Calculate the osmotic pressure in $atm$ of an aqueous solution of urea at $37\,^oC$,which has a freezing point of $0.52\,^oC$. Assume molality and molarity are numerically equal. $(K_f = 1.86\,^oC\, m^{-1})$

Which of the following graphs correctly represents the changes in thermodynamic properties during the formation of $1 \, mol$ of an ideal binary solution?

Identify the false statement from the following.

$20\%$ of acetic acid is dissociated when its $5\ g$ is added to $500\ mL$ of water. The depression in freezing point of such water is $..... \times 10^{-3} \ { }^{\circ}C$. Atomic mass of $C$,$H$,and $O$ are $12$,$1$,and $16 \ \text{a.m.u.}$ respectively.
[Given: Molal depression constant and density of water are $1.86 \ K \ kg \ mol^{-1}$ and $1 \ g \ cm^{-3}$ respectively.]

At $35^{\circ} C$,the vapour pressure of $CS_{2}$ is $512 \; mm \; Hg$ and that of acetone is $344 \; mm \; Hg$. $A$ solution of $CS_{2}$ in acetone has a total vapour pressure of $600 \; mm \; Hg$. The false statement amongst the following is

Column-$I$ (Various solutions)	Column-$II$ (Their freezing point)
$a$. $0.1 \ M \ BaCl_2$ solution	$p$. $271 \ K$
$b$. $0.1 \ M \ NaCl$ solution	$q$. $270 \ K$
$c$. $0.1 \ M \ K_3[Fe(CN)_6]$ solution	$s$. $269 \ K$
$d$. $0.1 \ M \ Al_2(SO_4)_3$ solution	$r$. $268 \ K$

Given: Freezing point of $0.1 \ M$ sucrose solution $= 272 \ K$ and Freezing point of water $= 273 \ K$. Assume molarity $=$ molality. Which of the following options shows the correct matches?