Chapter 5

The colligative properties of electrolytes require a slightly different approach than the one used for the colligative properties of non- electrolytes. The electrolytes dissociate into ions in solution. It is the number of solute particles that determine the colligative properties of a solution. The electrolyte solutions, therefore show abnormal colligative properties. To account for this effect we define a quantity; called the van't Hoff factor which is given by [solution] \(i=\) \(\frac{\text { Actual number of particles in solution after dissociation }}{\text { Number of formula units initally dissolved in solution }}\) \(\mathrm{i}=1\) (for non - electrolytes); \(\mathrm{i}>1\) (for electrolytes, undergoing dissociation) \(\mathrm{i}<1\) (for solute, undergoing association) For a solution of a non electrolyte in water, the van't Hoff factor is (a) Always equal to 2 (b) Always equal to 0 (c) \(>1\) but \(<2\) (d) \(\leq 1\)

The colligative properties of electrolytes require a slightly different approach than the one used for the colligative properties of non- electrolytes. The electrolytes dissociate into ions in solution. It is the number of solute particles that determine the colligative properties of a solution. The electrolyte solutions, therefore show abnormal colligative properties. To account for this effect we define a quantity; called the van't Hoff factor which is given by [solution] \(i=\) \(\frac{\text { Actual number of particles in solution after dissociation }}{\text { Number of formula units initally dissolved in solution }}\) \(\mathrm{i}=1\) (for non - electrolytes); \(\mathrm{i}>1\) (for electrolytes, undergoing dissociation) \(\mathrm{i}<1\) (for solute, undergoing association) \(0.1 \mathrm{M} \mathrm{K}_{4}\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]\) is \(60 \%\) ionized. What will be its van't Hoff factor? (a) \(3.4\) (b) \(1.7\) (c) \(2.4\) (d) \(2.2\)

A molecule Bn dissolves in water and is non- volatile. A solution of certain molality showed a depression of \(0.93 \mathrm{~K}\) in freezing point. The same solution boiled at \(100.26^{\circ} \mathrm{C}\). When \(7.9 \mathrm{~g}\) of Bn was dissolved in \(100 \mathrm{~g}\) water, the solution boiled at \(100.44^{\circ} \mathrm{C}\). Given \(\mathrm{K}_{\mathrm{f}}\) for water \(=1.86 \mathrm{~K} \mathrm{~mol}^{-1} \mathrm{~kg}\) and Atomic mass of \(\mathrm{B}=31\) The value of ' \(n\) ' is

A \(0.001\) molal solution of \(\left[\mathrm{Pt}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{Cl}_{4}\right]\) in water had a freezing point depression, \(0.0056^{\circ} \mathrm{C} . \mathrm{K}_{\mathrm{f}}\) for water is \(1.86^{\circ} \mathrm{cm}^{-1} .\) The number of moles of \(\mathrm{AgNO}_{3}\) required to react with one mole of the complex in aqueous solution is

\(\mathrm{K}_{2} \mathrm{HgI}_{4}\) is \(50 \%\) ionized in aqueous solution. Find the value of \(i\).

What would be the \(\mathrm{pH}\) of a \(0.1\) molal aqueous solution of a monoprotic acid 'HA', that freezes at \(-0.2046^{\circ} \mathrm{C}\) ? \(\left[\mathrm{K}_{\mathrm{f}}\left(\mathrm{H}_{2} \mathrm{O}\right)=1.86^{\circ} \mathrm{mol}^{-1} \mathrm{~kg} ;\right.\) assuming molality \(=\) molarity]

What would be the \(\mathrm{pH}\) of a \(0.1\) molal aqueous solution of a monoprotic acid 'HA', that freezes at \(-0.2046^{\circ} \mathrm{C}\) ? \(\left[\mathrm{K}_{\mathrm{f}}\left(\mathrm{H}_{2} \mathrm{O}\right)=1.86^{\circ} \mathrm{mol}^{-1} \mathrm{~kg} ;\right.\) assuming molality \(=\) molarity]

An aqueous solution containing ionic salt having molality equal to \(0.1892\) freezes at \(-0.704^{\circ} \mathrm{C}\). The van't Hoff factor of the ionic salt will be equal to \(\left(\mathrm{K}_{\mathrm{f}}=1.86 \mathrm{Km}^{-1}\right)\)

