Chapter 16

A set of solutions is prepared using \(180 \mathrm{~g}\) of water as a solvent and \(10 \mathrm{~g}\) of different non-volatile solutes \(\mathrm{A}, \mathrm{B}\) and \(\mathrm{C}\). The relative lowering of vapour pressure in the presence of these solutes are in the order [Given, molar mass of \(\mathrm{A}=100 \mathrm{~g} \mathrm{~mol}^{-1} ; \mathrm{B}=200 \mathrm{~g} \mathrm{~mol}^{-1} ; \mathrm{C}=10,000 \mathrm{~g}\) \(\left.\mathrm{mol}^{-1}\right]\) (a) \(\mathrm{B}>\mathrm{C}>\mathrm{A}\) (b) \(\mathrm{C}>\mathrm{B}>\mathrm{A}\) (c) \(\mathrm{A}>\mathrm{B}>\mathrm{C}\) (d) \(\mathrm{A}>\mathrm{C}>\mathrm{B}\)

A solution is prepared by dissolving \(0.6 \mathrm{~g}\) of urea (molar mass \(=60 \mathrm{~g}\) \(\mathrm{mol}^{-1}\) ) and \(1.8 \mathrm{~g}\) of glucose (molar mass \(=180 \mathrm{~g} \mathrm{~mol}^{-1}\) ) in \(100 \mathrm{~mL}\), of water at \(27^{\circ} \mathrm{C}\). The osmotic pressure of the solution is : \(\left(\mathrm{R}=0.08206 \mathrm{~L} \mathrm{~atm} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}\right)\) (a) \(8.2 \mathrm{~atm}\) (b) \(2.46 \mathrm{~atm}\) (c) \(4.92 \mathrm{~atm}\) (d) \(1.64 \mathrm{~atm}\)

At room temperature, a dilute solution of urea is prepared by dissolving \(0.60 \mathrm{~g}\) of urea in \(360 \mathrm{~g}\) of water. If the vapour pressure of pure water at this temperature is \(35 \mathrm{mmHg}\), lowering of vapour pressure will be : (molar mass of urea \(=60 \mathrm{~g} \mathrm{~mol}^{-1}\) ) (a) \(0.027 \mathrm{mmHg}\) (b) \(0.028 \mathrm{mmHg}\) (c) \(0.017 \mathrm{mmHg}\) (d) \(0.031 \mathrm{mmHg}\)

An open beaker of water in equilibrium with water vapour is in a sealed container. When a few grams of glucose are added to the beaker of water, the rate at which water molecules: (a) leaves the vapour increases (b) leaves the solution increases (c) leaves the solution decreases (d) leaves the vapour decreases

Molal depression constant for a solvent is \(4.0 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}\). The depression in the freezing point of the solvent for \(0.03 \mathrm{~mol} \mathrm{~kg}^{-1}\) solution \(\mathrm{K}_{2} \mathrm{SO}_{4}\) is: (Assume complete dissociation of the electrolyte) (a) \(0.18 \mathrm{~K}\) (b) \(0.24 \mathrm{~K}\) (c) \(0.12 \mathrm{~K}\) (d) \(0.36 \mathrm{~K}\)

\(\mathrm{K}_{2} \mathrm{HgI}_{4}\) is \(40 \%\) ionised in aqueous solution. The value of its van't Hoff factor (i) is : (a) \(1.6\) (b) \(1.8\) (c) \(2.0\) (d) \(2.2\)

At \(35{ }^{\circ} \mathrm{C}\), the vapour pressure of \(\mathrm{CS}_{2}\) is \(512 \mathrm{~mm} \mathrm{Hg}\) and that of acetone is \(344 \mathrm{~mm} \mathrm{Hg}\). A solution of \(\mathrm{CS}_{2}\) in acetone has a total vapour pressure of \(600 \mathrm{~mm} \mathrm{Hg}\). The false statement amongst the following is: (a) Raoult's law is not obeyed by this system (b) a mixture of \(100 \mathrm{~mL} \mathrm{CS}_{2}\) and \(100 \mathrm{~mL}\) acetone has a volume \(<200 \mathrm{~mL}\) (c) \(\mathrm{CS}_{2}\) and acetone are less attracted to each other than to themselves (d) heat must be absorbed in order to produce the solution at \(35^{\circ} \mathrm{C}\)

