Colligative Properties

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JEE Advanced 2025

LEVELJEE Advanced

At 300 K, an ideal dilute solution of a macromolecule exerts osmotic pressure that is expressed in terms of the height (h) of the solution (density = $1.00 g cm^{- 3}$ ) where h is equal to $2.00 cm$ . If the concentration of the dilute solution of the macromolecule is $2.00 g dm^{- 3}$ , the molar mass of the macromolecule is calculated to be $X \times 1 0^{4} g mol^{- 1}$ . The value of $X$ is ______. Use : Universal gas constant (R) = $8.3 J K^{- 1} mol^{- 1}$ and acceleration due to gravity (g) = $10 m s^{- 2}$

JEE Advanced 2017

LEVELJEE Advanced

Pure water freezes at 273 K and 1 bar. The addition of 34.5 g of ethanol to 500 g of water changes the freezing point of the solution. Use the freezing point depression constant of water as $2 K kg mol^{- 1}$ . The figures shown below represents plots of vapour pressure (V.P.) versus temperature (T). [Molecular weight of ethanol is $46 g mol^{- 1}$ ] Among the following, the option representing change in the freezing point is -

If the freezing point of a $0.01$ molal aqueous solution of a cobalt(III) chloride-ammonia complex (which behaves as a strong electrolyte) is $- 0.055 8^{\circ} C$ , the number of chloride(s) in the coordination sphere of the complex is [ $K_{f}$ of water = $1.86 K kg mol^{- 1}$ ]

JEE Advanced 2019

LEVELJEE Advanced

On dissolving 0.5 g of a non-volatile non-ionic solute to 39 g of benzene, its vapor pressure decreases from 650 mm Hg to 640 mm Hg. The depression of freezing point of benzene (in K) upon addition of the solute is _______. (Given data : Molar mass and the molal freezing point depression constant of benzene are $78 g mol^{- 1}$ and $5.12 K kg mol^{- 1}$ , respectively)

JEE Advanced 2021

LEVELJEE Advanced

Comprehension Passage

The boiling point of water in a

0.1

molal silver nitrate solution (solution A) is

x^{\circ} C

. To this solution A, an equal volume of

0.1

molal aqueous barium chloride solution is added to make a new solution B. The difference in the boiling points of water in the two solutions A and B is

y \times 1 0^{- 2}^{\circ} C

. (Assume : Densities of the solutions A and B are the same as that of water and the soluble salts dissociate completely.) Use: Molal elevation constant (Ebullioscopic Constant),

K_{b} = 0.5 K kg mol^{- 1}

; Boiling point of pure water as

10 0^{\circ} C

Question 1:

The value of $x$ is _______.

Question 2:

The value of $∣ y ∣$ is _______.

JEE Advanced 2018

LEVELJEE Advanced

The plot given below shows P–T curves (where P is the pressure and T is the temperature) for two solvents X and Y and isomolal solutions of NaCl in these solvents. NaCl completely dissociates in both the solvents. On addition of equal number of moles a non-volatile solute S in equal amount (in kg) of these solvents, the elevation of boiling point of solvent X is three times that of solvent Y. Solute S is known to undergo dimerization in these solvents. If the degree of dimerization is 0.7 in solvent Y, the degree of dimerization in solvent X is ___.

JEE Advanced 2023

LEVELJEE Advanced

50 mL of 0.2 molal urea solution (density = $1.012 g mL^{- 1}$ at 300 K) is mixed with 250 mL of a solution containing 0.06 g of urea. Both the solutions were prepared in the same solvent. The osmotic pressure (in Torr) of the resulting solution at 300 K is ________. [JEE(Advanced) 2023] [Use : Molar mass of urea = $60 g mol^{- 1}$ ; gas constant, $R = 62 L Torr K^{- 1} mol^{- 1}$ ; Assume, $Δ_{mix} H = 0$ , $Δ_{mix} V = 0$ ]

JEE Advanced 2022

LEVELJEE Advanced

An aqueous solution is prepared by dissolving $0.1 mol$ of an ionic salt in $1.8 kg$ of water at $3 5^{\circ} C$ . The salt remains $90%$ dissociated in the solution. The vapour pressure of the solution is $59.724 mm of Hg$ . Vapor pressure of water at $3 5^{\circ} C$ is $60.000 mm of Hg$ . The number of ions present per formula unit of the ionic salt is ________.

