JEE MainsJEE AdvanceBITSAT

JEE Mains | PYQ

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

If the boiling points of two solvents \( X \) and \( Y \) (having same molecular weights) are in the ratio \( 2:1 \) and their enthalpy of vaporizations are in the ratio \( 1:2 \), then the boiling point elevation constant of \( X \) is \( m \) times the boiling point elevation constant of \( Y \). The value of \( m \) is _____________ (nearest integer)

At \( T(\mathrm{K}) \), \( 2 \) moles of liquid \( \mathrm{A} \) and \( 3 \) moles of liquid \( \mathrm{B} \) are mixed. The vapour pressure of ideal solution formed is \( 320 \, \text{mm Hg} \). At this stage, one mole of \( \mathrm{A} \) and one mole of \( \mathrm{B} \) are added to the solution. The vapour pressure is now measured as \( 328.6 \, \text{mm Hg} \). The vapour pressure (in mm Hg) of \( \mathrm{A} \) and \( \mathrm{B} \) are respectively:

A box contains \( 0.90 \, \text{g} \) of liquid water in equilibrium with water vapour at \( 27^\circ \mathrm{C} \). The equilibrium vapour pressure of water at \( 27^\circ \mathrm{C} \) is \( 32.0 \, \text{Torr} \). When the volume of the box is increased, some of the liquid water evaporates to maintain the equilibrium pressure. If all the liquid water evaporates, then the volume of the box must be ______ litre. [Nearest integer]
(Given: \( R = 0.082 \, \mathrm{L \, atm \, K^{-1} \, mol^{-1}} \) )
(Ignore the volume of the liquid water and assume water vapours behave as an ideal gas).

Density of \( 3 \, \text{M} \) \( \mathrm{NaCl} \) solution is \( 1.25 \, \text{g/mL} \). The molality of the solution 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)?

\( 2 \) moles each of ethylene glycol and glucose are dissolved in \( 500 \, \text{g} \) of water. The boiling point of the resulting solution is: (Given: Ebullioscopic constant of water \( = 0.52 \, \text{K kg mol}^{-1} \))

Given below are two statements:

Statement I: The Henry’s law constant \( K_H \) is constant with respect to variations in solution’s concentration over the range for which the solution is ideally dilute.

Statement II: \( K_H \) does not differ for the same solute in different solvents.

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

\( 80 \) mole percent of \( \mathrm{MgCl_2} \) is dissociated in aqueous solution. The vapour pressure of \( 1.0 \) molal aqueous solution of \( \mathrm{MgCl_2} \) at \( 38^\circ\text{C} \) is ____ \( \text{mm Hg} \). (Nearest integer)
Given: Vapour pressure of water at \( 38^\circ\text{C} \) is \( 50 \, \text{mm Hg} \).

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)

‘\( W \) g’ of a non-volatile electrolyte solid solute of molar mass ‘\( M \)’ \( \mathrm{g \, mol^{-1}} \) when dissolved in \( 100 \, \mathrm{mL} \) water, decreases vapour pressure of water from \( 640 \, \mathrm{mm \, Hg} \) to \( 600 \, \mathrm{mm \, Hg} \). If aqueous solution of the electrolyte boils at \( 375 \, \mathrm{K} \) and \( K_b \) for water is \( 0.52 \, \mathrm{K \, kg \, mol^{-1}} \), then the mole fraction of the electrolyte solute (\( x_2 \)) in the solution can be expressed as (Given: density of water = \( 1 \, \mathrm{g/mL} \) and boiling point of water = \( 373 \, \mathrm{K} \))

If \( \mathrm{O_2} \) gas is bubbled through water at \( 303 \, \text{K} \), the number of millimoles of \( \mathrm{O_2} \) gas that dissolve in \( 1 \) litre of water is __________. (Nearest Integer)
(Given: Henry’s Law constant for \( \mathrm{O_2} \) at \( 303 \, \text{K} \) is \( 46.82 \; k \, \text{bar} \) and partial pressure of \( \mathrm{O_2} = 0.920 \; \text{bar} \))
(Assume solubility of \( \mathrm{O_2} \) in water is too small, nearly negligible)