Elevation in the boiling point for 1 molal solution of glucose is \(2 \mathrm{~K}\). The depression in the freezing point for 2 molal solution of glucose in the same solvent is \(2 \mathrm{~K}\). The relation between \(\mathrm{K}_{\mathrm{b}}\) and \(\mathrm{K}_{\mathrm{f}}\) is: (a) \(\mathrm{K}_{\mathrm{b}}=1.5 \mathrm{~K}_{\mathrm{f}}\) (b) \(\mathrm{K}_{\mathrm{b}}=\mathrm{K}_{\mathrm{f}}\) (c) \(\mathrm{K}_{\mathrm{b}}=0.5 \mathrm{~K}_{\mathrm{f}}\) (d) \(\mathrm{K}_{\mathrm{b}}=2 \mathrm{~K}_{\mathrm{f}}\)

Two open beakers one containing a solvent and the other containing a mixture of that solvent with a non volatile solute are together sealed in a container. Over time: (a) the volume of the solution increases and the volume of the solvent decreases (b) the volume of the solution decreases and the volume of the solvent increases (c) the volume of the solution and the solvent does not change (d) the volume of the solution does not change and the volume of the solvent decreases

For 1 molal aqueous solution of the following compounds, which one will show the highest freezing point? (a) \(\left[\mathrm{Co}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right] \mathrm{Cl}_{3}\) (b) \(\left[\mathrm{Co}\left(\mathrm{H}_{2} \mathrm{O}\right)_{5} \mathrm{Cl}\right] \mathrm{Cl}_{2} \cdot \mathrm{H}_{2} \mathrm{O}\) (c) \(\left[\mathrm{Co}\left(\mathrm{H}_{2} \mathrm{O}\right)_{4} \mathrm{Cl}_{2}\right] \mathrm{Cl} .2 \mathrm{H}_{2} \mathrm{O}\) (d) \(\left[\mathrm{Co}\left(\mathrm{H}_{2} \mathrm{O}\right)_{3} \mathrm{Cl}_{3}\right] .3 \mathrm{H}_{2} \mathrm{O}\)

The mole fraction of a solvent in aqueous solution of a solute is \(0.8\). The molality (in \(\mathrm{mol} \mathrm{kg}^{-1}\) ) of the aqueous solution is : (a) \(13.88 \times 10^{-2}\) (b) \(13.88 \times 10^{-1}\) (c) \(13.88\) (d) \(13.88 \times 10^{-3}\)

The freezing point of benzene decreases by \(0.45^{\circ} \mathrm{C}\) when \(0.2 \mathrm{~g}\) of acetic acid is added to \(20 \mathrm{~g}\) of benzene. If acetic acid associates to form a dimer in benzene, percentage association of acetic acid in benzene will be : \(\left(K_{f}\right.\) for benzene \(\left.=5.12 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}\right)\) (a) \(64.6 \%\) (b) \(80.4 \%\) (c) \(74.6 \%\) (d) \(94.6 \%\)

What would be the molality of \(20 \%\) (mass/mass) aqueous solution of \(\mathrm{Kl} ?\) (molar mass of \(\left.\mathrm{Kl}=166 \mathrm{~g} \mathrm{~mol}^{-1}\right)\) (a) \(1.08\) (b) \(1.35\) (c) \(1.48\) (d) \(1.51\)

