+200}\text{.4}\right)\text{mmHg}\\ \text{=410}\text{mmHg}\end{array}$

The ideal pressure of the solution is $\text{410}\text{mmHg}$. The given vapor pressure of the solution is $\text{615}\text{mmHg}$ which is greater than the ideal vapor pressure.

(c)

Interpretation Introduction

Interpretation:

The sign of ${\text{ΔH}}_{\text{soln}}$ should be identified.

Concept Introduction:

Enthalpy $\text{H}$: It is the total amount of heat in a particular system.

Enthalpy is the amount energy absorbed or released in a process.

The enthalpy change in a system $\text{(Δ}{{\rm H}}_{\text{sys}}\text{)}$ can be calculated by the following equation.

${\text{ΔH}}_{\text{rxn}}{\text{ = ΔH}}^{\text{°}}{}_{\text{produdcts}}{\text{- ΔH}}^{\text{°}}{}_{\text{reactants}}$

Where,

${\text{ΔH}}^{\text{°}}{}_{\text{reactants}}$ is the standard entropy of the reactants

${\text{ΔH}}^{\text{°}}{}_{\text{produdcts}}$ is the standard entropy of the products

Explanation of Solution

The given molecule acetone is polar whereas the molecule carbon disulfide is nonpolar molecule.

According to Like dissolves like principle, the attraction between acetone and $C{S}_2$ is weaker since one is polar and other is non polar. Hence, the interaction between acetone molecules and carbon disulfide molecules are stronger.

Due to weak attractions the molecules will leave the solution that result in increased vapor pressure of the solution than the sum of vapor pressures by Raoutl’s law.

Therefore, the solution deviates positively from Raoutl’s law which says that heat of solution is positive that means mixing is an endothermic process (heat is absorbed by the system).