We have three aqueous solutions of \( \text{NaCl} \) labelled as ‘A’, ‘B’ and ‘C’ with concentration \( 0.1 \, \text{M} \), \( 0.01 \, \text{M} \), \( 0.001 \, \text{M} \), respectively. The value of van’t Hoff factor \( (i) \) for these solutions will be in the order:

Liquid A and B form an ideal solution. The vapour pressure of pure liquids A and B are \( 350 \) and \( 750 \) mm Hg respectively at the same temperature. If \( X_A \) and \( X_B \) are the mole fraction of A and B in solution while \( Y_A \) and \( Y_B \) are the mole fraction of A and B in vapour phase then,

Two liquids \( A \) and \( B \) form an ideal solution. At \( 320 \, \text{K} \), the vapour pressure of the solution, containing \( 3 \) mol of \( A \) and \( 1 \) mol of \( B \) is \( 500 \, \text{mm Hg} \). At the same temperature, if \( 1 \) mol of \( A \) is further added to this solution, vapour pressure of the solution increases by \( 20 \, \text{mm Hg} \). Vapour pressure \( \)(in mm Hg\( \)) of \( B \) in pure state is _________ \( \). \( \)(Nearest integer\( \))

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:

\( 2 \) 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 \( = 0^\circ \mathrm{C} \)]

Sea water contains \( 29.25\% \) \( \mathrm{NaCl} \) and \( 19\% \) \( \mathrm{MgCl_2} \) by weight of solution. The normal boiling point of the sea water is ________ \( ^\circ\mathrm{C} \) (Nearest integer)
Assume \( 100\% \) ionization for both \( \mathrm{NaCl} \) and \( \mathrm{MgCl_2} \)
Given : \( K_b(\mathrm{H_2O}) = 0.52 \, \mathrm{K\,kg\,mol^{-1}} \)
Molar mass of \( \mathrm{NaCl} \) and \( \mathrm{MgCl_2} \) is \( 58.5 \) and \( 95 \, \mathrm{g\,mol^{-1}} \) respectively.

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

Statement I : For colloidal particles, the values of colligative properties are of small order as compared to values shown by true solutions at same concentration.
Statement II : For colloidal particles, the potential difference between the fixed layer and the diffused layer of same charges is called the electrokinetic potential or zeta potential.
In the above statements, choose the correct answer from the options given below

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: \( (R = 0.083 \, \mathrm{L \, bar \, mol^{-1} \, K^{-1}}) \)

The osmotic pressure of blood is \( 7.47 \, \text{bar} \) at \( 300 \, \text{K} \). To inject glucose to a patient intravenously, it has to be isotonic with blood. The concentration of glucose solution in \( \text{g L}^{-1} \) is __________.
(Molar mass of glucose \( = 180 \, \text{g mol}^{-1} \), \( R = 0.083 \, \text{L bar K}^{-1} \, \text{mol}^{-1} \)) (Nearest integer)

Some amount of dichloromethane \( (\mathrm{CH_2Cl_2}) \) is added to \( 671.141 \, \text{mL} \) of chloroform \( (\mathrm{CHCl_3}) \) to prepare \( 2.6 \times 10^{-3} \, \text{M} \) solution of \( \mathrm{CH_2Cl_2} \) (DCM). The concentration of DCM is ________ ppm (by mass). [Given : Atomic mass : \( \mathrm{C} = 12 \), \( \mathrm{H} = 1 \), \( \mathrm{Cl} = 35.5 \) density of \( \mathrm{CHCl_3} = 1.49 \, \text{g cm}^{-3} \)]

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 \( 5.0 \, \text{K kg mol}^{-1} \)]

Match List I and List II

Choose the correct answer from the options given below:

What weight of glucose must be dissolved in \( 100 \, \text{g} \) of water to lower the vapour pressure by \( 0.20 \, \text{mm Hg} \)? (Assume dilute solution is being formed)
Given: Vapour pressure of pure water is \( 54.2 \, \text{mm Hg} \) at room temperature. Molar mass of glucose is \( 180 \, \text{g mol}^{-1} \).