\(5 \mathrm{~g}\) of \(\mathrm{Na}_{2} \mathrm{SO}_{4}\) was dissolved in \(x \mathrm{~g}\) of \(\mathrm{H}_{2} \mathrm{O}\). The change in freezing point was found to be \(3.82^{\circ} \mathrm{C}\). If \(\mathrm{Na}_{2} \mathrm{SO}_{4}\) is \(81.5 \%\) ionised, the value of \(x\) \(\left(K_{f}\right.\) for water \(\left.=1.86^{\circ} \mathrm{C} \mathrm{kg} \mathrm{mol}^{-1}\right)\) is approximately : (molar mass of \(\mathrm{S}=32 \mathrm{~g} \mathrm{~mol}^{-1}\) and that of \(\mathrm{Na}=23 \mathrm{~g} \mathrm{~mol}^{-1}\) ) (a) \(15 \mathrm{~g}\) (b) \(25 \mathrm{~g}\) (c) \(45 \mathrm{~g}\) (d) \(65 \mathrm{~g}\)

The vapour pressures of pure liquids \(\mathrm{A}\) and \(\mathrm{B}\) are 400 and \(600 \mathrm{mmHg}\), respectively at \(298 \mathrm{~K}\). On mixing the two liquids, the sum of their initial volumes is equal to the volume of the final mixture. The mole fraction of liquid \(\mathrm{B}\) is \(0.5\) in the mixture. The vapour pressure of the final solution, the mole fractions of components \(\mathrm{A}\) and \(\mathrm{B}\) in vapour phase, respectively are: (a) \(450 \mathrm{mmHg}, 0.4,0.6\) (b) \(500 \mathrm{mmHg}, 0.5,0.5\) (c) \(450 \mathrm{mmHg}, 0.5,0.5\) (d) \(500 \mathrm{mmHg}, 0.4,06\)

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

The solubility of \(\mathrm{N}_{2}\) in water at \(300 \mathrm{~K}\) and 500 torr partial pressure is \(0.01 \mathrm{~g} \mathrm{~L}^{-1}\). The solubility (in \(\mathrm{g} \mathrm{L}^{-1}\) )at 750 torr partial pressure is : (a) \(0.0075\) (b) \(0.005\) (c) \(0.02\) (d) \(0.015\)

A solution at \(20^{\circ} \mathrm{C}\) is composed of \(1.5 \mathrm{~mol}\) of benzene and \(3.5 \mathrm{~mol}\) of toluene. If the vapour pressure of pure benzene and pure toluene at this temperature are \(74.7\) torr and \(22.3\) torr, respectively, then the total vapour pressure of the solution and the benzene mole fraction in equilibrium with it will be, respectively : (a) \(35.8\) torr and \(0.280\) (b) \(38.0\) torr and \(0.589\) (c) \(30.5\) torr and \(0.389\) (d) \(30.5\) torr and \(0.480\)

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) 128 (b) 488 (c) 32 (d) 64

For an ideal solution of two components \(\mathrm{A}\) and \(\mathrm{B}\), which of the following is true? (a) \(\Delta \mathrm{H}_{\text {mixing }}<0\) (zero) (b) \(\Delta \mathrm{H}_{\text {mixing }}>0\) (zero) (c) \(\mathrm{A}-\mathrm{B}\) interaction is stronger than \(\mathrm{A}-\mathrm{A}\) and \(\mathrm{B}-\mathrm{B}\) interactions (d) \(\mathrm{A}-\mathrm{A}, \mathrm{B}-\mathrm{B}\) and \(\mathrm{A}-\mathrm{B}\) interactions are identical.

