Solutions — JEE Main PYQs

Solution A is prepared by dissolving 1 g of a protein (molar mass = 50000 g mol$^{-1}$) in 0.5 L of water at 300 K. Its osmotic pressure is $x$ bar. Solution B is made by dissolving 2 g of same protein in 1 L of water at 300 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 L bar mol$^{-1}$ K$^{-1}$)

A non-volatile, non-electrolyte solid solute when dissolved in 40 g of a solvent, the vapour pressure of the solvent decreased from 760 mm Hg to 750 mm Hg. If the same solution boils at 320 K, then the number of moles of the solvent present in the solution is ________. (Nearest integer) [Given: boiling point of the pure solvent = 319.5 K, $K_b$ of the solvent = 0.3 K kg mol$^{-1}$]

At 27 °C, 0.1 M, 1 L $\mathrm{K_4[Fe(CN)_6]}$ aqueous solution and 0.1 M, 1 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?

[Figure: a container divided by a semi-permeable membrane AB; left compartment: 0.1 M, 1 L $\mathrm{K_4[Fe(CN)_6]}$, side 'x'; right compartment: 0.1 M, 1 L $\mathrm{FeCl_3}$, side 'y']

What is the mole fraction of water in 10% by weight (w/w) of aqueous urea solution?

[Given: Molar mass of H, O, C and N are 1, 16, 12 and 14 $\mathrm{g\ mol^{-1}}$ respectively.]

20 g hemoglobin in a 1 L aqueous solution (A) at 300 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 mm higher than the tube dipped in water.

The molar mass of hemoglobin is ________ $\mathrm{kg\ mol^{-1}}$. (Nearest integer)

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

When 0.25 moles of a non-volatile, non-ionizable solute was dissolved in 1 mole of a solvent the vapor pressure of solution was $x$ % of vapor pressure of pure solvent. What is $x$ %?

Given below are two statements :

[Figure: Two chambers separated by a semi-permeable membrane. Chamber 1 contains 18 g glucose in 100 mL aqueous solution; Chamber 2 contains 30 g glucose in 250 mL aqueous solution.]

Statement I : $\mathrm{H_2O}$ molecules move from the chamber 1 to chamber 2.

Statement II : The osmotic pressure of a solution prepared by dissolving 50 mg of potassium sulphate (molar mass = 174 g/mol) in 2 L of water (at 27 °C) is 0.0107 bar. (Given: $R = 0.083\ \mathrm{dm^3\ bar\ K^{-1}\ mol^{-1}}$ and assume complete dissociation of electrolyte)

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

Given below are two statements :

Given : Molar mass of C, H, O, Cl are 12, 1, 16 and 35.5 g mol$^{-1}$, respectively

Statement I : In 30% (w/w) solution of methanol in $\mathrm{CCl_4}$ (at T 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 Raoult's law.

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

Which of the following statements are not correct ?

A. For water, magnitude of $\mathrm{K_b}$ is more than the magnitude of $\mathrm{K_f}$.

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 $\mathrm{C_6H_5{-}C(=O){-}OH \cdots\cdots O{=}C(OH){-}C_6H_5}$

Choose the correct answer from the options given below :

Which of the following graph correctly represents the plots of $K_H$ at 1 bar for gases in water versus temperature?

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 mm Hg and that of the solution is 500 mm Hg. The vapour pressure of pure B and the least volatile component of the solution, respectively, are :

$x$ g of NaCl is added to water in a beaker with a lid. The temperature of the system is raised from 1°C to 25°C. Which out of the following plots, is best suited for the change in the molarity (M) of the solution with respect to temperature ?

[Consider the solubility of NaCl remains unchanged over the temperature range]

When 1 g each of compounds AB and $\mathrm{AB_2}$ are dissolved in 15 g of water separately, they increased the boiling point of water by 2.7 K and 1.5 K respectively. The atomic mass of A (in amu) is __________ $\times 10^{-1}$ (Nearest integer)

(Given : Molal boiling point elevation constant is $0.5\ \mathrm{K\ kg\ mol^{-1}}$)

Which of the following properties will change when system containing solution 1 will become solution 2?

[Figure: a box labelled “10 mol of solute x + 10 L of water” (Solution 1) with an arrow to a box labelled “1 L of solution 1 + 1 mol of solute x + 1 L of water” (Solution 2)]

2 moles each of ethylene glycol and glucose are dissolved in 500 g of water. The boiling point of the resulting solution is:

(Given : Ebullioscopic constant of water $= 0.52~\mathrm{K~kg~mol^{-1}}$)

Given below are two statements :

Statement (I) : Molal depression constant $\mathrm{K}_f$ is given by $\frac{\mathrm{M_1 R T}_f}{\Delta \mathrm{S_{fus}}}$, where symbols have their usual meaning.