Which of the following concentration factor is affected by change in temperature? (a) molarity (b) molality (c) mole fraction (d) weight fraction

In a mixture of \(\mathrm{A}\) and \(\mathrm{B}\), components show negative deviation when: (a) \(\mathrm{A}-\mathrm{B}\) interaction is stronger than \(\mathrm{A}-\mathrm{A}\) and \(\mathrm{B}-\mathrm{B}\) interaction (b) \(\mathrm{A}-\mathrm{B}\) interaction is weaker than \(\mathrm{A}-\mathrm{A}\) and \(\mathrm{B}-\mathrm{B}\) interaction (c) \(\Delta \mathrm{V}_{\text {mix }}>0, \Delta \mathrm{S}_{\operatorname{mix}}>0\) (d) \(\Delta \mathrm{V}_{\operatorname{mix}}=0, \Delta \mathrm{S}_{\operatorname{mix}}>0\)

For an aqueous solution, freezing point is \(-0.186^{\circ} \mathrm{C}\). Elevation of the boiling point of the same solution is $$ \left(\mathrm{K}_{\ell}=1.86^{\circ} \mathrm{mol}^{-1} \mathrm{~kg} \text { and } \mathrm{K}_{\mathrm{b}}=0.512^{\circ} \mathrm{mol}^{-1} \mathrm{~kg}\right) $$ (a) \(0.186^{\circ}\) (b) \(0.0512^{\circ}\) (c) \(1.86^{\circ}\) (d) \(5.12^{\circ}\)

In a \(0.2\) molal aqueous solution of a weak acid HX, the degree of ionization is \(0.3 .\) Taking \(K_{f}\) for water as \(1.85 \mathrm{k} \mathrm{kg}\) melt, the freezing point of the solution will be nearest to (a) \(-0.480^{\circ} \mathrm{C}\) (b) \(-0.360^{\circ} \mathrm{C}\) (c) \(-0.260^{\circ} \mathrm{C}\) (d) \(+0.480^{\circ} \mathrm{C}\)

If liquids A and B form an ideal solution, the (a) enthalpy of mixing is zero (b) entropy of mixing is zero (c) free energy of mixing is zero (d) free energy as well as the entropy of mixing are each zero

If liquids A and B form an ideal solution, the [2003] (a) enthalpy of mixing is zero(b) entropy of mixing is zero (c) free energy of mixing is zero (d) free energy as well as the entropy of mixing are each zero

Which one of the following aqueous solutions will exhibit highest boiling point? (a) \(0.05 \mathrm{M}\) glucose (b) \(0.01 \mathrm{M} \mathrm{KNO}_{3}\) (c) \(0.015 \mathrm{M}\) urea (d) \(0.01 \mathrm{M} \mathrm{Na}_{2} \mathrm{SO}_{4}\)

Which of the following liquid pairs shows a positivedeviation from Raoult' law? (a) water-nitric acid (b) water-hydrochloric acid (c) benzene-methanol (d) acetone-chloroform

If a is the degree of dissociation of \(\mathrm{Na}_{2} \mathrm{SO}_{4}\) the van't Hoff factor (i) used for calculating the molecular mass is (a) \(1+\alpha\) (b) \(1-\alpha\) (c) \(1+2 \alpha\) (d) \(1-2 \alpha\)

Benzene and toluene form nearly ideal solutions. At \(20^{\circ} \mathrm{C}\), the vapour pressure of benzene is 75 torr and that of toluene is 22 torr. The partial vapour pressure of benzene at \(20^{\circ} \mathrm{C}\) for a solution containing \(78 \mathrm{~g}\) of benzene and \(46 \mathrm{~g}\) of toluene in torr is (a) 25 (b) 50 (c) \(37.5\) (d) \(53.5\)

Two solutions of a substance (non-electrolyte) are mixed in the following manner. \(480 \mathrm{~mL}\) of \(1.5 \mathrm{M}\) first solution \(+520 \mathrm{~mL}\) of \(1.2 \mathrm{M}\) second solution. What is the molarity of the final mixture? (a) \(1.344 \mathrm{M}\) (b) \(2.70 \mathrm{M}\) (c) \(1.50 \mathrm{M}\) (d) \(1.20 \mathrm{M}\)