Assume a living cell with \( 0.9\% \) \( (\omega/\omega) \) of glucose solution (aqueous). This cell is immersed in another solution having equal mole fraction of glucose and water. (Consider the data upto first decimal place only)
The cell will:

Considering acetic acid dissociates in water, its dissociation constant is \( 6.25 \times 10^{-5} \). If \( 5 \, \text{mL} \) of acetic acid is dissolved in \( 1 \, \text{litre} \) water, the solution will freeze at \( - \, x \times 10^{-2} \, ^\circ \text{C} \), provided pure water freezes at \( 0^\circ \text{C} \).
\( x = \_ \_ \_ \_ \_ \). (Nearest integer)
\( (K_f)_{\text{water}} = 1.86 \, \text{K kg mol}^{-1} \).
density of acetic acid is \( 1.2 \, \text{g mol}^{-1} \).
molar mass of water = \( 18 \, \text{g mol}^{-1} \).
molar mass of acetic acid = \( 60 \, \text{g mol}^{-1} \).
density of water = \( 1 \, \text{g cm}^{-3} \).
Acetic acid dissociates as \( \mathrm{CH_3COOH} \rightleftharpoons \mathrm{CH_3COO^\ominus} + \mathrm{H^\oplus} \).

\( 0.05 \, \text{M} \) \( \text{CuSO}_{4} \) when treated with \( 0.01 \, \text{M} \) \( \text{K}_{2}\text{Cr}_{2}\text{O}_{7} \) gives green colour solution of \( \text{Cu}_{2}\text{Cr}_{2}\text{O}_{7} \). The two solutions are separated as shown below
[SPM: Semi Permeable Membrane]

Due to osmosis:

The molality of a \( 10\% \) (v/v) solution of di-bromine solution in \( \mathrm{CCl_4} \) (carbon tetrachloride) is ‘\( x \)’.
\( x = \_\_\_\_\_ \times 10^{-2}\,\mathrm{M} \). [Nearest integer]
(Given: molar mass of \( \mathrm{Br_2} = 160 \, \mathrm{g\,mol^{-1}} \), atomic mass of \( \mathrm{C} = 12 \, \mathrm{g\,mol^{-1}} \), atomic mass of \( \mathrm{Cl} = 35.5 \, \mathrm{g\,mol^{-1}} \), density of dibromine \( = 3.2 \, \mathrm{g\,cm^{-3}} \), density of \( \mathrm{CCl_4} = 1.6 \, \mathrm{g\,cm^{-3}} \)).

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)
\( (i) \) \( 0.10 \, \mathrm{M} \) \( \mathrm{Ba_3(PO_4)_2} \) \( (ii) \) \( 0.10 \, \mathrm{M} \) \( \mathrm{Na_2SO_4} \) \( (iii) \) \( 0.10 \, \mathrm{M} \) \( \mathrm{KCl} \) \( (iv) \) \( 0.10 \, \mathrm{M} \) \( \mathrm{Li_3PO_4} \)

The solution from the following with highest depression in freezing point/lowest freezing point is:

Evaluate the following statements for their correctness.
(A) The elevation in boiling point temperature of water will be same for \( 0.1 \, \mathrm{M} \) \( \mathrm{NaCl} \) and \( 0.1 \, \mathrm{M} \) urea.
(B) Azeotropic mixtures boil without change in their composition.
(C) Osmosis always takes place from hypertonic to hypotonic solution.
(D) The density of \( 32\% \) \( \mathrm{H_2SO_4} \) solution having molarity \( 4.09 \, \mathrm{M} \) is approximately \( 1.26 \, \mathrm{g\, mL^{-1}} \).
(E) A negatively charged sol is obtained when KI solution is added to silver nitrate solution.
Choose the correct answer from the options given below:

Given below are two statements:
Statement (I): \( \mathrm{NaCl} \) is added to the ice at \( 0^{\circ} \text{C} \), present in the ice cream box to prevent the melting of ice cream.
Statement (II): On addition of \( \mathrm{NaCl} \) to ice at \( 0^{\circ} \text{C} \), there is a depression in freezing point.
In the light of the above statements, choose the correct answer from the options given below:

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 \( 6.5 \times 10^{7} \, \text{mm Hg} \) )

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 \( 1.86 \, \text{K} \, \text{kg} \, \text{mol}^{-1} \)]

In the depression of freezing point experiment
I. Vapour pressure of the solutions is less than that of pure solvent
II. Vapour pressure of the solution is more than that of pure solvent
III. Only solute molecules solidify at the freezing point
IV. Only solvent molecules solidify at the freezing point
Choose the most appropriate answer from the options given below :

\( 1.2 \, \text{mL} \) of acetic acid is dissolved in water to make \( 2.0 \, \text{L} \) of solution. The depression in freezing point observed for this strength of acid is \( 0.0198^\circ \text{C} \). The percentage of dissociation of the acid is ________ (Nearest integer)
[Given: Density of acetic acid is \( 1.02 \, \text{g mL}^{-1} \) ]
Molar mass of acetic acid is \( 60 \, \text{g mol}^{-1} \)
\( K_f ( \text{H}_2\text{O} ) = 1.85 \, \text{K kg mol}^{-1} \)

Two solutions A and B are prepared by dissolving \( 1 \, \mathrm{g} \) of non-volatile solutes X and Y, respectively in \( 1 \, \mathrm{kg} \) of water. The ratio of depression in freezing points for A and B is found to be \( 1:4 \). The ratio of molar masses of X and Y is:

\( 2 \, \mathrm{g} \) of a non-volatile non-electrolyte solute is dissolved in \( 200 \, \mathrm{g} \) of two different solvents A and B whose ebullioscopic constants are in the ratio of \( 1 : 8 \). The elevation in boiling points of A and B are in the ratio \( \dfrac{x}{y} \; (x : y) \). The value of \( y \) is ________ (Nearest Integer).

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 \( 1 \) 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 \( = 1.0 \ \text{g cm}^{-3} \)]

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 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 : \( 18 \))

\( 25 \, \mathrm{mL} \) of an aqueous solution of \( \mathrm{KCl} \) was found to require \( 20 \, \mathrm{mL} \) of \( 1 \, \mathrm{M} \) \( \mathrm{AgNO}_3 \) solution when titrated using \( \mathrm{K}_2\mathrm{CrO}_4 \) as an indicator. What is the depression in freezing point of \( \mathrm{KCl} \) solution of the given concentration? ______ (Nearest integer).
(Given: \( K_f = 2.0 \, \mathrm{K\, kg\, mol^{-1}} \) )
Assume \( (1) \) \( 100\% \) ionization and \( (2) \) density of the aqueous solution as \( 1 \, \mathrm{g\, mL^{-1}} \)

If the degree of dissociations of aqueous solution of weak monobasic acid is determined to be \( 0.3 \), then the observed freezing point will be ______\( \% \) higher tan the expected/theoretical freezing point. (Nearest integer)

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 \( [\text{Given: } R = 0.082 \, \mathrm{L\, atm\, K^{-1}\, mol^{-1}}] \)

\( XY \) is the membrane/partition between two chambers \( 1 \) and \( 2 \) containing sugar solutions of concentration \( c_1 \) and \( c_2 \) (\( c_1 > c_2 \)) \( \text{mol L}^{-1} \). For the reverse osmosis to take place identify the correct condition. (Here \( p_1 \) and \( p_2 \) are pressures applied on chamber \( 1 \) and \( 2 \)).