Determination of the molar mass of acetic acid in benzene using freezing point depression is affected by : (a) partial ionization (b) dissociation (c) complex formation (d) association

The molarity of a solution obtained by mixing \(750 \mathrm{~mL}\) of \(0.5(\mathrm{M}) \mathrm{HCl}\) with \(250 \mathrm{~mL}\) of \(2(\mathrm{M}) \mathrm{HCl}\) will be : (a) \(0.875 \mathrm{M}\) (b) \(1.00 \mathrm{M}\) (c) \(1.75 \mathrm{M}\) (d) \(0.975 \mathrm{M}\)

Consider separate solutions of \(0.500 \mathrm{M} \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(a q), 0.100 \mathrm{M} \mathrm{Mg}_{3}\) \(\left(\mathrm{PO}_{4}\right)_{2}(a q), 0.250 \mathrm{M} \mathrm{KBr}(a q)\) and \(0.125 \mathrm{M}\) \(\mathrm{Na}_{3} \mathrm{PO}_{4}(a q)\) at \(25^{\circ} \mathrm{C}\). Which statement is true about these solutions, assuming all salts to be strong electrolytes? (a) They all have the same osmotic pressure. (b) \(0.100 \mathrm{M} \mathrm{Mg}_{3}\left(\mathrm{PO}_{4}\right)_{2}(a q)\) has the highest osmotic pressure. (c) \(0.125 \mathrm{M} \mathrm{Na}_{3} \mathrm{PO}_{4}(a q)\) has the highest osmotic pressure. (d) \(0.500 \mathrm{M} \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(a q)\) has the highest osmotic pressure.

Vapour pressure of pure benzene is 119 torr and that of toluene is \(37.0\) torr at the same temperature. Mole fraction of toluene in vapour phase which is in equilibrium with a solution of benzene and toluene having a mole fraction of toluene \(0.50\), will be : (a) \(0.137\) (b) \(0.237\) (c) \(0.435\) (d) \(0.205\)

The observed osmotic pressure for a \(0.10 \mathrm{M}\) solution of \(\mathrm{Fe}\left(\mathrm{NH}_{4}\right)_{2}\left(\mathrm{SO}_{4}\right)_{2}\) at \(25^{\circ} \mathrm{C}\) is \(10.8 \mathrm{~atm} .\) The expected and experimental (observed) values of van't Hoff factor \((i)\) will be respectively: \(\left(\mathrm{R}=0.082 \mathrm{~L} \mathrm{~atm} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}\right)\) (a) 5 and \(4.42\) (b) 4 and \(4.00\) (c) 5 and \(3.42\) (d) 3 and \(5.42\)

Dissolving \(120 \mathrm{~g}\) of urea (mol. wt. 60 ) in \(1000 \mathrm{~g}\) of water gave a solution of density \(1.15 \mathrm{~g} / \mathrm{mL}\). The molarity of the solution is (a) \(1.78 \mathrm{M}\) (b) \(2.00 \mathrm{M}\) (c) \(2.05 \mathrm{M}\) (d) \(2.22 \mathrm{M}\)

\(12 \mathrm{~g}\) of a nonvolatile solute dissolved in \(108 \mathrm{~g}\) of water produces the relative lowering of vapour pressure of \(0.1 .\) The molecular mass of the solute is : (a) 80 (b) 60 (c) 20 (d) 40

The Henry's law constant for the solubility of \(\mathrm{N}_{2}\) gas in water at \(298 \mathrm{~K}\) is \(1.0 \times 10^{5}\) atm. The mole fraction of \(\mathrm{N}_{2}\) in air is \(0.8\). The number of moles of \(\mathrm{N}_{2}\) from air dissolved in 10 moles of water at \(298 \mathrm{~K}\) and 5 atm pressure is (a) \(4.0 \times 10^{-4}\) (b) \(4.0 \times 10^{5}\) (c) \(5.0 \times 10^{-4}\) (d) \(4.0 \times 10^{-6}\)

For a dilute solution, Raoult's law states that : (a) the lowering of vapour pressure is equal to the mole fraction of solute. (b) the relative lowering of vapour pressure is equal to the mole fraction of solute. (c) the relative lowering of vapour pressure is proportional to the amount of solute in solution. (d) the vapour pressure of the solution is equal to the mole fraction of solvent.

