Abnormal Molecular Mass and Distribution Law

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JEE Advanced 2026

LEVELJEE Advanced

In a solvent S, a compound B is partially dissociated into C and D as given below : B $⇌$ 2C + 2D B, C and D are non-volatile in nature. The molar mass of B is 10 times the molar mass of S. The standard boiling point and the standard enthalpy of vaporization of S are 400 K and $10 R J mol^{- 1}$ , respectively ( $R$ is the gas constant in $J K^{- 1} mol^{- 1}$ ). A solution of B in S with an intial concentration of B as 0.25% (mass/mass) has a boiling point of 408 K at 1 bar pressure. In this solution, the mole percent of B that has been dissociated is _____.

JEE Advanced 2014

LEVELJEE Main

$MX_{2}$ dissociates into $M^{2 +}$ and $X^{-}$ ions in an aqueous solution, with a degree of dissociation ( $α$ ) of $0.5$ . The ratio of the observed depression of freezing point of the aqueous solution to the value of the depression of freezing point in the absence of ionic dissociation is

JEE Main 2021

LEVELJEE Main

When $12.2 g$ of benzoic acid is dissolved in $100 g$ of water, the freezing point of solution was found to be $- 0.9 3^{\circ} C$ ( $K_{f} (H_{2} O) = 1.86 K kg mol^{- 1}$ ). The number ( $n$ ) of benzoic acid molecules associated (assuming 100% association) is ……… .

JEE Main 2019

LEVELJEE Main

The osmotic pressure of a dilute solution of an ionic compound $X Y$ in water is four times that of a solution of $0.01 M BaCl_{2}$ in water. Assuming complete dissociation of the given ionic compounds in water, the concentration of $X Y$ (in $mol L^{- 1}$ ) in solution is

(A)

4 \times 1 0^{- 2}

(B)

16 \times 1 0^{- 4}

(C)

4 \times 1 0^{- 4}

(D)

6 \times 1 0^{- 2}

JEE Main 2019

LEVELJEE Advanced

Molecules of benzoic acid ( $C_{6} H_{5} COOH$ ) dimerise in benzene. ' $w$ ' g of the acid dissolved in $30 g$ of benzene shows a depression in freezing point equal to $2 K$ . If the percentage association of the acid to form dimer in the solution is $80$ , then $w$ is (Given that $K_{f} = 5 K kg mol^{- 1}$ , molar mass of benzoic acid $= 122 g mol^{- 1}$ )

1.22 g of an organic acid is separately dissolved in 100 g of benzene ( $K_{b} = 2.6 K kg mol^{- 1}$ ) and 100 g of acetone ( $K_{b} = 1.7 K kg mol^{- 1}$ ). The acid is known to dimerise in benzene but remain as a monomer in acetone. The boiling point of the solution in acetone increases by $0.1 7^{\circ} C$ . The increase in boiling point of solution in benzene in $^{\circ} C$ is $x \times 1 0^{- 2}$ . The value of $x$ is ........ (Nearest integer) [Atomic mass : C = 12.0, H = 1.0, O= 16.0]

JEE Main 2020

LEVELJEE Advanced

The elevation of boiling point of $0.10 m$ aqueous $CrCl_{3} \cdot x NH_{3}$ solution is two times that of $0.05 m$ aqueous $CaCl_{2}$ solution. The value of $x$ is ....... . [Assume 100% ionisation of the complex and $CaCl_{2}$ , coordination number of Cr as 6, and that all $NH_{3}$ molecules are present inside the coordination sphere]

LEVELJEE Main

The degree of dissociation ( $α$ ) of a weak electrolyte, $A_{x} B_{y}$ is related to van't Hoff factor ( $i$ ) by the expression

(A)

α = \frac{i - 1}{( x + y - 1 )}

(B)

α = \frac{i - 1}{x + y + 1}

(C)

α = \frac{x + y - 1}{i - 1}

(D)

α = \frac{x + y + 1}{i - 1}

JEE Main 2017

LEVELJEE Advanced

The freezing point of benzene decreases by $0.4 5^{\circ} C$ when $0.2 g$ of acetic acid is added to $20 g$ of benzene. If acetic acid associates to form a dimer in benzene, percentage association of acetic acid in benzene will be ( $K_{f}$ for benzene = $5.12 K kg mol^{- 1}$ )

For 1 molal aqueous solution of the following compounds, which one will show the highest freezing point?

(A)

[C o (H_{2} O)_{6}] C l_{3}

(B)

[C o (H_{2} O)_{5} C l] C l_{2} \cdot H_{2} O

(C)

[C o (H_{2} O)_{4} C l_{2}] C l \cdot 2 H_{2} O

(D)

[C o (H_{2} O)_{3} C l_{3}] \cdot 3 H_{2} O

JEE Main 2021

LEVELJEE Advanced

2 molal solution of a weak acid HA has a freezing point of $3.88 5^{\circ} C$ . The degree of dissociation of this acid is ......... $\times 1 0^{- 3}$ . (Round off to the nearest integer). [Given : Molal depression constant of water = $1.85 K kg mol^{- 1}$ , freezing point of pure water = $0^{\circ} C$ ]

JEE Main 2021

LEVELJEE Main

Which one of the following $0.10 M$ aqueous solutions will exhibit the largest freezing point depression?

