Q.1. At 35°C, the vapor pressure of CS_{2} is 512 mm Hg and that of acetone is 344 mm Hg. A solution of CS_{2} in acetone has a total vapor pressure of 600 mm Hg. The false statement amongst the following is (2020)
(a) Raoult’s law is not obeyed by this system.
(b) A mixture of 100 mL CS_{2} and 100 mL acetone has a volume < 200 mL.
(c) 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°C.
Ans. (b)
Solution.
Since, in the given mixture, the solvent – solvent and solute – solute interaction is more than that of solvent – solute interaction, thus, the above mixture shows positive deviation from Raoult’s law.
Hence, statement (b) is incorrect.
Q.2. Two open beakers one containing a solvent and the other containing a mixture of that solvent with a nonvolatile solute are together sealed in a container. Over the time, (2020)
(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.
Ans. (a)
Solution.
Due to the nonvolatile solute in the mixture, there is a lowering of vapor pressure, thus, the volume of solution increases. Since, volume of container is constant, so on increasing the volume of solution, the volume of solvent alone decreases.
Q.3. A graph of vapor pressure and temperature for three different liquids X, Y, and Z is shown below: (2020)
The following inferences are made
(I) X has higher intermolecular interactions compared to Y.
(II) X has lower intermolecular interactions compared to Y.
(III) Z has lower intermolecular interactions compared to Y.
The correct inference(s) is/are
(a) (I) and (III)
(b) (I)
(c) (II)
(d) (III)
Ans. (c)
Solution.
Since, the boiling point of X is lower than Y, thus, the intermolecular interaction between molecules of X is less than that of Y.
Q.4. How much amount of NaCl should be added to 600 g of water (ρ = 1.00 g mL^{–1}) to decrease the freezing point of water to −0.2°C ? (The freezing point depression constant for water = 2 K kg mol^{−1}) (2020)
Ans. (1.74)
Solution.
Given, ΔT_{f} = 0.2°C
We know
ΔT_{f} = T iK_{f} m (1)
Substituting the values in Eq. (1), we get
Thus, 1.75 g of NaCl should be added to 600 g of water to decrease the freezing point of water to –0.2°C
Q.5. 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 ______. (2020)
(Given, K_{f} (water) = 2.0 K kg mol^{−1}, R = 0.08 dm^{3 }atm K^{−1} mol^{−1})
Ans. (2.18)
Solution.
We know
ΔT_{f} = K_{f}m
⇒ 273  T_{f} = 2 x 0.5
⇒ T_{f} = 272 K
Using Ideal gas equation,
pV = nRT (1)
Substituting the values in Eq. (1), we get
Since, ideal gas is in thermal equilibrium with aqueous solution of ethylene glycol
⇒ P_{1}V_{1} = P_{2}V_{2}
Q.6. Which one of the following statements regarding Henry's law is not correct? (2019)
(a) Higher the value of K_{H} at a given pressure, higher is the solubility of the gas in liquids.
(b) Different gases have different K_{H} (Henry's law constant) values at the same temperature.
(c) The partial pressure of the gas in vapour phase is proportional to the mole fraction of the gas in the solution.
(d) The value of K_{H} increases with increase of temperature and K_{H} is function of the nature of the gas.
Ans. (a)
Solution.
The solubility of the gas in liquids decreases with the increase in value of K_{H} at a given pressure.
Q.7. A solution containing 62 g ethylene glycol in 250 g water is cooled to  10°C. If K_{f} for water is 1.86 K kg mol^{1}, the amount of water (in g) separated as ice is: (2019)
(a) 48
(b) 32
(c) 64
(d) 16
Ans. (c)
Solution.
As we know,
ΔT_{f} = K_{f } x m
Total amount of water = 250 g
∴ The amount of water separated as ice = 250  186 = 64 g
Q.8. Liquids A and B form an ideal solution in the entire composition range. At 350 K, the vapour pressures of pure A and pure B are 7 x 10^{3} Pa and 12 x 10^{3} Pa, respectively. The composition of the vapour is in equilibrium with a solution containing 40 mole percent of A at this temperature is: (2019)
(a) x_{A} = 0.37 ; x_{B} = 0.63
(b) x_{A} = 0.28 ; x_{B} = 0.72
(c) x_{A }= 0.4 ; x_{B} = 0.6
(d) x_{A} = 0.76 ; x_{B }= 0.24
Ans. (b)
Solution.
