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When \( x \times 10^{-2} \, \text{mL} \) methanol (molar mass \( = 32 \, \text{g} \); density \( = 0.792 \, \text{g}/ \, \text{cm}^{-3} \)) is added to \( 100 \, \text{mL} \) water (density \( = 1 \, \text{g} \,/ \text{cm}^{-3} \)), the following diagram is obtained.

\( x = \) __________ (nearest integer).
[Given: Molal freezing point depression constant of water at \( 273.15 \, \text{K} \) is \( 1.86 \, \text{K} \, \text{kg} \, \text{mol}^{-1} \)]

The osmotic pressure of a dilute solution is \( 7 \times 10^{5} \, \mathrm{Pa} \) at \( 273 \, \mathrm{K} \). Osmotic pressure of the same solution at \( 283 \, \mathrm{K} \) is __________ \( \times 10^{4} \, \mathrm{N \, m^{-2}} \).

A solution in prepared by adding \( 1 \) mole ethyl alcohol in \( 9 \) mole water. The mass precent of solute in the solution is ______ (Integer anser) (Given : Molar mass is \( \text{g mol}^{-1} \) Ethyl alcohol : \( 46 \), water : \( 18 \))

The vapor pressure of pure benzene and methyl benzene at \( 27^\circ \text{C} \) is given as \( 80 \, \text{Torr} \) and \( 24 \, \text{Torr} \), respectively. The mole fraction of methyl benzene in vapor phase, in equilibrium with an equimolar mixture of those two liquids (ideal solution) at the same temperature is _____ \( \times 10^{-2} \) (nearest integer)

A solution containing \( 10 \) g of an electrolyte \( \mathrm{AB_2} \) in \( 100 \) g of water boils at \( 100.52^\circ \mathrm{C} \). The degree of ionization of the electrolyte \( (\alpha) \) is ______ \( \times 10^{-1} \). (Nearest integer)
[Given: Molar mass of \( \mathrm{AB_2} = 200 \) g \( \mathrm{mol^{-1}} \), \( K_b \) (molal boiling point elevation const. of water) \( = 0.52 \) K kg \( \mathrm{mol^{-1}} \), boiling point of water \( = 100^\circ \mathrm{C} \); \( \mathrm{AB_2} \) ionises as \( \mathrm{AB_2 \rightarrow A^{2+} + 2B^{-}} \)]

Identify the mixture that shows positive deviations from Raoult's Law:

A solution of two miscible liquids showing negative deviation from Raoult’s law will have:

\( 2.7 \, \text{kg} \) of each of water and acetic acid are mixed. The freezing point of the solution will be \( -x \, ^\circ \text{C} \). Consider the acetic acid does not dimerise in water, nor dissociates in water. \( x = \_\_\_\_\_\_\_\_ \).
[Given: Molar mass of water = \( 18 \, \text{g} \, \text{mol}^{-1} \), acetic acid = \( 60 \, \text{g} \, \text{mol}^{-1} \)]
\( K_f \, H_2O : 1.86 \, K \, kg \, mol^{-1} \)
\( K_f \, \text{acetic acid}: 3.90 \, K \, kg \, mol^{-1} \)
freezing point: \( H_2O = 273 \, K \), acetic acid = \( 290 \, K \)

Mass of ethylene glycol (antifreeze) to be added to \( 18.6 \) kg of water to protect the freezing point at \( -24^\circ\mathrm{C} \) is __________ kg (Molar mass in \( \mathrm{g\, mol^{-1}} \) for ethylene glycol \( 62 \), \( K_f \) of water = \( 1.86 \, \mathrm{K\, kg\, mol^{-1}} \))

What happens to freezing point of benzene when small quantity of naphthalene is added to benzene?