JEE Main 2020

LEVELJEE Advanced

The osmotic pressure of a solution of NaCl is $0.10 atm$ and that of a glucose solution is $0.20 atm$ . The osmotic pressure of a solution formed by mixing $1 L$ of the sodium chloride solution with $2 L$ of the glucose solution is $x \times 1 0^{- 3} atm$ . $x$ is ......... (nearest integer).

JEE Main 2020

LEVELJEE Main

How much amount of NaCl should be added to 600 g of water ( $ρ = 1.00 g/mL$ ) to decrease the freezing point of water to $- 0. 2^{\circ} C$ ? ...... (The freezing point depression constant for water $= 2 K kg mol^{- 1}$ )

LEVELJEE Main

Which one of the following aqueous solutions will exhibit highest boiling point?

(A)

0.01 M

N a_{2} S O_{4}

(B)

0.01 M

K N O_{3}

Freezing point of a $4%$ aqueous solution of $X$ is equal to freezing point of $12%$ aqueous solution of $Y$ . If molecular weight of $X$ is $A$ , then molecular weight of $Y$ is

(A)

4 A

(B)

2 A

(C)

3 A

(D)

A

JEE Main 2021

LEVELJEE Main

When $3.00 g$ of a substance 'X' is dissolved in $100 g$ of $CCl_{4}$ , it raises the boiling point by $0.60 K$ . The molar mass of the substance 'X' is ......... $g mol^{- 1}$ . (Nearest integer) [Given, $K_{b}$ for $CCl_{4}$ is $5.0 K kg mol^{- 1}$ ]

JEE Main 2019

LEVELJEE Main

The freezing point of a diluted milk sample is found to be $- 0. 2^{\circ} C$ , while it should have been $- 0. 5^{\circ} C$ for pure milk. How much water has been added to pure milk to make the diluted sample?

(A)

2 cups of water to 3 cups of pure milk

(B)

1 cup of water to 3 cups of pure milk

(C)

3 cups of water to 2 cups of pure milk

(D)

1 cup of water to 2 cups of pure milk

JEE Main 2019

LEVELJEE Main

Molal depression constant for a solvent is $4.0 K kg mol^{- 1}$ . The depression in the freezing point of the solvent for $0.03 mol kg^{- 1}$ solution of $K_{2} SO_{4}$ is (Assume complete dissociation of the electrolyte)

(A)

0.18 K

(B)

0.36 K

(C)

0.12 K

(D)

0.24 K

JEE Main 2021

LEVELJEE Main

1.46 g of a biopolymer dissolved in a 100 mL water at 300 K exerted an osmotic pressure of $2.42 \times 1 0^{- 3}$ bar. The molar mass of the biopolymer is ......... $\times 1 0^{4} g mol^{- 1}$ . (Round off to the nearest integer) [Use : $R = 0.083 L bar mol^{- 1} K^{- 1}$ ]

JEE Main 2020

LEVELJEE Advanced

A cylinder containing an ideal gas ( $0.1 mol$ of $1.0 dm^{3}$ ) is in thermal equilibrium with a large volume of $0.5 molal$ aqueous solution of ethylene glycol at its freezing point. If the stoppers $S_{1}$ and $S_{2}$ (as shown in the figure) are suddenly withdrawn, the volume of the gas in litres after equilibrium is achieved will be ……… (Given, $K_{f} (water) = 2.0 K kg mol^{- 1}$ , $R = 0.08 dm^{3} atm K^{- 1} mol^{- 1}$ )

JEE Main 2020

LEVELJEE Main

The size of a raw mango shrinks to a much smaller size when kept in a concentrated salt solution. Which one of the following processes can explain this?

