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JEE Mains | PYQ

Elements P and Q form two types of non-volatile, non-ionizable compounds \( \mathrm{PQ} \) and \( \mathrm{PQ_2} \). When \( 1 \, \mathrm{g} \) of \( \mathrm{PQ} \) is dissolved in \( 50 \, \mathrm{g} \) of solvent ‘A’, \( \Delta T_b \) was \( 1.176 \, \mathrm{K} \) while when \( 1 \, \mathrm{g} \) of \( \mathrm{PQ_2} \) is dissolved in \( 50 \, \mathrm{g} \) of solvent ‘A’, \( \Delta T_b \) was \( 0.689 \, \mathrm{K} \). \( (K_b \) of ‘A’ \( = 5 \, \mathrm{K\,kg\,mol^{-1}} ) \). The molar masses of elements P and Q (in \( \mathrm{g\,mol^{-1}} \)) respectively, are:

Given below are two statements:

Statement (I): \( 1,2,3 \)-Trihydroxypropane can be separated from water by simple distillation.

Statement (II): An azeotropic mixture cannot be separated by fractional distillation.

In the light of the above statements, choose the correct answer from the options given below:

Solution A is prepared by dissolving \( 1 \, \mathrm{g} \) of a protein (molar mass \( = 50000 \, \mathrm{g \, mol^{-1}} \)) in \( 0.5 \, \mathrm{L} \) of water at \( 300 \, \mathrm{K} \). Its osmotic pressure is \( x \) bar. Solution B is made by dissolving \( 2 \, \mathrm{g} \) of same protein in \( 1 \, \mathrm{L} \) of water at \( 300 \, \mathrm{K} \). Osmotic pressure of solution B is \( y \) bar. Entire solution of A is mixed with entire solution of B at same temperature. The osmotic pressure of resultant solution is \( z \) bar. \( x \), \( y \) and \( z \) respectively are: \( (R = 0.083 \, \mathrm{L \, bar \, mol^{-1} \, K^{-1}}) \)

At \( 298 \, \text{K} \), the mole percentage of \( \mathrm{N_2(g)} \) in air is \( 80\% \). Water is in equilibrium with air at a pressure of \( 10 \, \text{atm} \). What is the mole fraction of \( \mathrm{N_2(g)} \) in water at \( 298 \, \text{K} \)? ( \( K_H \) for \( \mathrm{N_2} \) is \( 6.5 \times 10^{7} \, \text{mm Hg} \) )

Consider a solution of \( \mathrm{CO_2(g)} \) dissolved in water in a closed container. Which one of the following plots correctly represents variation of \( \log \) (partial pressure of \( \mathrm{CO_2} \) in vapour phase above water) [y-axis] with \( \log \) (mole fraction of \( \mathrm{CO_2} \) in water) [x-axis] at \( 25^\circ \mathrm{C} \)?

A solution is prepared by dissolving \( 0.3 \, \text{g} \) of a non-volatile non-electrolyte solute 'A' of molar mass \( 60 \, \text{g mol}^{-1} \) and \( 0.9 \, \text{g} \) of a non-volatile non-electrolyte solute 'B' of molar mass \( 180 \, \text{g mol}^{-1} \) in \( 100 \, \text{mL} \) \( \mathrm{H_2O} \) at \( 27^{\circ}\mathrm{C} \). Osmotic pressure of the solution will be \( [\text{Given: } R = 0.082 \, \mathrm{L\, atm\, K^{-1}\, mol^{-1}}] \)

Which of the following statements are not correct?
A. For water, magnitude of \( K_b \) is more than the magnitude of \( K_f \).
B. The elevation in boiling point of water when a non-volatile solute is added to it is larger in magnitude than its depression in freezing point.
C. Osmotic pressure measurement is preferred over any other colligative property to determine molar mass of proteins and polymers.
D. The dimerised form of benzoic acid in benzene is
Choose the correct answer from the options given below:

