$A$ solution has a $1:4$ mole ratio of pentane to hexane. The vapour pressure of the pure hydrocarbons at $20 \ ^oC$ are $440 \ mm \ Hg$ for pentane and $120 \ mm \ Hg$ for hexane. The mole fraction of pentane in the vapour phase would be

Match List-$I$ with List-$II$

List-$I$	List-$II$
$A$. Solution of chloroform and acetone	$I$. Minimum boiling azeotrope
$B$. Solution of ethanol and water	$II$. Dimerizes
$C$. Solution of benzene and toluene	$III$. Maximum boiling azeotrope
$D$. Solution of acetic acid in benzene	$IV$. $\Delta V_{mix}=0$

Choose the correct answer from the options given below $:$

An aqueous solution of a non-volatile solute boils at $100.15\,^{\circ}C$. If the solution is diluted with an equal volume of water,the freezing point of the resulting solution will be ...... $^{\circ}C$. (Given: $K_b = 0.512\,K\,kg\,mol^{-1}$ and $K_f = 1.86\,K\,kg\,mol^{-1}$ for water)

Which of the following mixtures represents Proof Spirit (by volume)?

An aqueous solution contains $6\%$ and $4\%$ by weight of a weak acid $(HA)$ and urea respectively. If the depression in freezing point is $\frac{13.6}{3} \, ^{\circ}C$,calculate the $K_a$ of $HA$. [Given: $K_f = 1.8 \, K \, kg/mol$,Molecular weight of $HA = 60$,$d_{solution} = 1 \, g/mL$]

Which of the following aqueous solutions produce the same osmotic pressure?