Statement (II) : $\mathrm{K}_f$ for benzene is less than the $\mathrm{K}_f$ for water.

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

Sea water, which can be considered as a 6 molar (6 M) solution of NaCl, has a density of $2\ \mathrm{g\ mL^{-1}}$. The concentration of dissolved oxygen $(\mathrm{O_2})$ in sea water is 5.8 ppm. Then the concentration of dissolved oxygen $(\mathrm{O_2})$ in sea water, is $x \times 10^{-4}$ m.

$x =$ _________. (Nearest integer)

Given : Molar mass of NaCl is $58.5\ \mathrm{g\ mol^{-1}}$

Molar mass of $\mathrm{O_2}$ is $32\ \mathrm{g\ mol^{-1}}$

The percentage dissociation of a salt ($\mathrm{MX_3}$) solution at given temperature (van't Hoff factor i = 2) is ___________ %(Nearest integer)

Match List - I with List - II.

List - I	List - II
(A) Solution of chloroform and acetone	(I) Minimum boiling azeotrope
(B) Solution of ethanol and water	(II) Dimerizes
(C) Solution of benzene and toluene	(III) Maximum boiling azeotrope
(D) Solution of acetic acid in benzene	(IV) $\Delta \mathrm{V_{mix}} = 0$

Choose the correct answer from the options given below :

Liquid A and B form an ideal solution. The vapour pressures 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,

Which of the following binary mixture does not show the behaviour of minimum boiling azeotropes?

$$\mathrm{HA}(aq) \rightleftharpoons \mathrm{H^+}(aq) + \mathrm{A^-}(aq)$$

The freezing point depression of a 0.1 m aqueous solution of a monobasic weak acid HA is 0.20 °C. The dissociation constant for the acid is

Given : $K_f(\mathrm{H_2O}) = 1.8\ \mathrm{K\ kg\ mol^{-1}}$, molality = molarity

Arrange the following solutions in order of their increasing boiling points.

(i) $10^{-4}$ M NaCl (ii) $10^{-4}$ M Urea (iii) $10^{-3}$ M NaCl (iv) $10^{-2}$ M NaCl

Density of $3$ M NaCl solution is $1.25\ \mathrm{g/mL}$. The molality of the solution is :

$\mathrm{CrCl_3.xNH_3}$ can exist as a complex. 0.1 molal aqueous solution of this complex shows a depression in freezing point of $0.558°\mathrm{C}$. Assuming 100% ionisation of this complex and coordination number of Cr is 6, the complex will be

(Given $\mathrm{K_f} = 1.86$ K kg mol$^{-1}$)

When a non-volatile solute is added to the solvent, the vapour pressure of the solvent decreases by 10 mm of Hg. The mole fraction of the solute in the solution is 0.2. What would be the mole fraction of the solvent if decrease in vapour pressure is 20 mm of Hg ?

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 $\dfrac{1}{x_1}$ vs $\dfrac{1}{y_1}$ are given respectively as :

Consider the given plots of vapour pressure (VP) vs temperature (T/K). Which amongst the following options is correct graphical representation showing $\Delta T_f$, depression in the freezing point of a solvent in a solution?

The observed and normal molar masses of compound $\mathrm{MX_2}$ are respectively 65.6 and 164. The percentage degree of ionization of $\mathrm{MX_2}$ is _______ % (nearest integer).

What is the freezing point depression constant of a solvent, 50 g of which contain 1 g non volatile solute (molar mass 256 g mol$^{-1}$) and the decrease in freezing point is 0.40 K ?

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 :

2.5 g of a non-volatile, non-electrolyte is dissolved in 100 g of water at 25°C. The solution showed a boiling point elevation by 2°C. Assuming the solute concentration is negligible with respect to the solvent concentration, the vapor pressure of the resulting aqueous solution is ________ mm of Hg (nearest integer)

[Given : Molal boiling point elevation constant of water ($K_b$) = 0.52 K. kg mol$^{-1}$, 1 atm pressure = 760 mm of Hg, molar mass of water = 18 g mol$^{-1}$]

2.7 kg of each of water and acetic acid are mixed. The freezing point of the solution will be $-x\ {}^\circ\mathrm{C}$. Consider the acetic acid does not dimerise in water, nor dissociates in water. $x =$ ________ (nearest integer)

[Given: Molar mass of water = $18\ \mathrm{g\ mol^{-1}}$, acetic acid = $60\ \mathrm{g\ mol^{-1}}$

$\mathrm{K_f}$ $\mathrm{H_2O}$ : $1.86\ \mathrm{K\ kg\ mol^{-1}}$

$\mathrm{K_f}$ acetic acid : $3.90\ \mathrm{K\ kg\ mol^{-1}}$

freezing point : $\mathrm{H_2O} = 273$ K, acetic acid $= 290$ K]

An artificial cell is made by encapsulating 0.2 M glucose solution within a semipermeable membrane. The osmotic pressure developed when the artificial cell is placed within a 0.05 M solution of NaCl at 300 K is ________ $\times~10^{-1}$ bar. (nearest integer).