= 7 x 10^{3} x 0.4 + 12 x 10^{3} x 0.6
= (7 x 0.4 + 12 x 0.6) x 10^{3} = 10^{4}
∴ x_{A }= 0.28, x_{B} = 10.28 = 0.72
Q.9. The amount of sugar (C_{12}H_{22}O_{11}) required to prepare 2 L of its 0.1 M aqueous solution is: (2019)
(a) 136.8 g
(b) 17.1 g
(c) 68.4 g
(d) 34.2 g
Ans. (c)
Solution.
As we know,
So, no. of moles of sugar = 0.2 mole
Mass of sugar = No. of moles of sugar × Molar mass of sugar
= 0.2 × 342 = 68.4 g
Q.10. 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: (2019)
(a) K_{b}= 1.5K_{f}
(b) K_{b} = K_{f}
(c) K_{b} = 0.5K_{f}
(d) K_{b} = 2K_{f}
Ans. (d)
Solution.
According to the question we can write
ΔT_{b} = K_{b}m ⇒ K_{b} (1) = 2 ⇒ K_{b} = 2Km^{1}
ΔT_{f} = K_{f}m ⇒ K_{f} (2) = 2 ⇒ K_{f} = 1 Km^{1}
∴ K_{f} = 0.5 K_{b}
∴ K_{b} = 2 K_{f}
Q.11. The freezing point of a diluted milk sample is found to be  0.2°C, while it should have been  0.5°C for pure milk. How much water has been added to pure milk to make the diluted sample? (2019)
(a) 1 cup of water to 2 cups of pure milk
(b) 3 cups of water to 2 cups of pure milk
(c) 1 cup of water to 3 cups of pure milk
(d) 2 cups of water to 3 cups of pure milk
Ans. (b)
Solution.
Freezing point of diluted milk = 0.2°C
ΔT'_{f} = 0.2ºC
Freezing point of pure milk = 0.5°C
ΔT_{f} = 0.5ºC
∵ Moles of solute are same in both samples
2 cups of pure milk is mixed with 3 cups of water to make 5 cups of diluted milk.
Q.12. K_{2}HgI_{4} is 40% ionised in aqueous solution. The value of its van’t Hoff factor (i) is: (2019)
(a) 1.6
(b) 1.8
(c) 2.0
(d) 2.2
Ans. (b)
Solution.
K_{2}Hgl_{4} ⇋ 2K^{+} + [Hgl_{4}]^{2} ; n=3
Q.13. 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: (2019)
(a) 3A
(b) 2A
(c) A
(d) 4A
Ans. (a)
Solution.
(ΔT_{f})_{x} = (ΔT_{f})_{y}
K_{f}.m_{x} = K_{f}.m_{y}
m_{y}= 3.27 A; y ≈ 3 A
Q.14. 8 g of NaOH is dissolved in 18 g of H_{2}O. Mole fraction of NaOH in solution and molality (in mol kg^{1}) of the solution respectively are: (2019)
(a) 0.2,22.20
(b) 0.2,11.11
(c) 0.167,11.11
(d) 0.167,22.20
Ans. (c)
Solution.
No. of moles of H_{2}O (n_{1}) = 18/18 = 1
No. of moles of NaOH (n_{2}) = 8/40 = 1/5
Q.15. 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}) (2019)
(a) 2.4 g
(b) 1.0 g
(c) 1.5 g
(d) 1.8 g
Ans. (a)
Solution.
Q.16. The vapour pressures of pure liquids A and B are 400 and 600 mm Hg, respectively at 298K. 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 B is 0.5 in the mixture. The vapour pressure of the final solution, the mole fractions of components A and B in vapour phase, respectively are: (2019)
(a) 450 mm Hg, 0.4, 0.6
(b) 500 mm Hg, 0.5, 0.5
(c) 450 mm Hg, 0.5, 0.5
(d) 500 mm Hg, 0.4, 06
Ans. (d)
Solution.
= 0.5 × 600 + 0.5 × 400 = 300 + 200 = 500
Using the relation p_{i} = y_{i} P_{Total}, we can calculate the mole fractions of the components in vapour phase.