KHSO_{4}

JEE Main 2019

LEVELJEE Main

$K_{2} H g I_{4}$ is $40%$ ionised in aqueous solution. The value of its van't Hoff factor ( $i$ ) is

(A)

1.6

(B)

1.8

(C)

2.2

(D)

2.0

LEVELJEE Main

If $α$ is the degree of dissociation of $Na_{2} SO_{4}$ , the van't Hoff factor ( $i$ ) used for calculating the molecular mass is

(A)

1 - 2 α

(B)

1 + 2 α

(C)

1 - α

(D)

1 + α

LEVELJEE Main

In a $0.2$ molal aqueous solution of a weak acid $HX$ , the degree of ionisation is $0.3$ . Taking $K_{f}$ for water as $1.85$ , the freezing point of the solution will be nearest to

(A)

- 0.48 0^{\circ} C

(B)

- 0.36 0^{\circ} C

(C)

- 0.26 0^{\circ} C

(D)

+ 0.48 0^{\circ} C

JEE Main 2021

LEVELJEE Main

1 molal aqueous solution of an electrolyte $A_{2} B_{3}$ is 60% ionised. The boiling point of the solution at 1 atm is ………… K (Rounded off to the nearest integer). [Given, $K_{b}$ for $(H_{2} O) = 0.52 K kg mol^{- 1}$ ]

JEE Main 2021

LEVELJEE Advanced

A 1 molal $K_{4} F e (C N)_{6}$ solution has a degree of dissociation of 0.4. Its boiling point is equal to that of another solution which contains 18.1 weight per cent of a non-electrolytic solute A. The molar mass of A is ....... u. (Round off to the nearest integer). [Density of water = $1.0 g cm^{- 3}$ ]

JEE Main 2021

LEVELJEE Main

If a compound $A B$ dissociates to the extent of $75%$ in an aqueous solution, the molality of the solution which shows a $2.5 K$ rise in the boiling point of the solution is ......... molal. (Rounded off to the nearest integer) [ $K_{b} = 0.52 K kg mol^{- 1}$ ]

JEE Main 2014

LEVELJEE Main

Consider the separate solution of $0.500 M$ $C_{2} H_{5} OH (aq)$ , $0.100 M$ $Mg_{3} (PO_{4})_{2} (aq)$ , $0.250 M$ $KBr (aq)$ and $0.125 M$ $Na_{3} PO_{4} (aq)$ at $2 5^{\circ} C$ . Which statement is true about these solutions, assuming all salts to be strong electrolytes?

(A)

They all have same osmotic pressure

(B)

0.100 M

Mg_{3} (PO_{4})_{2} (aq)

has the highest osmotic pressure

(C)

0.125 M

Na_{3} PO_{4} (aq)

has the highest osmotic pressure

(D)

0.5000 M

C_{2} H_{5} OH (aq)

has the highest osmotic pressure

JEE Main 2021

LEVELJEE Advanced

In a solvent 50% of an acid HA dimerises and the rest dissociates. The van't Hoff factor of the acid is ………… $\times 1 0^{- 2}$ . (Round off to the nearest integer)

JEE Main 2021

LEVELJEE Main

A solute A dimerises in water. The boiling point of a 2 molar solution of A is $100.5 2^{\circ} C$ . The percentage association of A is ......... . (Round off to the nearest integer) [Use : $K_{b}$ for water $= 0.52 K kg mol^{- 1}$ , boiling point of water $= 10 0^{\circ} C$ ]

JEE Main 2021

LEVELJEE Main

Of the following four aqueous solutions, total number of those solutions whose freezing point is lower than that of $0.10 M C_{2} H_{5} OH$ is ………… . (Integer answer) (i) $0.10 M Ba_{3} (PO_{4})_{2}$ (ii) $0.10 M Na_{2} SO_{4}$ (iii) $0.10 M KCl$ (iv) $0.10 M Li_{3} PO_{4}$

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The degree of dissociation (α) of a weak electrolyte, Ax​By​ is related to van't Hoff factor (i) by the expression

For 1 molal aqueous solution of the following compounds, which one will show the highest freezing point?

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Which one of the following 0.10 M aqueous solutions will exhibit the largest freezing point depression?

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } K2​HgI4​ is 40% ionised in aqueous solution. The value of its van't Hoff factor (i) is

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } If α is the degree of dissociation of Na2​SO4​, the van't Hoff factor (i) used for calculating the molecular mass is

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } In a 0.2 molal aqueous solution of a weak acid HX, the degree of ionisation is 0.3. Taking Kf​ for water as 1.85, the freezing point of the solution will be nearest to

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } In a solvent 50% of an acid HA dimerises and the rest dissociates. The van't Hoff factor of the acid is ………… ×10−2. (Round off to the nearest integer)

The degree of dissociation ( $α$ ) of a weak electrolyte, $A_{x} B_{y}$ is related to van't Hoff factor ( $i$ ) by the expression

Which one of the following $0.10 M$ aqueous solutions will exhibit the largest freezing point depression?

$K_{2} H g I_{4}$ is $40%$ ionised in aqueous solution. The value of its van't Hoff factor ( $i$ ) is

If $α$ is the degree of dissociation of $Na_{2} SO_{4}$ , the van't Hoff factor ( $i$ ) used for calculating the molecular mass is

In a $0.2$ molal aqueous solution of a weak acid $HX$ , the degree of ionisation is $0.3$ . Taking $K_{f}$ for water as $1.85$ , the freezing point of the solution will be nearest to

In a solvent 50% of an acid HA dimerises and the rest dissociates. The van't Hoff factor of the acid is ………… $\times 1 0^{- 2}$ . (Round off to the nearest integer)