[Given : $\mathrm{R} = 0.083~\mathrm{L~bar~mol^{-1}~K^{-1}}$]

Assume complete dissociation of NaCl

Considering acetic acid dissociates in water, its dissociation constant is $6.25 \times 10^{-5}$. If 5 mL of acetic acid is dissolved in 1 litre water, the solution will freeze at $-x \times 10^{-2}\,°\mathrm{C}$, provided pure water freezes at $0\,°\mathrm{C}$.

$x =$ ________. (Nearest integer)

Given : $(\mathrm{K}_f)_{\text{water}} = 1.86 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}$.

density of acetic acid is $1.2 \mathrm{~g} \mathrm{~mol}^{-1}$.

molar mass of water $= 18 \mathrm{~g} \mathrm{~mol}^{-1}$.

molar mass of acetic acid $= 60 \mathrm{~g} \mathrm{~mol}^{-1}$.

density of water $= 1 \mathrm{~g} \mathrm{~cm}^{-3}$

Acetic acid dissociates as $\mathrm{CH_3COOH \rightleftharpoons CH_3COO^{\ominus} + H^{\oplus}}$

The density of '$x$' M solution ('$x$' molar) of NaOH is $1.12 \mathrm{~g~mL^{-1}}$, while in molality, the concentration of the solution is $3 \mathrm{~m}$ (3 molal). Then $x$ is

(Given : Molar mass of NaOH is $40 \mathrm{~g/mol}$)

Consider the dissociation of the weak acid HX as given below

$\mathrm{HX(aq) \rightleftharpoons H^+(aq) + X^-(aq)}$, $\mathrm{K_a} = 1.2 \times 10^{-5}$

[$\mathrm{K_a}$ : dissociation constant]

The osmotic pressure of 0.03 M aqueous solution of HX at 300 K is _________ $\times 10^{-2}$ bar (nearest integer).

[Given : $\mathrm{R} = 0.083 \mathrm{~L~bar~mol^{-1}~K^{-1}}$]

Molality (m) of 3 M aqueous solution of NaCl is : (Given : Density of solution $= 1.25\ \mathrm{g\ mL^{-1}}$, Molar mass in $\mathrm{g\ mol^{-1}}$ : Na-23, Cl-35.5)

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

[Figure: vapour pressure vs temperature graph showing curves for the frozen system, water and methanolic solution; the water curve meets the frozen-system curve at 273.15 K and the methanolic solution curve at 270.65 K]

$x =$ ________ (nearest integer).

[Given : Molal freezing point depression constant of water at 273.15 K is $1.86\ \mathrm{K\ kg\ mol^{-1}}$]

A solution containing 10 g of an electrolyte $\mathrm{AB_2}$ in 100 g of water boils at 100.52°C. The degree of ionization of the electrolyte ($\alpha$) is _________ $\times 10^{-1}$. (nearest integer)

[Given : Molar mass of $\mathrm{AB_2}$ = 200 $\mathrm{g\ mol^{-1}}$, $K_b$ (molal boiling point elevation const. of water) = 0.52 $\mathrm{K\ kg\ mol^{-1}}$, boiling point of water = 100°C ; $\mathrm{AB_2}$ ionises as $\mathrm{AB_2 \rightarrow A^{2+} + 2B^-}$]

Molality of an aqueous solution of urea is 4.44 m. Mole fraction of urea in solution is $x \times 10^{-3}$. Value of $x$ is ________. (Integer answer)

0.05M $\mathrm{CuSO_4}$ when treated with 0.01M $\mathrm{K_2Cr_2O_7}$ gives green colour solution of $\mathrm{Cu_2Cr_2O_7}$. The two solutions are separated as shown below : [SPM : Semi Permeable Membrane]

[Figure: two compartments separated by a semi permeable membrane; Side X contains $\mathrm{K_2Cr_2O_7}$ solution, Side Y contains $\mathrm{CuSO_4}$ solution]

Due to osmosis :

Molarity (M) of an aqueous solution containing $x$ g of anhyd. $\mathrm{CuSO_4}$ in 500 mL solution at 32 °C is $2 \times 10^{-1}$ M. Its molality will be ________ $\times 10^{-3}$ m. (nearest integer). [Given density of the solution = 1.25 g/mL]

The vapor pressure of pure benzene and methyl benzene at $27^{\circ}\mathrm{C}$ is given as 80 Torr and 24 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)

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

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

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

The osmotic pressure of a dilute solution is $7 \times 10^5\,\mathrm{Pa}$ at 273K. Osmotic pressure of the same solution at 283K is ________ $\times 10^4\,\mathrm{Nm^{-2}}$.

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

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

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