A. Membrane/Partition: Cellophane, \( p_1 > \pi \)
B. Membrane/Partition: Porous, \( p_2 > \pi \)
C. Membrane/Partition: Parchment paper, \( p_1 > \pi \)
D. Membrane/Partition: Cellophane, \( p_2 > \pi \)
Choose the correct answer from the option given below:

\( 1.46 \)\( \text{g} \) 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 : \( R = 0.083 \) \( \text{L bar mol}^{-1} \text{K}^{-1} \)]

Boiling point of a \( 2\% \) aqueous solution of a non-volatile solute A is equal to the boiling point of \( 8\% \) aqueous solution of a non-volatile solute B. The relation between molecular weights of A and B is:

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).

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:

The depression in freezing point observed for a formic acid solution of concentration \( 0.5 \,\mathrm{mL \, L^{-1}} \) is \( 0.0405^\circ \mathrm{C} \). Density of formic acid is \( 1.05 \,\mathrm{g \, mL^{-1}} \). The Van’t Hoff factor of the formic acid solution is nearly : (Given for water \( k_f = 1.86 \,\mathrm{kg \, mol^{-1}} \))

At \( 27^\circ\text{C} \), a solution containing \( 2.5\,\text{g} \) of solute in \( 250.0\,mL \) of solution exerts an osmotic pressure of \( 400\,\text{Pa} \). The molar mass of solute is \( \_\_\_\_\,\text{g mol}^{-1} \). (Nearest integer)
(Given: \( R = 0.083\,\text{L bar K}^{-1}\text{ mol}^{-1} \))

A gaseous mixture of two substances A and B, under a total pressure of \( 0.8 \, \text{atm} \) is in equilibrium with an ideal liquid solution. The mole fraction of substance A is \( 0.5 \) in the vapour phase and \( 0.2 \) in the liquid phase. The vapour pressure of pure liquid A is __________ \( \text{atm} \). (Nearest integer)

Mass of Urea (\( \text{NH}_2\text{CONH}_2 \)) required to be dissolved in \( 1000 \, \text{g} \) of water in order to reduce the vapour pressure of water by \( 25\% \) is _______ \( \text{g} \). (Nearest integer)
Given: Molar mass of N, C, O and H are \( 14 \), \( 12 \), \( 16 \) and \( 1 \, \text{g mol}^{-1} \) respectively.

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:

\( 2.5 \, \text{g} \) of protein containing only glycine \( \left( \mathrm{C_2H_5NO_2} \right) \) is dissolved in water to make \( 500 \, \text{mL} \) of solution. The osmotic pressure of this solution at \( 300 \, \mathrm{K} \) is found to be \( 5.03 \times 10^{-3} \, \text{bar} \). The total number of glycine units present in the protein is _______________.
(Given : \( R = 0.083 \, \text{L bar K}^{-1} \, \text{mol}^{-1} \) )

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 total pressure observed by mixing two liquids A and B is \( 350 \, \text{mm Hg} \) when their mole fractions are \( 0.7 \) and \( 0.3 \) respectively.
The total pressure becomes \( 410 \, \text{mm Hg} \) if the mole fractions are changed to \( 0.2 \) and \( 0.8 \) respectively for A and B. The vapour pressure of pure A is __________ mm Hg. (Nearest integer)
Consider the liquids and solutions behave ideally.

Given below are two statements:
Statement (I): Molal depression constant \( K_f \) is given by \( \frac{M_1 R T_f}{\Delta S_{fus}} \), where symbols have their usual meaning.
Statement (II): \( K_f \) for benzene is less than the \( K_f \) for water.
In the light of the above statements, choose the most appropriate answer from the options given below:

An aqueous solution of volume \( 300 \, \text{cm}^3 \) contains \( 0.63 \, \text{g} \) of protein. The osmotic pressure of the solution at \( 300 \, \text{K} \) is \( 1.29 \, \text{m bar} \). The molar mass of the protein is ______ \( \text{g mol}^{-1} \).
[Given: \( R = 0.083 \, \text{L bar K}^{-1} \, \text{mol}^{-1} \)]

The number of pairs of the solutions having the same value of the osmotic pressure from the following is ______.