The vapour pressure of water at $2 0^{\circ} C$ is $17.5 mmHg$ . If $18 g$ of glucose ( $C_{6} H_{12} O_{6}$ ) is added to $178.2 g$ of water at $2 0^{\circ} C$ , the vapour pressure of the resulting solution will be

(A)

17.675 mmHg

(B)

15.750 mmHg

(C)

16.500 mmHg

(D)

17.325 mmHg

JEE Main 2015

LEVELJEE Main

The vapour pressure of acetone at $2 0^{\circ} C$ is $185 torr$ . When $1.2 g$ of a non-volatile substance was dissolved in $100 g$ of acetone at $2 0^{\circ} C$ , its vapour pressure was $183 torr$ . The molar mass ( $g mol^{- 1}$ ) of the substance is

1 g of a non-volatile, non-electrolyte solute is dissolved in 100 g of two different solvents A and B, whose ebullisocopic constants are in the ratio of 1 : 5. The ratio of the elevation in their boiling points, $\frac{Δ T _{b} ( A )}{Δ T _{b} ( B )}$ , is

(A)

5 : 1

(B)

10 : 1

(C)

1 : 5

(D)

1 : 0.2

LEVELJEE Main

If sodium sulphate is considered to be completely dissociated into cations and anions in aqueous solution, the change in freezing point of water ( $Δ T_{f}$ ), when $0.01$ mole of sodium sulphate is dissolved in $1 kg$ of water, is ( $K_{f} = 1.86 K kg mol^{- 1}$ )

(A)

0.0372 K

(B)

0.0558 K

(C)

0.0744 K

(D)

0.0186 K

JEE Main 2019

LEVELJEE Main

Elevation in the boiling point for $1$ molal solution of glucose is $2 K$ . The depression in the freezing point for $2$ molal solution of glucose in the same solvent is $2 K$ . The relation between $K_{b}$ and $K_{f}$ is

(A)

K_{b} = 1.5 K_{f}

(B)

K_{b} = 0.5 K_{f}

(C)

K_{b} = K_{f}

(D)

K_{b} = 2 K_{f}

LEVELJEE Main

Which one of the following statements is false?

(A)

Raoult's law states that the vapour pressure of a component over a solution is proportional to its mole fraction

(B)

The osmotic pressure (

π

) of a solution is given by the equation

π = M R T

, where

M

is the molarity of the solution

(C)

The correct order of osmotic pressure for

0.01 M

aqueous solution of each compound is

BaCl_{2} > KCl > CH_{3} COOH > sucrose

(D)

Two sucrose solutions of same molality prepared in different solvents will have the same freezing point depression

JEE Main 2021

LEVELJEE Main

Which one of the following 0.06 M aqueous solutions has lowest freezing point? [2021, 22 July Shift-II]

(A)

Al_{2} (SO_{4})_{3}

(B)

C_{6} H_{12} O_{6}

(C)

KI

(D)

K_{2} SO_{4}

Comprehension Passage

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The value of x is _______.

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The value of ∣y∣ is _______.

Which one of the following aqueous solutions will exhibit highest boiling point?

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Freezing point of a 4% aqueous solution of X is equal to freezing point of 12% aqueous solution of Y. If molecular weight of X is A, then molecular weight of Y is

The size of a raw mango shrinks to a much smaller size when kept in a concentrated salt solution. Which one of the following processes can explain this?

Which one of the following statements is false?

Which one of the following 0.06 M aqueous solutions has lowest freezing point? [2021, 22 July Shift-II]

The value of $x$ is _______.

The value of $∣ y ∣$ is _______.

Freezing point of a $4%$ aqueous solution of $X$ is equal to freezing point of $12%$ aqueous solution of $Y$ . If molecular weight of $X$ is $A$ , then molecular weight of $Y$ is