Density of a \(2.05 \mathrm{M}\) solution of acetic acid in water is \(1.02 \mathrm{~g} / \mathrm{mL}\). The molality of the solution is (a) \(1.14 \mathrm{~mol} \mathrm{~kg}^{-1}\) (b) \(3.28 \mathrm{~mol} \mathrm{~kg}^{-1}\) (c) \(2.28 \mathrm{~mol} \mathrm{~kg}^{-1}\) (d) \(0.44 \mathrm{~mol} \mathrm{~kg}^{-1}\)

\(18 \mathrm{~g}\) of glucose \(\left(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\right)\) is added to \(178.2 \mathrm{~g}\) of water. The vapour pressure of water for this aqueous solution at \(100^{\circ} \mathrm{C}\) is (a) \(759.00\) torr (b) \(7.60\) torr (c) \(76.00\) torr (d) \(752.40\) torr

A \(5.25 \%\) solution of a substance is isotonic with a \(1.5 \%\) solution of urea (molar mass \(=60 \mathrm{~g} \mathrm{~mol}^{-1}\) ) in the same solvent. If the densities of both the solutions are assumed to be equal to \(1.0 \mathrm{~g} \mathrm{~cm}^{-3}\), molar mass of the substance will be (a) \(115.0 \mathrm{~g} \mathrm{~mol}^{-1}\) (b) \(105.0 \mathrm{~g} \mathrm{~mol}^{-1}\) (c) \(210.0 \mathrm{~g} \mathrm{~mol}^{-1}\) (d) \(90.0 \mathrm{~g} \mathrm{~mol}^{-1}\)

A mixture of ethyl alcohol and propyl alcohol has a vapour pressure of \(290 \mathrm{~mm}\) at \(300 \mathrm{~K}\). The vapour pressure of propyl alcohol is \(200 \mathrm{~mm}\). If the mole fraction of ethyl alcohol is \(0.6\), its vapour pressure (in \(\mathrm{mm}\) ) at the same temperature will be (a) 300 (b) 700 (c) 360 (c) 350

At \(80^{\circ} \mathrm{C}\), the vapour pressure of pure liquid 'A' is 520 \(\mathrm{mm} \mathrm{Hg}\) and that of pure liquid 'B' is \(1000 \mathrm{~mm} \mathrm{Hg}\). If a mixture solution of 'A' and 'B' boils at \(80^{\circ} \mathrm{C}\) and \(\mathrm{I}\) atm pressure, the amount of 'A' in the mixture is ( \(1 \mathrm{~atm}=\) \(760 \mathrm{~mm} \mathrm{Hg}\) ). (a) \(52 \mathrm{~mol}\) per cent (b) 34 mol per cent (c) 48 mol per cent (d) \(50 \mathrm{~mol}\) per cent

At \(80^{\circ} \mathrm{C}\), the vapour pressure of pure liquid 'A' is 520 \(\mathrm{mm} \mathrm{Hg}\) and that of pure liquid 'B' is \(1000 \mathrm{~mm} \mathrm{Hg}\). If a mixture solution of 'A' and 'B' boils at \(80^{\circ} \mathrm{C}\) and \(\mathrm{I}\) atm pressure, the amount of 'A' in the mixture is ( \(1 \mathrm{~atm}=\) \(760 \mathrm{~mm} \mathrm{Hg}\) ). (a) \(52 \mathrm{~mol}\) per cent (b) 34 mol per cent (c) 48 mol per cent (d) \(50 \mathrm{~mol}\) per cent

A binary liquid solution is prepared by mixing n-heptane and ethanol. Which on of the following statement is correct regarding the behavior of the solution? (a) The solution in non-ideal, showing +ve deviation from Raoult's Law. (b) The solution in non-ideal, showing -ve deviation from Raoult's Law. (c) n-heptane shows tre deviation while ethanol shows -ve deviation from Raoult's Law. (d) The solution formed is an ideal solution.

