Question

Based on the given diagram, which of the following statements regarding the solution of two miscible volatile liquids $A$ and $B$ are correct?

(I) Plots $AC$ and $BD$ show that Raoult's law is obeyed for the solution in which $A$ is solute and $B$ is solvent and as well as for that in which $B$ is solute and $A$ is solvent.
(II) Plots $CD$ shows that Dalton's law of partial pressure is observed for the binary solution of components $A$ and $B$.
(III) In pure state, vapour pressures of volatile liquid differ by $50$ units.
(IV) Vapour pressure of a mixture containing $40\%$ mole of $B$ is about $105$ units. Select the correct answer using the codes given below.

• A. All except IV
• B. All except I
• C. All except III
• D. All of these

Answer 1

Answer: (D)

Figure shows ideal behaviour of solution.

At point $A,{\chi }_A=0,{\chi }_B=1$, thus

$AD=$ vapour pressure of pure $B=135$ units,

At point $B,{\chi }_B=0,{\chi }_A=1$, thus

$BC=$ vapour pressure of pure $A=85$ units

As $A$ is added into $B$, vapour pressure of $A$ decreases and that of $B$ increases.

Thus, $AC$ shows Raoult's law for a solution of $B$ in $A$(solvent)

and $BD$ shows Raoult's law for a solution of $A$ in $B$ (solvent).

Thus (I) is correct

Total vapour pressure at any composition is given by line $CD$,

thus (II) is correct.

$p_B^o-p_A^o=135-85=50$ units

Thus, (III) is correct. When,

${\chi }_B=0.4,{\chi }_A=0.6$

Vapour pressure of the mixture is given by $CD$.

$p_{\text{total }}=p_A^o{\chi }_A+p_B^o{\chi }_B$

$=85\times 0.6+135\times 0.4=105$

It is same as given by graph.

Thus, (IV) is also correct.