Given below are two statements:
Given: Molar mass of \( \mathrm{C, H, O, Cl} \) are \( 12 \), \( 1 \), \( 16 \) and \( 35.5 \, \mathrm{g\, mol^{-1}} \), respectively:
Statement-I: In \( 30\% \) (w/w) solution of methanol in \( \mathrm{CCl_{4}} \) (at \( T \, \mathrm{K} \)), the mole fraction of \( \mathrm{CCl_{4}} \) is equal to \( 0.33 \).
Statement-II: Mixture of methanol and \( \mathrm{CCl_{4}} \) shows positive deviation from Raoul’s law.
In the light of the above statements, choose the correct answer from the options given below:

The osmotic pressure of a living cell is \( 12 \, \text{atm} \) at \( 300 \, \text{K} \). The strength of sodium chloride solution that is isotonic with the living cell at this temperature is _____ \( \text{g L}^{-1} \). (Nearest integer)
Given: \( R = 0.08 \, \text{L atm K}^{-1} \, \text{mol}^{-1} \)
Assume complete dissociation of NaCl
(Given: Molar mass of Na and Cl are \( 23 \) and \( 35.5 \, \text{g mol}^{-1} \) respectively.)

At \( 27^\circ \text{C} \), \( 0.1 \, \text{M} \), \( 1 \, \text{L} \) \( \mathrm{K_4[Fe(CN)_6]} \) aqueous solution and \( 0.1 \, \text{M} \), \( 1 \, \text{L} \) \( \mathrm{FeCl_3} \) aqueous solution are placed in a container separated by a semi permeable membrane AB. Assume complete dissociation of both the solutes. Which of the following statement is correct?

\( 19.5 \, \text{g} \) of fluoro acetic acid (molar mass \( = 78 \, \text{g mol}^{-1} \)) is dissolved in \( 500 \, \text{g} \) of water at \( 298 \, \text{K} \). The depression in the freezing point of water was \( 1^\circ \text{C} \). What is \( K_a \) of fluoro acetic acid ? (For water, \( K_f = 1.86 \, \text{K kg mol}^{-1} \)). Assume molarity and molality to have same values.

Two liquids \( \mathrm{A} \) and \( \mathrm{B} \) form an ideal solution at temperature \( T \, \text{K} \). At \( T \, \text{K} \), the vapour pressures of pure \( \mathrm{A} \) and \( \mathrm{B} \) are \( 55 \) and \( 15 \, \text{kN m}^{-2} \) respectively. What is the mole fraction of \( \mathrm{A} \) in solution of \( \mathrm{A} \) and \( \mathrm{B} \) in equilibrium with a vapour in which the mole fraction of \( \mathrm{A} \) is \( 0.8 \)?

A substance 'X' (\( 1.5 \, \text{g} \)) dissolved in \( 150 \, \text{g} \) of a solvent 'Y' (molar mass \( = 300 \, \text{g mol}^{-1} \)) led to an elevation of the boiling point by \( 0.5 \, \text{K} \). The relative lowering in the vapor pressure of the solvent 'Y' is _____ \( \times 10^{-2} \). (nearest integer)
[Given: \( K_b \) of the solvent \( = 5.0 \, \text{K kg mol}^{-1} \) ]
Assume the solution to be dilute and no association or dissociation of X takes place in solution.

\( 20 \, \text{g} \) hemoglobin in a \( 1 \, \text{L} \) aqueous solution (A) at \( 300 \, \text{K} \) is separated from pure water by semi permeable membrane. At equilibrium the height of solution in a tube dipped in a solution (A) is found to be \( 80.0 \, \text{mm} \) higher than the tube dipped in water.

\(
\text{The molar mass of hemoglobin is }
\underline{\hspace{3cm}}
\ \mathrm{kg\,mol^{-1}}.
\qquad
\text{(Nearest integer)}
\)

\(
(\text{Given: }
g=10\,\mathrm{m\,s^{-2}},\quad
R=8.3\,\mathrm{kPa\,dm^3\,K^{-1}\,mol^{-1}},\quad
\text{density of solution}=1000\,\mathrm{kg\,m^{-3}}
)\)