An azeotropic solution of two liquids has boiling point lower than either of them when it (a) shows negative deviation from Raoult's law (b) shows no deviation from Raoult's law (c) shows positive deviation from Raoult's law (d) is saturated

When \(20 \mathrm{~g}\) of naphthoic acid \(\left(\mathrm{C}_{11} \mathrm{H}_{8} \mathrm{O}_{2}\right)\) is dissolved in \(50 \mathrm{~g}\) of benzene \(\left(K_{f}=1.72 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}\right)\), a freezing point depression of \(2 \mathrm{~K}\) is observed. The van't Hoff factor \((i)\) is (a) \(0.5\) (b) 1 (c) 2 (d) 3

Liquids A and B form ideal solution over the entire range of composition. At temperature \(T\), equimolar binary solution of liquids \(\mathbf{A}\) and \(\mathbf{B}\) has vapour pressure 45 Torr. At the same temperature, a new solution of \(\mathbf{A}\) and \(\mathbf{B}\) having mole fractions \(x_{A}\) and \(x_{B}\), respectively, has vapour pressure of \(22.5\) Torr. The value of \(x_{A} / x_{B}\) in the new solution is ____ . (given that the vapour pressure of pure liquid \(\mathbf{A}\) is 20 Torr at temperature \(T\) )

The elevation in boiling point of a solution of \(13.44 \mathrm{~g}\) of \(\mathrm{CuCl}_{2}\) in \(1 \mathrm{~kg}\) of water using the following information will be (Molecular weight of \(\mathrm{CuCl}_{2}=134.4\) and \(K_{b}=0.52 \mathrm{~K}\) molal \(\left.^{-1}\right)\) (a) \(0.16\) (b) \(0.05\) (c) \(0.1\) (d) \(0.2\)

The mole fraction of a solute in a solution is \(0.1\). At \(298 \mathrm{~K}\), molarity of this solution is the same as its molality. Density of this solution at \(298 \mathrm{~K}\) is \(2.0 \mathrm{~g} \mathrm{~cm}^{-3}\). The ratio of the molecular weights of the solute and solvent, \(\left(\frac{\mathrm{MW}_{\text {solute }}}{\mathrm{MW}_{\text {solvent }}}\right)\), is ____ .

During depression of freezing point in a solution, the following are in equililbrium (a) liquid solvent, solid solvent (b) liquid solvent, solid solute (c) liquid solute, solid solute (d) liquid solute, solid solvent

A compound \(\mathrm{H}_{2} X\) with molar weight of \(80 \mathrm{~g}\) is dissolved in a solvent having density of \(0.4 \mathrm{~g} \mathrm{~mL}^{-1}\). Assuming no change in volume upon dissolution, the molality of a 3.2 molar solution is _____ .

The molecular weight of benzoic acid in benzene as determined by depression in freezing point method corresponds to: (a) ionization of benzoic acid. (b) dimerization of benzoic acid. (c) trimerization of benzoic acid. (d) solvation of benzoic acid.

\(29.2 \%(\mathrm{w} / \mathrm{w}) \mathrm{HCl}\) stock solution has a density of \(1.25 \mathrm{~g} \mathrm{~mL}^{-1}\). The molecular weight of \(\mathrm{HCl}\) is \(36.5 \mathrm{~g} \mathrm{~mol}^{-1}\). The volume \((\mathrm{mL})\) of stock solution required to prepare a \(200 \mathrm{~mL}\) solution of \(0.4 \mathrm{M} \mathrm{HCl}\) is :

\(0.2\) molal acid \(\mathrm{H} X\) is \(20 \%\) ionised in solution. \(K_{f}=1.86 \mathrm{~K}\) molality \(^{-1}\). The freezing point of the solution is : (a) \(-0.45\) (b) \(-0.90\) (c) \(-0.31\) (d) \(-0.53\)

At \(300 \mathrm{~K}\), the vapour pressure of a solution containing 1 mole of \(n\) hexane and 3 moles of \(n\)-heptane is \(550 \mathrm{~mm}\) of \(\mathrm{Hg}\). At the same temperature, if one more mole of \(n\)-heptane is added to this solution, the vapour pressure of the solution increases by \(10 \mathrm{~mm}\) of \(\mathrm{Hg}\). What is the vapour pressure in \(\mathrm{mm} \mathrm{Hg}\) of \(n\)-heptane in its pure state _____ ?