If sodium sulphate is considered to be completely dissociated into cations and anions in aqueous solution, the change in freezing point of water \(\left(\Delta \mathrm{T}_{\mathrm{p}}\right)\), when \(0.01 \mathrm{~mol}\) of sodium sulphate is dissolved in \(1 \mathrm{Kg}\) of water, is \(\left(\mathrm{K}_{\mathrm{f}}=1.86 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}\right)\) (a) \(0.0372 \mathrm{~K}\) (b) \(0.0558 \mathrm{~K}\) (c) \(0.0744 \mathrm{~K}\) (d) \(0.0186 \mathrm{~K}\)

On mixing, heptane and octane form an ideal solution. At \(373 \mathrm{~K}\), the vapour pressures of the two liquid components (heptane and octane) are \(105 \mathrm{kPa}\) and \(45 \mathrm{kPa}\) respectively. Vapour pressure of the solution obtained by mixing \(25.0 \mathrm{~g}\) of heptane and \(35 \mathrm{~g}\) of octane will be (molar mass of heptane \(=100 \mathrm{~g} \mathrm{~mol}^{-1}\) and of octane \(=\) \(114 \mathrm{~g} \mathrm{~mol}^{-1}\) ) (a) \(72.0 \mathrm{kPa}\) (b) \(36.1 \mathrm{kPa}\) (c) \(96.2 \mathrm{kPa}\) (d) \(144.5 \mathrm{kPa}\)

The degree of dissociation \((\alpha)\) of a weak electrolyte, \(\mathrm{A}_{\mathrm{x}} \mathrm{B}_{\mathrm{y}}\) is related to van't Hoff factor (i) by the expression: (a) \(\alpha=\frac{x+y-1}{i-1}\) (b) \(\alpha=\frac{x+y+1}{i-1}\) (c) \(\alpha=\frac{1-1}{(x+y-1)}\) (d) \(\alpha=\frac{1-1}{x+y+1}\)

Ethylene glycol is used as antifreeze in a cold climate. Mass of ethylene glycol which should be added to \(4 \mathrm{~kg}\) of water to prevent it form freezing at \(-6^{\circ} \mathrm{C}\) will be: \(\left(\mathrm{K}_{f}\right.\) for water \(=1.86 \mathrm{~kg} \mathrm{~mol}^{-1}\), and molar mass of ethylene glycol \(=62 \mathrm{~g} \mathrm{~mol}^{-1}\) ) (a) \(204.11 \mathrm{~g}\) (b) \(804.32 \mathrm{~g}\) (c) \(600.20 \mathrm{~g}\) (d) \(302.40 \mathrm{~g}\)

\(K_{t}\) for water is \(1.86 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1} .\) If your automobile radiator holds \(1.0 \mathrm{~kg}\) of water, how many grams of ethylene glycol \(\left(\mathrm{C}_{2} \mathrm{H}_{6} \mathrm{O}_{2}\right)\) must you add to get the freezing point of the solution lowered to \(-2.8^{\circ} \mathrm{C}\) ? (a) \(39 \mathrm{~g}\) (b) \(93 \mathrm{~g}\) (c) \(72 \mathrm{~g}\) (d) \(27 \mathrm{~g}\)

\(K_{t}\) for water is \(1.86 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1} .\) If your automobile radiator holds \(1.0 \mathrm{~kg}\) of water, how many grams of ethylene glycol \(\left(\mathrm{C}_{2} \mathrm{H}_{6} \mathrm{O}_{2}\right)\) must you add to get the freezing point of the solution lowered to \(-2.8^{\circ} \mathrm{C}\) ? (a) \(39 \mathrm{~g}\) (b) \(93 \mathrm{~g}\) (c) \(72 \mathrm{~g}\) (d) \(27 \mathrm{~g}\)

The vapour pressure of acetone at \(20^{\circ} \mathrm{C}\) is 185 torr. When \(1.2 \mathrm{~g}\) of a non-volatile substance was dissolved in \(100 \mathrm{~g}\) of acetone at \(20^{\circ} \mathrm{C}\), its vapour pressure was 183 torr. The molar mass \(\left(\mathrm{g} \mathrm{mol}^{-1}\right)\) of the substance is (a) 32 (b) 64 (c) 128 (d) 488