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Q 1 :

We have three aqueous solutions of 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: [2024]

$i_{A} < i_{B} < i_{C}$
$i_{A} < i_{C} < i_{B}$
$i_{A} = i_{B} = i_{C}$
$i_{A} > i_{B} > i_{C}$

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(1)

Van't Hoff factor (i) is given by:

$i = \frac{Number of particles after dissociation}{Number of particles before dissociation}$

With dilution, degree of dissociation increases hence $i$ increases with dilution. Hence $i$ for A (0.1M NaCl), B (0.01M NaCl) and C (0.001M NaCl) is: $i_{A} < i_{B} < i_{C}$

Q 2 :

A solution containing 10 g of an electrolyte ${AB}_{2}$ in 100 g of water boils at 100.52 ${}^{°}C$ . The degree of ionization of the electrolyte ( $α$ ) is _____ $\times 10^{- 1}$ . (nearest integer)

[Given : Molar mass of ${AB}_{2} = 200 g$ ${mol}^{- 1}$ . $K_{b}$ (molal boiling point elevation const. of water) = 0.52 K kg ${mol}^{- 1}$ , boiling point of water = 100°C; ${AB}_{2}$ ionises as ${AB}_{2} \to A^{2 +} + 2 B^{-}$ ] [2024]

(5)

$Δ T_{b} = T_{b} - T_{b}^{°} = (100.52 - 100) K = 0.52 K$

$i m k_{b} = 0.52 K$

$i \frac{w_{solute} \times 1000}{M_{solute} \times W_{solvent} (in g)} k_{b} = 0.52 K$

$i \frac{10 \times 1000}{200 \times 100} \times 0.52 = 0.52$

$i = 2$

${AB}_{2} ⇌ A^{2 +} + 2 B^{-}$

$i = 1 + (n - 1) α$

$2 = 1 + (3 - 1) α$

$α = 0.5 = 5 \times 10^{- 1}$

Q 3 :

Arrange the following solutions in order of their increasing boiling points. [2025]

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

(ii) < (i) ≡ (iii) < (iv)
(iv) < (iii) < (i) < (ii)
(ii) < (i) < (iii) < (iv)
(i) < (ii) < (iii) < (iv)

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(3)

$NaCl \to {Na}^{+} + {Cl}^{-}$

$i = 2$

Urea is non-electrolyte so, $i = 1$ .

Elevation in boiling point $Δ T_{b} = i k_{b} m .$ So higher is concentration and more is $i$ , more will be the boiling point.

Q 4 :

${CrCl}_{3} \cdot {xNH}_{3}$ can exist as a complex. 0.1 molal aqueous solution of this complex shows a depression in freezing point of 0.558 ${}^{o}C$ . Assuming 100% ionisation of this complex and coordination number of Cr is 6, the complex will be

(Given $K_{f}$ = 1.86 K kg ${mol}^{- 1}$ ) [2025]

$[Cr {({NH}_{3})}_{5} Cl] {Cl}_{2}$
$[Cr {({NH}_{3})}_{6}] {Cl}_{3}$
$[Cr {({NH}_{3})}_{3} {Cl}_{3}]$
$[Cr {({NH}_{3})}_{4} {Cl}_{2}] Cl$

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(1)

$Δ T_{f} = i k_{f} m$

$0.558 = i \times 1.86 \times 0.1$

$i = 3$

$[Cr {({NH}_{3})}_{5} Cl] {Cl}_{2} \to {[Cr {({NH}_{3})}_{5} Cl]}^{2 +} + 2 {Cl}^{-},$ $n = 3$

Q 5 :

1.24 g of $A X_{2}$ (molar mass 124 g ${mol}^{- 1}$ ) is dissolved in 1 kg of water to form a solution with boiling point of 100.0156°C, while 25.4 g of $A Y_{2}$ (molar mass 250 g ${mol}^{- 1}$ ) in 2 kg of water constitutes a solution with a boiling point of 100.0260°C.

$K_{b} (H_{2} O) = {0.52 K kg mol}^{- 1}$

Which of the following is correct? [2025]

${AX}_{2}$ and $A Y_{2}$ (both) are completely unionised.
${AX}_{2}$ is fully ionised while $A Y_{2}$ is completely unionised.
${AX}_{2}$ and $A Y_{2}$ (both) are fully ionised.
${AX}_{2}$ is completely unionised while $A Y_{2}$ is fully ionised.