The freezing point of equimolal aqueous solutions will be highest for : (a) \(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{NH}_{3} \mathrm{Cl}\) (aniline hydrochloride) (b) \(\mathrm{Ca}\left(\mathrm{NO}_{3}\right)_{2}\) (c) \(\mathrm{La}\left(\mathrm{NO}_{3}\right)_{3}\) (d) \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\) (glucose)

Liquids A and B form ideal solution for all compositions of \(\mathbf{A}\) and \(\mathbf{B}\) at \(25^{\circ} \mathrm{C}\). Two such solutions with \(0.25\) and \(0.50\) mole fractions of \(\mathbf{A}\) have the total vapor pressures of \(0.3\) and \(0.4\) bar, respectively. What is the vapor pressure of pure liquid \(\mathbf{B}\) in bar?

Which of the following \(0.1 \mathrm{M}\) aqueous solutions will have the lowest freezing point? (a) Potassium sulphate (b) Sodium chloride (c) Urea (d) Glucose

The elevation of boiling point of \(0.10 \mathrm{~m}\) aqueous \(\mathrm{CrCl}_{3} x \mathrm{NH}_{3}\) solution is two times that of \(0.05 \mathrm{~m}\) aqueous \(\mathrm{CaCl}_{2}\) solution. The value of \(x\) is [Assume \(100 \%\) ionisation of the complex and \(\mathrm{CaCl}_{2}\), coordination number of \(\mathrm{Cr}\) as 6 , and that all \(\mathrm{NH}_{3}\) molecules are present inside the coordination sphere]

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 \(-0.0558^{\circ} \mathrm{C}\), the number of chloride(s) in the coordination sphere of the complex is \(\left[K_{f}\right.\) of water \(\left.=1.86 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}\right]\)

Mixture(s) showing positive deviation from Raoult's law at \(35{ }^{\circ} \mathrm{C}\) is (are) (a) carbon tetrachloride + methanol (b) carbon disulphide + acetone (c) benzene \(+\) toluene (d) phenol + aniline

If \(250 \mathrm{~cm}^{3}\) of an aqueous solution containing \(0.73 \mathrm{~g}\) of a protein \(\mathrm{A}\) is isotonic with one litre of another aqueous solution containing \(1.65 \mathrm{~g}\) of a protein \(\mathrm{B}\), at \(298 \mathrm{~K}\), the ratio of the molecular masses of \(\mathrm{A}\) and \(\mathrm{B}\) is \( ____ \times 10^{-2}\) (to the nearest integer).

Benzene and naphthalene form an ideal solution at room temperature. For this process, the true statement(s) is(are) (a) \(\Delta G\) is positive (b) \(\Delta S_{\text {system }}\) is positive (c) \(\Delta S_{\text {surroundings }}=0\) (d) \(\Delta H=0\)

How much amount of \(\mathrm{NaCl}\) should be added to \(600 \mathrm{~g}\) of water \((\mathrm{r}=\) \(1.00 \mathrm{~g} / \mathrm{mL}\) ) to decrease the freezing point of water to \(-0.2^{\circ} \mathrm{C}\) ? (The freezing point depression constant for water \(=2 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}\) )

The vapour pressure of ethanol and methanol are \(44.5 \mathrm{~mm}\) and \(88.7\) Hg respectively. An ideal solution is formed at the same temperature by mixing \(60 \mathrm{~g}\) of ethanol with \(40 \mathrm{~g}\) of methanol. Calculate the total vapour pressure of the solution and the mole fraction of methanol in the vapour.