Question

A mixture of two miscible volatile ideal liquids $P$ and $Q$ $($obeying Raoult’s law $)$ is kept in a vessel molar ratio of $P$ and $Q$ in the mixture is $m)$. At a suitable temperature $T$, the vapour above the liquid is condensed in another vessel. The liquid obtained on condensation is allowed to evaporate and establish equilibrium with its vapour . The vapour is then condensed in another vessel. The process of such evaporation and condensation is repeated for $n$ times. If the ratio of the vapour pressure of pure $P$ to that of pure $Q$ is $p$, the molar ratio of $P$ and $Q$ in the condensed liquid obtained after ${n^{th}}$ cycle $($for finite $n > 1)$is
$A){p^n}m \\\ B)p{m^n} \\\ C){p^{n/2}}{m^{n/2}} \\\ D){p^n}{m^n} \\\ \\\$

Answer 1

To solve this question we must know the formula that is being used in this question. We are using Raoult’s law in this question, it states that the partial pressure of each component of an ideal mixture of liquids is equal to the vapor pressure of the pure component multiplied by its mole fraction in the mixture

Complete step by step solution:
Raoult’s law expresses that the incomplete pressing factor of every part of an ideal combination of liquids is equivalent to the vapor pressure factor of the pure segment multiplied by its mole portion in the mixture. An outcome, the general lowering of vapor pressure factor of a weakened arrangement of nonvolatile solute is equivalent to the mole part of solute in the solution.
=$\dfrac{{{p^ \circ } - {p^ \circ }}}{{{p^ \circ }}} = \dfrac{{{n_2}}}{{{n_1} + {n_2}}}{X_{{n_2}}}$.
We know the formula to calculate the vapour pressure of a compound
=vapor pressure of pure substance $\times$ mole fraction
The ratio of moles in liquid which is obtained by condensing is equal to the ratio of the vapor pressure of $P$ and $Q$ above the initial solution and repeating this
$n$ times gives ${p^n}m$.

So the correct answer is $A)$

Note:
Raoult's law is a phenomenological law that expects ideal gas behavior dependent on the basic assumption that intermolecular forces between dissimilar to particles are equivalent to those between comparable atoms: the states of an ideal arrangement. Raoult's law is rather valid if the actual properties of the components are indistinguishable.