(Assume \( 100\% \) ionization)

A. \( 0.50 \, \text{M} \, \text{C}_2\text{H}_5\text{OH} (\text{aq}) \) and \( 0.25 \, \text{M} \, \text{KBr} (\text{aq}) \).

B. \( 0.100 \, \text{M} \, \text{K}_4[\text{Fe}(\text{CN})_6](\text{aq}) \) and \( 0.100 \, \text{M} \, \text{FeSO}_4 \, (\text{NH}_4)_2 \text{SO}_4 (\text{aq}) \).

C. \( 0.05 \, \text{M} \, \text{K}_4[\text{Fe}(\text{CN})_6](\text{aq}) \) and \( 0.25 \, \text{M} \, \text{NaCl} (\text{aq}) \).

D. \( 0.15 \, \text{M} \, \text{NaCl} (\text{aq}) \) and \( 0.1 \, \text{M} \, \text{BaCl}_2 (\text{aq}) \).

E. \( 0.02 \, \text{M} \, \text{KCl} \cdot \text{MgCl}_2 \cdot 6\text{H}_2\text{O} (\text{aq}) \) and \( 0.05 \, \text{M} \, \text{KCl} (\text{aq}) \).

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)

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.)

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 \( \mathrm{AB_2 \rightarrow A^{2+} + 2B^{-}} \)]

Elevation in boiling point for \( 1.5 \) molal solution of glucose in water is \( 4 \, \mathrm{K} \). The depression in freezing point for \( 4.5 \) molal of glucose in water is \( 4 \, \mathrm{K} \). The ratio of molal elevation constant to molal depression constant \( \left( \frac{K_b}{K_f} \right) \) is ______.

Solid Lead nitrate is dissolved in \( 1 \) litre of water. The solution was found to boil at \( 100.15^\circ \mathrm{C} \). When \( 0.2 \) mol of \( \mathrm{NaCl} \) is added to the resulting solution, it was observed that the solution froze at \( -0.8^\circ \mathrm{C} \). the solubility product of \( \mathrm{PbCl_2} \) formed is __________ \( \times 10^{-6} \) at \( 298 \, \mathrm{K} \). (Nearest integer)

Given : \( K_b = 0.5 \, \mathrm{K \, kg \, mol^{-1}} \) and \( K_f = 1.8 \, \mathrm{K \, kg \, mol^{-1}} \). Assume molality to be equal to molarity in all cases.

\( 150 \, \text{g} \) of acetic acid was contaminated with \( 10.2 \, \text{g} \) ascorbic acid \( (\mathrm{C_6H_8O_6}) \) to lower down its freezing point by \( (x \times 10^{-1})^\circ \text{C} \). The value of \( x \) is __________. (Nearest integer)
Molar mas of ascorbic acid \( = 176 \, \text{g mol}^{-1} \)

A solution containing \( 2.5 \times 10^{-3} \, \mathrm{kg} \) of a solute dissolved in \( 75 \times 10^{-3} \, \mathrm{kg} \) of water boils at \( 373..535 \, \mathrm{K} \). The molar mass of the solute is _______ \( \mathrm{g\,mol^{-1}} \). [nearest integer]
\( \left( \text{Given : } K_b\,(\mathrm{H_2O}) = 0.52 \, \mathrm{K\,mol^{-1}} \text{ and boiling point of water } = 373.15 \, \mathrm{K} \right) \)

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

A solution containing \( 2 \, \text{g} \) of a non-volatile solute in \( 20 \, \text{g} \) of water boils at \( 373.52 \, \text{K} \). The molecular mass of the solute is ________ \( \text{g mol}^{-1} \). (Nearest integer)
[Given, water boils at \( 373 \, \text{K} \), \( K_b \) for water \( = 0.52 \, \text{K kg mol}^{-1} \)]

The osmotic pressure of solutions of PVC in cyclohexanone at \(300 \ \mathrm{K}\) are plotted on the graph. The molar mass of PVC is ______ \( \mathrm{g \ mol^{-1}} \) (Nearest integer) [Given: \( R = 0.083 \ \mathrm{L \ atm \ K^{-1} \ mol^{-1}} \)]

