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\( \mathrm{C}_6\mathrm{H}_6 \) freezes at \( 5.5\,^{\circ}\text{C} \). The temperature at which a solution of \( 10 \, \text{g} \) of \( \mathrm{C}_4\mathrm{H}_{10} \) in \( 200 \, \text{g} \) of \( \mathrm{C}_6\mathrm{H}_6 \) freeze is _________ \( ^{\circ}\text{C} \). (The molal freezing point depression constant of \( \mathrm{C}_6\mathrm{H}_6 \) is \( 5.12\,^{\circ}\text{C}/\text{m} \).)

The water having more dissolved \( \mathrm{O_2} \) is:

\( 1 \, \text{kg} \) of \( 0.75 \) molal aqueous solution of sucrose can be cooled up to \( -4^\circ \text{C} \) before freezing. The amount of ice (in \( \text{g} \)) that will be separated out is ______________. (Nearest integer)
[Given: \( K_f(\mathrm{H_2O}) = 1.86 \, \text{K} \, \text{kg} \, \text{mol}^{-1} \)]

Which purification technique is used for high boiling organic liquid compound (decomposes near its boiling point)?

At \( 20^\circ \text{C} \), the vapour pressure of benzene is \( 70 \) torr and that of methyl benzene is \( 20 \) torr. The mole fraction of benzene in the vapor phase at \( 20^\circ \text{C} \) above an equimolar mixture of benzene and methyl benzene is _____ \( \times 10^{-2} \). (Nearest integer)

\( 2 \) molal solution of a weak acid \( \mathrm{HA} \) has a freezing point of \( 3.885^\circ \mathrm{C} \). The degree of dissociation of this acid is ____________ \( \times 10^{-3} \). (Round off to the Nearest Integer).
[Given: Molal depression constant of water \( = 1.85 \, \mathrm{K \, kg \, mol^{-1}} \), Freezing point of pure water \( = 0^\circ \mathrm{C} \)]

Which one of the following \( 0.06 \, \text{M} \) aqueous solutions has lowest freezing point?

When \( 3.00 \, \text{g} \) of a substance 'X' is dissolved in \( 100 \, \text{g} \) of \( \mathrm{CCl_4} \), it raises the boiling point by \( 0.60 \, \text{K} \). The molar mass of the substance 'X' is ________ \( \text{g mol}^{-1} \). (Nearest integer)
[Given \( K_b \) for \( \mathrm{CCl_4} \) is \( 5.0 \, \text{K kg mol}^{-1} \)]

Of the following four aqueous solutions, total number of those solutions whose freezing point is lower than that of \( 0.10 \, \mathrm{M} \) \( \mathrm{C_2H_5OH} \) is ________. (Integer answer)
\( (i) \) \( 0.10 \, \mathrm{M} \) \( \mathrm{Ba_3(PO_4)_2} \) \( (ii) \) \( 0.10 \, \mathrm{M} \) \( \mathrm{Na_2SO_4} \) \( (iii) \) \( 0.10 \, \mathrm{M} \) \( \mathrm{KCl} \) \( (iv) \) \( 0.10 \, \mathrm{M} \) \( \mathrm{Li_3PO_4} \)

A \( 1 \) molal \( K_4 \,Fe(CN)_6 \) solution has a degree of dissociation of \( 0.4 \). Its boiling point is equal to that of another solution which contains \( 18.1 \) weight percent of a non electrolytic solute \( A \).
The molar mass of \( A \) is ________ \( \text{u} \). (Round off to the Nearest Integer) [Density of water \( = 1.0 \ \text{g cm}^{-3} \)]

\( 1.46 \)\( \text{g} \) of a biopolymer dissolved in a \( 100 \) \( \text{mL} \) water \( 300 \)\( \text{K} \) exerted an osmotic pressure of \( 2.42 \times 10^{-3} \) \( \text{bar} \).
The molar mass of the biopolymer is ______ \( \times 10^{4} \) \( \text{g mol}^{-1} \). (Round off to the Nearest Integer)
[Use : \( R = 0.083 \) \( \text{L bar mol}^{-1} \text{K}^{-1} \)]

In a solvent \( 50\% \) of an acid \( \mathrm{HA} \) dimerizes and the rest dissociates. The van’t Hoff factor of the acid is _______ \( \times 10^{-2} \). (Round off to the Nearest Integer).