P_{B} = y_{B} P_{total}
Q.17. For the solution of the gases w, x,y and z in water at 298K, the Henry's law constants (K_{H}) are 0.5, 2, 35 and 40 kbar, respectively. The correct plot for the given data is: (2019)
(a)
(b)
(c)
(d)
Ans. (a)
Solution.
According to Henry’s law
y = c + mx
Q.18. Liquid 'M' and liquid 'N' form an ideal solution. The vapour pressures of pure liquids 'M' and 'N' are 450 and 700 mm Hg, respectively, at the same temperature. Then correct statement is:
(x_{M} = Mole fraction of 'M' in solution;
x_{N} = Mole fraction of'N' in solution;
y_{M} = Mole fraction of 'M' in vapour phase;
y_{N} = Mole fraction of 'N’ in vapour phase) (2019)
(a)
(b)
(c)
(d)
Ans. (d)
Solution.
Q.19. The osmotic pressure of a dilute solution of an ionic compound XY 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 XY (in mol L^{1}) in solution is: (2019)
(a) 4 x 10^{2}
(b) 6 x 10^{2}
(c) 4 x 10^{4}
(d) 16 x 10^{4}
Ans. (b)
Solution.
we know,
∴ 2[XY] = 4(0.01)3
[XY] = 0.06
= 6 × 10^{2} mol/L
Q.20. 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 K_{2}SO_{4} is:
(Assume complete dissociation of the electrolyte) (2019)
(a) 0.18 K
(b) 0.24 K
(c) 0.12 K
(d) 0.36 K
Ans. (d)
Solution.
Dissociation of Potassium Sulphate (K_{2}SO_{4}),
i (Van’t Hoff factor) = 3
We know that, ΔT_{f}= iK_{f}m
where, K_{f }is molal depression constant and m is molality.
= 3 × 4 × 0.03 = 0.36 K
Q.21. What would be the molality of 20% (mass/mass) aqueous solution of Kl? (molar mass of KI = 166 g mol^{1}) (2019)
(a) 1.08
(b) 1.35
(c) 1.48
(d) 1.51
Ans. (d)
Solution.
20% W/W KI solution (Given)
i.e. 100 g solution contains 20 g KI
∴ Mass of solvent = 100  20 = 80 g
Q.22. At room temperature, a dilute solution of urea is prepared by dissolving 0.60 g of urea in 360 g of water. If the vapour pressure of pure water at this temperature is 35 mm Hg, lowering of vapour pressure will be:
(molar mass of urea = 60 g mol^{1}) (2019)
(a) 0.027 mm Hg
(b) 0.028 mm Hg
(c) 0.017 mm Hg
(d) 0.031 mm Hg
Ans. (c)
Solution.
Relative lowering of vapour pressure, is given by,
Given,
Δp = pº  p = 0.017
Q.23. 1 g of a nonvolatile nonelectrolyte solute is dissolved in 100 g of two different solvents A and B whose ebullioscopic constants are in the ratio of 1 : 5. The ratio of the elevation in their boiling points, ΔT_{b}(A)/ΔT_{b}(B) is: (2019)
(a) 5 : 1
(b) 10 : 1
(c) 1 : 5
(d) 1 : 0.2
Ans. (c)
Solution.
Ebullioscopic constant (molal elevation const.) is given by,
Q.24. For 1 molal aqueous solution of the following compounds, which one will show the highest freezing point? (2018)
(a) [CO(H_{2}O)_{6}]Cl_{3}
(b)[CO(H_{2}O)_{5}CI]CI_{2}.H_{2}O
(c) [CO(H_{2}O)_{4}CI_{2}]CI.2H_{2}O
(d) [CO(H_{2}O)_{3}CI_{3}].3H_{2}O
Ans. (d)
Solution.
The complex giving least number of ions will have lowest depression in freezing point and therefore highest freezing point. Hence, option 1 is correct. (Van’t Hoff factor = 1)
Q.25. Which of the following statements about colloids is False? (2018)
(a) Freezing point of colloidal solution is lower than true solution at same concentration of a solute
(b) When silver nitrate solution is added to potassium iodide solution, a negatively charged colloidal solution is formed
(c) Colloidal particles can pass through ordinary filter paper
(d) When excess of electrolyte is added to colloidal solution, colloidal particle will be precipitated
Ans. (a)
Solution.
Freezing point of colloidal solution is higher than true solution at same concentration of a solute.