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: \( \mathrm{C} = 12.0 \), \( \mathrm{H} = 1.0 \), \( \mathrm{O} = 16.0 \))

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

The vapour pressure of \( 30\% \,(\text{w/v}) \) aqueous solution of glucose is __________ \( \text{mm Hg} \) AT \( 25^\circ \text{C} \).
[Given : The density to \( 30\% \,(\text{w/v}) \), aqueous solution of glucose is \( 1.2 \,\text{g cm}^{-3} \) and vapour pressure of pure water is \( 24 \,\text{mm Hg} \).]
(Molar mass of glucose is \( 180 \,\text{g mol}^{-1} \))

\( 83 \, \text{g} \) 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 : \( \text{C} : 12.0 \, \text{u} \), \( \text{O} : 16.0 \, \text{u} \), \( \text{H} : 1.0 \, \text{u} \)]

When a certain amount of solid A is dissolved in \( 100 \, \mathrm{g} \) of water at \( 25^\circ \mathrm{C} \) to make a dilute solution, the vapour pressure of the solution is reduced to one-half of that of pure water. The vapour pressure of pure water is \( 23.76 \, \mathrm{mm \, Hg} \). The number of moles of solute A added is ________. (Nearest Integer)

A company dissolves ‘x’ amount of \( \mathrm{CO_2} \) at \( 298 \, \mathrm{K} \) in \( 1 \) litre of water to prepare soda water. \( X = \) _______ \( \times 10^{-3} \, \mathrm{g} \). (nearest integer)
(Given: partial pressure of \( \mathrm{CO_2} \) at \( 298 \, \mathrm{K} = 0.835 \, \mathrm{bar} \).
Henry’s law constant for \( \mathrm{CO_2} \) at \( 298 \, \mathrm{K} = 1.67 \, k \, \mathrm{bar} \).
Atomic mass of H, C and O is \( 1 \), \( 12 \), and \( 6 \, \mathrm{g \, mol^{-1}} \), respectively)

Which of the following graph correctly represents the plots of \( K_H \) at \( 1 \, \text{bar} \) for gases in water versus temperature?

The elevation in boiling point for \( 1 \) molal solution of non-volatile solute A is \( 3 \, \text{K} \). The depression in freezing point for \( 2 \) molal solution of A in the same solvent is \( 6 \, \text{K} \). The ratio of \( K_b \) and \( K_f \) i.e., \( {K_b}/{K_f} \) is \( 1 : X \). The value of \( X \) is [nearest integer]

A \( 0.5 \) percent solution of potassium chloride was found to freeze at \( -0.24^\circ \mathrm{C} \). The percentage dissociation of potassium chloride is ____________ (Nearest integer).
Molal depression constant for water is \( 1.80 \, \text{K kg mol}^{-1} \) and molar mass of \( \mathrm{KCl} \) is \( 74.6 \, \text{g mol}^{-1} \).

\( 2.7 \, \text{kg} \) 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 = \( 290 \, K \)

Consider a binary solution of two volatile liquid components \( 1 \) and \( 2 \). \( x_1 \) and \( y_1 \) are the mole fractions of component \( 1 \) in liquid and vapour phase, respectively. The slope and intercept of the linear plot of \( \frac{1}{x_1} \) vs \( \frac{1}{y_1} \) are given respectively as:

\( 20 \, \text{mL} \) of \( 2 \, \text{M} \) NaOH solution is added to \( 400 \, \text{mL} \) of \( 0.5 \, \text{M} \) NaOH solution. The final concentration of the solution is __________ \( \times 10^{-2} \, \text{M} \). (Nearest integer)

The observed and normal molar masses of compound \( \mathrm{MX_2} \) are \( 65.6 \) and \( 164 \) respectively. The percent degree of ionisation of \( \mathrm{MX_2} \) is __________ \( \% \), (Nearest integer)

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 = \( 1.86 \, \mathrm{K\, kg\, mol^{-1}} \))

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.