The oxygen dissolved in water exerts a partial pressure of \( 20 \, \text{kPa} \) in the vapour above water. The molar solubility of oxygen in water is _________ \( \times 10^{-5} \, \text{mol dm}^{-3} \).
(Round off to the Nearest Integer).
[Given : Henry's law constant \( = k_H = 8.0 \times 10^{4} \, \text{kPa} \) for \( \mathrm{O_2} \) , Density of water with dissolved oxygen \( = 1.0 \, \text{kg dm}^{-3} \) ]

The mole fraction of a solute in a \( 100 \) molal aqueous solutions is ______ \( \times 10^{-2} \).
(Round off to the Nearest Integer).
[Given : Atomic masses \( \mathrm{H:1.0 \, u , \ O:16.0 \, u} \)]

Which one of the following \( 0.10 \, \mathrm{M} \) aqueous solutions will exhibit the largest freezing point depression?

\( 1.22 \, \text{g} \) of an organic acid is separately dissolved in \( 100 \, \text{g} \) of benzene \( (K_b = 2.6 \, \text{K kg mol}^{-1}) \) and \( 100 \, \text{g} \) of acetone \( (K_b = 1.7 \, \text{K kg mol}^{-1}) \). The acid is known to dimerize in benzene but remain as a monomer in acetone. The boiling point of the solution in acetone increases by \( 0.17 ^\circ \text{C} \). The increase in boiling point of solution in benzene in \( ^\circ \text{C} \) is \( x \times 10^{-2} \). The value of \( x \) is _______. (Nearest integer) (Atomic mass: \( \mathrm{C} = 12.0 \), \( \mathrm{H} = 1.0 \), \( \mathrm{O} = 16.0 \))

\( 83 \, \text{g} \) of ethylene glycol dissolved in \( 625 \, \text{g} \) of water. The freezing point of the solution is ______ \( \text{K} \). (Nearest integer)
[Use : Molal Freezing point depression constant of water \( = 1.86 \, \text{K kg mol}^{-1} \)
Freezing point of water \( = 273 \, \text{K} \)
Atomic masses : \( \text{C} : 12.0 \, \text{u} \), \( \text{O} : 16.0 \, \text{u} \), \( \text{H} : 1.0 \, \text{u} \)]

A solute A dimerizes in water. The boiling point of a \( 2 \) molal solution of A is \( 100.52^\circ \mathrm{C} \). The percentage association of A is ______
[Use: \( K_b \) for water \( = 0.52 \, \mathrm{K\,kg\,mol^{-1}} \) Boiling point of water \( = 100^\circ \mathrm{C} \)]

The vapour pressure of \( A \) and \( B \) at \( 25^\circ \text{C} \) are \( 90 \, \text{mm Hg} \) and \( 15 \, \text{mm Hg} \) respectively. If \( A \) and \( B \) are mixed such that the mole fraction of \( A \) in the mixture is \( 0.6 \), then the mole fraction of \( B \) in the vapour phase is \( x \times 10^{-1} \). The value of \( x \) is __________. (Nearest integer)

\( 40 \, \text{g} \) of glucose (Molar mass = \( 180 \)) is mixed with \( 200 \, \text{mL} \) of water. The freezing point of solution is _______ \( \text{K} \). (Nearest integer)
[Given : \( K_f = 1.86 \, \text{K} \, \text{kg} \, \text{mol}^{-1} \); Density of water = \( 1.00 \, \text{g} \, \text{cm}^{-3} \); Freezing point of water = \( 273.15 \, \text{K} \)]

\( \mathrm{CO_2} \) gas is bubbled through water during a soft drink manufacturing process at \( 298 \; \mathrm{K} \). If \( \mathrm{CO_2} \) exerts a partial pressure of \( 0.835 \; \mathrm{bar} \) then \( x \; \mathrm{m\,mol} \) of \( \mathrm{CO_2} \) would dissolve in \( 0.9 \; \mathrm{L} \) of water. The value of \( x \) is ________. (Nearest integer)
(Henry’s law constant for \( \mathrm{CO_2} \) at \( 298 \; \mathrm{K} \) is \( 1.67 \times 10^{3} \; \mathrm{bar} \))

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JEE Main 2021 17th March Morning Shift

The mole fraction of a solute in a \( 100 \) molal aqueous solutions is ______ \( \times 10^{-2} \).
(Round off to the Nearest Integer).
[Given : Atomic masses \( \mathrm{H:1.0 \, u , \ O:16.0 \, u} \)]