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(2)

$Moles of A X_{2} (n_{A X_{2}}) = \frac{W_{A X_{2}}}{M_{A X_{2}}} = \frac{1.24}{124} mol = 0.01 mol$

$Molality of A X_{2} solution (m_{A X_{2}}) = \frac{n_{A X_{2}}}{W_{water (in kg)}} = \frac{0.01 mol}{1 kg} = 0.01 m$

$Elevation in boiling point of A X_{2} solution (Δ T_{b} (A X_{2})) = (100.0156 - 100) ° C = i_{A X_{2}} m_{A X_{2}} k_{b}$

$0.0156 = i_{A X_{2}} \times 0.01 \times 0.52$

$i_{A X_{2}} = \frac{0.0156}{0.01 \times 0.52} = 3$

So, $A X_{2}$ is completely ionized.

$Moles of A Y_{2} (n_{A Y_{2}}) = \frac{W_{A Y_{2}}}{M_{A Y_{2}}} = \frac{25.4}{250} mol = 0.1016 mol$

$Molality of A Y_{2} solution (m_{A Y_{2}}) = \frac{n_{A Y_{2}}}{W_{water (in kg)}} = \frac{0.1016 mol}{2 kg} = 0.0508 m$

$Elevation in boiling point of A Y_{2} solution (Δ T_{b} (A Y_{2})) = (100.026 - 100) ° C = i_{A Y_{2}} m_{A Y_{2}} k_{b}$

$0.026 = i_{A Y_{2}} \times 0.0508 \times 0.52$

$i_{A Y_{2}} = \frac{0.026}{0.0508 \times 0.52} \approx 1$

So, $A Y_{2}$ is completely unionized.

Q 6 :

The observed and normal molar masses of compound ${MX}_{2}$ are 65.6 and 164 respectively. The percent degree of ionisation of ${MX}_{2}$ is _____ %. (Neatest integer) [2025]

(75)

$i = \frac{normal molar mass}{observed molar mass} = \frac{164}{65.6} = 2.5$

$MX ⇌ M^{2 +} + 2 X^{-}$

Moles in which one mole of $M X_{2}$ dissociates $(n) = 3$

$1 + (n - 1) α$ = 2.5

$1 + (3 - 1) α$ = 2.5

$α$ = 0.75 = 75%

Q 7 :

If $A_{2} B$ is 30% ionised in an aqueous solution, then the value of van’t Hoff factor $(i)$ is _____ $\times 10^{- 1}$ . [2025]

(16)

$A_{2} B ⇌ 2 A^{+} + B^{2 -}$

$i = 1 + (n - 1) α$

One molecule of $A_{2} B$ dissociates into three particles, so $n$ = 3.

$α$ = 0.3 as per question.

$i = 1 + (3 - 1) \times 0.3$

$i = 1.6 = 16 \times 10^{- 1}$

Q 8 :

The percentage dissociation of a salt ( ${MX}_{3}$ ) solution at given temperature (van’t Hoff factor $i$ = 2) is ................. % (Nearest integer) [2025]

(33)

${MX}_{3} \to M^{3 +} + 3 X^{-}$

Van’t Hoff factor $(i)$ is related to degree of dissociation $(α)$ as:

$i = 1 + (n - 1) α$

Where $n$ is the number of moles formed by complete dissociation of 1 mol of salt

$2 = 1 + (3 - 1) α$

$α$ = 0.3333

Percentage dissociation = 33.33% (nearest integer = 33)

Q 9 :

If the degree of dissociation of aqueous solution of weak monobasic acid is determined to be 0.3, then the observed freezing point will be _______% higher than the expected/theoretical freezing point. (Nearest integer) [2023]

(30)

For monobasic acid, $n = 2$

$i = 1 + (n - 1) α = 1 + (2 - 1) \times 0.3 = 1.3$

$% increase = \frac{{(Δ T_{f})}_{_{obs}} - {(Δ T_{f})}_{cal}}{{(Δ T_{f})}_{cal}} \times 100$

$= \frac{i \times K_{f} \times m - K_{f} \times m}{K_{f} \times m} \times 100$

$= (i - 1) \times 100 = 0.3 \times 100 = 30 %$

Q 10 :

0.004 M $K_{2} {SO}_{4}$ solution is isotonic with 0.01 M glucose solution. Percentage dissociation of $K_{2} {SO}_{4}$ is _______% (Nearest integer) [2023]

(75)

$Isotonic solution,$

$π_{K_{2} S O_{4}} = π_{Glucose}$

$i \times 0.004 \times R T = 0.01 \times R T$

$i = 2.5$

For $K_{2} S O_{4}$ {for dissociation $i = 1 + (n - 1) α$ }

$DOD (α) = \frac{i - 1}{n - 1} = \frac{2.5 - 1}{3 - 1} = 0.75$

$% dissociation = 75$

Q 11 :

Sea water contains 29.25% NaCl and 19% ${MgCl}_{2}$ by weight of solution. The normal boiling point of the sea water is ______ °C (Nearest integer)

Assume 100% ionization for both NaCl and ${MgCl}_{2}$

Given: $K_{b} (H_{2} O)$ = 0.52 K kg ${mol}^{- 1}$

Molar mass of NaCl and ${MgCl}_{2}$ is 58.5 and 95 g ${mol}^{- 1}$ respectively. [2023]