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)

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

When \( 1 \, \text{g} \) each of compounds \( \text{AB} \) and \( \text{AB}_2 \) are dissolved in \( 15 \, \text{g} \) of water separately, they increased the boiling point of water by \( 2.7 \, \text{K} \) and \( 1.5 \, \text{K} \) respectively. The atomic mass of \( \text{A} \) (in amu) is __________ \( \times 10^{-1} \) (Nearest integer)
(Given: Molal Boiling  point eevation constant is 0.5 k kg \(mol^{-1}\))

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 \( 0.8 \)?

Solute A associates in water. When \( 0.7 \, \mathrm{g} \) of solute A is dissolved in \( 42.0 \, \mathrm{g} \) of water, it depresses the freezing point by \( 0.2^{\circ}\mathrm{C} \). The percentage association of solute A in water, is:
[Given: Molar mass of A \( = 93 \, \mathrm{g \, mol^{-1}} \). Molal depression constant of water is \( 1.86 \, \mathrm{K \, kg \, mol^{-1}} \).]

Match List-I with List-II.

\( 1.80 \, \text{g} \) of solute A was dissolved in \( 62.5 \, \text{cm}^3 \) of ethanol and freezing point of the solution was found to be \( 155.1 \, \text{K} \). The molar mass of solute A is ____ \( \text{g mol}^{-1} \).
[Given: Freezing point of ethanol is \( 156.0 \, \text{K} \). Density of ethanol is \( 0.80 \, \text{g cm}^{-3} \). Freezing point depression constant of ethanol is \( 2.00 \, \text{K kg mol}^{-1} \)]

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.

The vapour pressure vs. temperature curve for a solution solvent system is shown below:

The boiling point of the solvent is ________ \( ^\circ \text{C} \).

Lead storage battery contains \( 38\% \) by weight solution of \( \mathrm{H_2SO_4} \). The van’t Hoff factor is \( 2.67 \) at this concentration. The temperature in Kelvin at which the solution in the battery will freeze is ______. (Nearest integer). (Given \( K_f = 1.8 \, \mathrm{K\,kg\,mol^{-1}} \))

The vapour pressures of two volatile liquids \( A \) and \( B \) at \( 25^\circ \text{C} \) are \( 50 \, \text{Torr} \) and \( 100 \, \text{Torr} \), respectively. If the liquid mixture contains \( 0.3 \) mole fraction of \( A \), then the mole fraction of liquid \( B \) in the vapour phase is \( \frac{x}{17} \). The value of \( x \) is ______.

Solution of \( 12 \, \text{g} \) of non-electrolyte (A) prepared by dissolving it in \( 1000 \, \text{mL} \) of water exerts then same osmotic pressure as that of \( 0.05 \, \mathrm{M} \) glucose solution at the same temperature. The empirical formula of A is \( \mathrm{CH_2O} \). The molecular mass of A is _____ \( \text{g} \). (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 = \( 273.15 \, \text{K} \)]

A solution is made by mixing one mole of volatile liquid \( A \) with \( 3 \) moles of volatile liquid \( B \). The vapour pressure of pure \( A \) is \( 200 \, \text{mm Hg} \) and that of the solution is \( 500 \, \text{mm Hg} \). The vapour pressure of pure \( B \) and the least volatile component of the solution, respectively, are:

\( \mathrm{CO_2} \) 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 \( 1.67 \times 10^{3} \; \mathrm{bar} \))

\( 20 \, \text{g} \) 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.

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

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

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

The osmotic pressure exerted by a solution prepared by dissolving \( 2.0 \, \text{g} \) of protein of molar mass \( 60 \, \text{kg mol}^{-1} \) in \( 200 \, \text{mL} \) of water at \( 27^\circ \text{C} \) is ________ \( \text{Pa} \). [Integer value] (Use \( R = 0.083 \, \text{L} \, \text{bar} \, \text{mol}^{-1} \, \text{K}^{-1} \))