Q.26. The mass of a nonvolatile, nonelectrolyte solute (molar mass = 50 g mol^{1}) needed to be dissolved in 114 g octane to reduce its vapour pressure to 75 %, is: (2018)
(a) 37.5 g
(b) 75 g
(c) 150 g
(d) 50 g
Ans. (d)
Solution.
Q.27. The freezing point of benzene decreases by 0.45ºC 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}) (2017)
(a) 64.6%
(b) 80.4%
(c) 74.6%
(d) 94.6%
Ans. (d)
Solution.
⇒ i = 0.527
α = 0.946
∴ % association = 94.6%
Q.28. 5 g of Na_{2}SO_{4} was dissolved in x g of H_{2}O. The change in freezing point was found to be 3.82°C. If Na_{2}SO_{4 }is 81.5% ionised, the value of x
(K_{f} for water = 1.86°C kg mol^{1}) is approximately:
(molar mass of S = 32 g mol^{1} and that of Na = 23 g mol^{1}) (2017)
(a) 25 g
(b) 65 g
(c) 15 g
(d) 45 g
Ans. (4)
Solution.
Q.29. A solution is prepared by mixing 8.5 g of CH_{2}Cl_{2} and 11.95 g of CHCl_{3}. If vapour pressure of CH_{2}Cl_{2} and CHCl_{3} at 298 K are 415 and 200 mm Hg respectively, the mole fraction of CHCl_{3} in vapour form is : (Molar mass of Cl = 35.5 g mol^{1}) (2017)
(a) 0.162
(b) 0.675
(c) 0.325
(d) 0.486
Ans. (c)
Solution.
Molar mass of CHCl_{3} = 119.5 g/mol.
Molar mass CH_{2}Cl_{2} = 85 g/mol.
Moles of CHCl_{3} = 11.95/119.5 = 0.1 mol.
Moles of CH_{2}Cl_{2} = 8.5/85 = 0.1 mol.
Mole of CHCl_{3} = 0.1/0.2 = 0.5 mol.
Mole fraction of CH_{2}Cl_{2} = 0.1/0.2 = 0.5 mol.
(Given  Vapour pressure of CHCl_{3} = 200 mm Hg = 0.263 atm.
Vapour pressure of CH_{2}Cl_{2} = 415 mm Hg = 0.546 atm.)(1 atm = 760 mm Hg)
∴ P_{(above solution)}
= mole fraction of CHCl_{3} × (Vapour pressure of CHCl_{3}) + Mole fraction of CH_{2}Cl_{2} × (Vapour pressure of CH_{2}Cl_{2})
= 0.5 × 0.263 + 0.5 × 0.546 = 0.4045
Mole fraction of CHCl_{3} in vapour form = 0.1315/0.4045 = 0.325.
Q.30. 18 g glucose (C_{6}H_{12}O_{6}) is added to 178.2 g water. The vapour pressure of water (in torr) for this aqueous solution is: (2016)
(a) 7.6
(b) 76.0
(c) 752.4
(d) 759.0
Ans. (c)
Solution.
According to Raoult's Law
Here P° = Vapour pressure of pure solvent,
P_{s} = Vapour pressure of solution
W_{B} = Mass of solute, W_{A }= Mass of solvent
M_{B}= Molar mass of solute, M_{A} = Molar mass of solvent
Vapour pressure of pure water at 100° C (by assumption = 760 torr)
By substituting values in equation (i) we get,
On solving (ii) we get
P_{s} = 752.4 torr
Q.31. The solubility of N_{2} in water at 300 K and 500 torr partial pressure is 0.01 g L^{1}. The solubility (in g L^{1}) at 750 torr partial pressure is: (2016)
(a) 0.02
(b) 0.015
(c) 0.0075
(d) 0.005
Ans. (c)
Solution.
According to Henry's law
S_{1} & S_{2} are solubility of gas (g/L)
Q.32. An aqueous solution of a salt MX_{2} at certain temperature has a van't Hoff factor of 2. The degree of dissociation for this solution of the salt is: (2016)
(a) 0.67
(b) 0.33
(c) 0.80
(d) 0.50
Ans. (d)
Solution.
For MX_{2} type salt
van 't Hoff factor (i) = 1 + 2α = 2
⇒ α = 0.5

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