(116)

$Total weight of solute in solution = 29.25 + 19 = 48.25 gm$

$Total weight of solvent in solution = 100 - 48.25 = 51.75 gm$

So $Δ T_{b} = i \times K_{b} \times m = (i \times m) \times K_{b}$

$Mole of NaCl = \frac{29.25}{58.5} = 0.5$

${Mole of MgCl}_{2} = \frac{19}{95} = 0.2$

$Δ T_{b} = (2 \times \frac{29.25}{58.5} \times \frac{1000}{51.75} + 3 \times \frac{19}{95} \times \frac{1000}{51.75}) \times 0.52$

$Δ T_{b} = 16.075$

$Δ T_{b} = {(T_{b})}_{solution} - {(T_{b})}_{_{solvent}}$

${(T_{b})}_{solution} = 100 + 16.07$

$= 116.07 ° C$

Q 12 :

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

$α = \frac{i - 1}{(x + y - 1)}$
$α = \frac{i - 1}{(x + y + 1)}$
$α = \frac{x + y - 1}{i - 1}$
$α = \frac{x + y + 1}{i - 1}$

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(1)

$\begin{matrix} A_{x} B_{y} & \to & x A^{y +} & + & y B^{x -} \\ 1 - α & x α & \begin{matrix} y α \end{matrix} \end{matrix}$

$i = 1 - α + x α + y α$

$α = \frac{i - 1}{(x + y - 1)}$

Q 13 :

19.5 g of fluoro acetic acid (molar mass = $78 {g mol}^{- 1}$ ) is dissolved in 500 g of water at 298 K. The depression in the freezing point of water was $1 ° C$ . What is $K_{a}$ of fluoro acetic acid? (For water, $K_{f} = 1.86 {K kg mol}^{- 1}$ ). Assume molarity and molality to have same values. [2026]

$10^{- 6}$
$4 \times 10^{- 4}$
$3 \times 10^{- 5}$
$3 \times 10^{- 3}$

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(4)

$m = \frac{W_{{FH}_{2} CCOOH} (in g) \times 1000}{M_{{FH}_{2} CCOOH} ({in g mol}^{- 1}) \times W_{H_{2} O} (in g)}$

$m = \frac{19.5 \times 1000}{78 \times 500} m = 0.5 m$

$Δ T_{f} = i m K_{f}$

$1 = i \times 0.5 \times 1.86$

$i = 1.075$

${FH}_{2} CCOOH ⇌ {FH}_{2} {CCOO}^{-} + H^{+}$

$i = 1 + (n - 1) α$

$1.075 = 1 + (2 - 1) α$

$α = 0.075$

$K_{a} = \frac{C α^{2}}{1 - α} = \frac{0.5 \times {(0.075)}^{2}}{1 - 0.075} = 3 \times 10^{- 3}$

Q 14 :

Given below are two statements:

[IMAGE 203]

Statement I: $H_{2} O$ 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: $R = 0.083 {dm}^{3} {bar K}^{- 1} {mol}^{- 1}$ and assume complete dissociation of electrolyte)

In the light of the above statements, choose the correct answer from the options given below: [2026]

Both Statement I and Statement II are true
Both Statement I and Statement II are false
Statement I is true but Statement II is false
Statement I is false but Statement II is true

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(4)

Statement I: Osmotic pressure of chamber 1,

$π_{1} = C_{1} R T = \frac{W_{glucose} \times 1000 R T}{M_{glucose} V_{solution} (in mL)}$

$= \frac{18 \times 1000}{180 \times 100} R T = R T$

Osmotic pressure of chamber 2,

$π_{2} = C_{2} R T = \frac{W_{glucose} \times 1000 R T}{M_{glucose} V_{solution} (in mL)}$

$= \frac{30 \times 1000}{180 \times 250} R T = 0.67 R T$

Solvent moves from a solution of low osmotic pressure to a solution of high osmotic pressure. Thus water molecules move from chamber 2 to chamber 1.

Statement II:

$π = i C R T = 3 \times \frac{W_{K_{2} {SO}_{4}} \times R T}{M_{K_{2} {SO}_{4}} V_{solution} (in L)}$

$= 3 \times \frac{50 \times 10^{- 3}}{174 \times 2} \times 0.083 \times 300 bar = 0.0107 bar$

Q 15 :

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

[IMAGE 204]

Choose the correct answer from the options given below: [2026]

A and B only
A and D only
A, B and D only
A, C and D only

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(3)

A. For water $K_{b} (0.52 {K kg mol}^{- 1}) < K_{f} (1.86 {K kg mol}^{- 1})$

B. $K_{f} > K_{b} \Rightarrow m K_{f} > m K_{b} \Rightarrow Δ T_{f} > Δ T_{b}$

C. The osmotic pressure method has the advantage over other methods as pressure measurement is around the room temperature and the molarity of the solution is used instead of molality. As compared to other colligative properties, its magnitude is large even for very dilute solutions. The technique of osmotic pressure for determination of molar mass of solutes is particularly useful for biomolecules as they are generally not stable at higher temperatures and polymers have poor solubility.

