Question

At $35°\mathrm{C}$, the vapour pressure of ${\mathrm{CS}}_2$ is $512\mathrm{mm}\mathrm{Hg}$ and that of Acetone is $344\mathrm{mm}\mathrm{Hg}$. A solution of ${\mathrm{CS}}_2$ in acetone has a total vapour pressure of $600\mathrm{mm}\mathrm{Hg}$. The false statement amongst the following is-

• A. ${\mathrm{CS}}_2$ and acetone are less attracted to each other than to themselves.
• B. Heat must be absorbed in order to produce the solution at $35°\mathrm{C}$.
• C. Raoult's law is not obeyed by this system.
• D. A mixture of $100$$\mathrm{mL}$ ${\mathrm{CS}}_2$ and $100$$\mathrm{mL}$ acetone has a volume $<200$ $\mathrm{mL}$.

Answer 1

The correct option is D

A mixture of $100$$\mathrm{mL}$ ${\mathrm{CS}}_2$ and $100$$\mathrm{mL}$ acetone has a volume $<200$ $\mathrm{mL}$.

1. Raoult's law of vapour pressure - it states that “for a solution containing volatile liquids the partial pressure of each component in the solution is directly proportional to its mole fraction in the solution”. Mathematically we can write -

${\mathrm{P}}_{\mathrm{T}}={\mathrm{P}}_{\mathrm{A}}^0{\mathrm{X}}_{\mathrm{A}}+{\mathrm{P}}_{\mathrm{B}}^0{\mathrm{X}}_{\mathrm{B}}\left(1\right)$

Where ${\mathrm{P}}_{\mathrm{T}}$ is the total vapour pressure of the solution, $X_{\mathrm{A}}$ and $X_{\mathrm{B}}$ are the mole fraction of component A and B respectively, ${\mathrm{P}}_{\mathrm{A}}^0$ is the vapour pressure of component A in its pure state and ${\mathrm{P}}_{\mathrm{B}}^0$ is the vapour pressure of component B in its pure state.

2. Positive deviation from Raoult's law- when the vapour pressure of solution is higher than that of the predicted by the Raoult's law, positive deviation from Raoult's law is seen and Raoult's law is not obeyed.

Negative deviation from Raoult's law- when the vapour pressure of the solution is lower than that predicted by Raoult's law, negative deviation from Raoult's law is seen and Raoult's law is not obeyed.

3. Characteristics of positive deviation from Raoult's law- $∆{\mathrm{H}}_{\mathrm{mix}}>0$, $∆{\mathrm{V}}_{\mathrm{mix}}>0$ and attraction forces between both the components is lesser than the attraction forces between themselves.

Characteristics of negative deviation from Raoult's law- $∆{\mathrm{H}}_{\mathrm{mix}}<0$, $∆{\mathrm{V}}_{\mathrm{mix}}<0$ and the attraction forces between both the components is higher than the attraction forces between themselves.

Explanation for correct option:

(D)

Step1: According to the given question ${\mathrm{P}}_{{\mathrm{CS}}_2}^0$ is $512\mathrm{mm}\mathrm{Hg}$, ${\mathrm{P}}_{\mathrm{Acetone}}^0$ is $344\mathrm{mm}\mathrm{Hg}$ and ${\mathrm{P}}_{\mathrm{T}}$ is $600\mathrm{mm}\mathrm{Hg}$.

if ${\mathrm{x}}_{\mathrm{A}}=1$in equation $\left(1\right)$, then the maximum value of ${\mathrm{P}}_{\mathrm{T}}$ can be $512\mathrm{mm}\mathrm{Hg}$ but ${\mathrm{P}}_{\mathrm{T}}$ given in the question is higher than $512\mathrm{mm}\mathrm{Hg}$ which means the positive deviation from Raoult's law is seen here.

Step 2: Since positive deviation from the Raoult's law is seen we can say that -

1. This system does not obey Raoult's law.

2. Attraction between ${\mathrm{CS}}_2$ and acetone is lesser than the attraction between the molecules of ${\mathrm{CS}}_2$ and the molecules of Acetone in their pure state.

3. Heat must be absorbed in order to produce the solution at $35°\mathrm{C}$ $(∆{\mathrm{H}}_{\mathrm{mix}}>0)$.

4. A mixture of $100\mathrm{mL}$ ${\mathrm{CS}}_2$ and $100$mL acetone has a volume $>200\mathrm{mL}$ $(∆{\mathrm{V}}_{\mathrm{mix}}>0)$

(A) The above detailed explanation shows that option(A) is Incorrect.

(B) The above detailed explanation shows that option(B) is Incorrect.

(C) The above detailed explanation shows that option(C) is Incorrect.

Hence, option D is the correct answer.