D. [IMAGE 205]

Topic Question Set

Q 1 :

We have three aqueous solutions of 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: [2024]

Q 3 :

Arrange the following solutions in order of their increasing boiling points. [2025]

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

Q 6 :

The observed and normal molar masses of compound ${MX}_{2}$ are 65.6 and 164 respectively. The percent degree of ionisation of ${MX}_{2}$ is _____ %. (Neatest integer) [2025]

Q 7 :

If $A_{2} B$ is 30% ionised in an aqueous solution, then the value of van’t Hoff factor $(i)$ is _____ $\times 10^{- 1}$ . [2025]

Q 8 :

The percentage dissociation of a salt ( ${MX}_{3}$ ) solution at given temperature (van’t Hoff factor $i$ = 2) is ................. % (Nearest integer) [2025]

Q 9 :

If the degree of dissociation of aqueous solution of weak monobasic acid is determined to be 0.3, then the observed freezing point will be _______% higher than the expected/theoretical freezing point. (Nearest integer) [2023]

Q 10 :

0.004 M $K_{2} {SO}_{4}$ solution is isotonic with 0.01 M glucose solution. Percentage dissociation of $K_{2} {SO}_{4}$ is _______% (Nearest integer) [2023]

Q 12 :

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

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Topic Question Set

Q 1 : We have three aqueous solutions of 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: [2024]

Q 3 : Arrange the following solutions in order of their increasing boiling points. [2025] (i) 10-4M NaCl (ii) 10-4M Urea (iii) 10-3M NaCl (iv) 10-2M NaCl

Q 4 : CrCl3·xNH3 can exist as a complex. 0.1 molal aqueous solution of this complex shows a depression in freezing point of 0.558Co. Assuming 100% ionisation of this complex and coordination number of Cr is 6, the complex will be (Given Kf = 1.86 K kg mol-1) [2025]

Q 6 : The observed and normal molar masses of compound MX2 are 65.6 and 164 respectively. The percent degree of ionisation of MX2 is _____ %. (Neatest integer) [2025]

Q 7 : If A2B is 30% ionised in an aqueous solution, then the value of van’t Hoff factor (i) is _____ ×10-1. [2025]

Q 8 : The percentage dissociation of a salt (MX3) solution at given temperature (van’t Hoff factor i = 2) is ................. % (Nearest integer) [2025]

Q 9 : If the degree of dissociation of aqueous solution of weak monobasic acid is determined to be 0.3, then the observed freezing point will be _______% higher than the expected/theoretical freezing point. (Nearest integer) [2023]

Q 10 : 0.004 M K2SO4 solution is isotonic with 0.01 M glucose solution. Percentage dissociation of K2SO4 is _______% (Nearest integer) [2023]

Q 12 : The degree of dissociation (α) of a weak electrolyte, AxBy is related to Van't Hoff factor (i) by the expression:

Q 13 : 19.5 g of fluoro acetic acid (molar mass = 78 g mol-1) is dissolved in 500 g of water at 298 K. The depression in the freezing point of water was 1°C. What is Ka of fluoro acetic acid? (For water, Kf=1.86 K kg mol-1). Assume molarity and molality to have same values. [2026]

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Q 1 :

We have three aqueous solutions of 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: [2024]

Q 3 :

Arrange the following solutions in order of their increasing boiling points. [2025]

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

Q 6 :

The observed and normal molar masses of compound ${MX}_{2}$ are 65.6 and 164 respectively. The percent degree of ionisation of ${MX}_{2}$ is _____ %. (Neatest integer) [2025]

Q 7 :

If $A_{2} B$ is 30% ionised in an aqueous solution, then the value of van’t Hoff factor $(i)$ is _____ $\times 10^{- 1}$ . [2025]

Q 8 :

The percentage dissociation of a salt ( ${MX}_{3}$ ) solution at given temperature (van’t Hoff factor $i$ = 2) is ................. % (Nearest integer) [2025]

Q 9 :

If the degree of dissociation of aqueous solution of weak monobasic acid is determined to be 0.3, then the observed freezing point will be _______% higher than the expected/theoretical freezing point. (Nearest integer) [2023]

Q 10 :

0.004 M $K_{2} {SO}_{4}$ solution is isotonic with 0.01 M glucose solution. Percentage dissociation of $K_{2} {SO}_{4}$ is _______% (Nearest integer) [2023]

Q 12 :

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