Solution and Colligative Properties Exercise # 4

Exercise # 4 [Subjective Type Questions] 1. (a) The vapour pressure of n-hexane and n-heptane at 273 K are 45.5 mm Hg and 11.4 mm Hg, respectively. What is the composition of a solution of these two liquids if its vapour pressure at 273 K is 37.3 mm Hg. (b) The mole fraction of n-hexane in the vapour above a solution of n-hexane and n-heptane is 0.75 at 273 K. What is the composition of the liquid solution. 2. A solution containing 30 g of a nonvolatile solute in exactly 90 g water has a vapour pressure of 21.85 mm Hg at 25°C. Further 18 g of water is then added to the solution. The resulting solution has vapour pressure of 22.18 mm Hg at 25°C. Calculate (a) molar mass of the solute, and (b) vapour pressure of water at 25°C. 3. The freezing point of ether was lowered by 0.60°C on dissolving 2.0 g of phenol in 100 g of ether. Calculate the –1 molar mass of phenol and comment on the result. Given : Kf (ether) = 5.12 K kg mol . 4. The vapour pressure of ethanol and methanol are 44.5 mm Hg and 88.7 mm Hg, respectively. An ideal solution is formed at the same temperature by mixing 60 g of ethanol and 40 g of methanol. Calculate the total vapour pressure of the solution and the mole fraction of methanol in the vapour. 5. The vapour pressure of pure benzene at a certain temperature is 640 mm Hg. A non-volatile solid weighing 2.175 g is added to 39.0 g of benzene. The vapour pressure of the solution is 600 mm Hg. What is the molar mass of the solid substance? 6. Addition of 0.643 g of a compound to 50 mL of benzene (density : 0.879 g mL ) lower the freezing –1 point from 5.51°C to 5.03°C. If K f for benzene is 5.12 K kg mol , calculate the molar mass of the compound. 7. A solution contains 3.22 g of HClO 2 in 47.0 g of water. The freezing point of the solution is + – 271.10 K. Calculate the fraction of HClO 2 that undergoes dissociation to H and ClO 2 . –1 Given : Kf(water) = 1.86 K kg mol . 8. A 0.1 molar solution of NaCl is found to be isotonic with 1% urea solution. Calculate (a) Van't Hoff factor, and (b) –3 degree of dissociation of sodium chloride. Assume density of 1% urea equal to 1 g cm . 9. The addition of 3 g of a substance to 100 g CCl4 (M = 154 g mol ) raises the boiling point of CCl4 by 0.60°C. If –1 Kb (CCl4) is 5 K mol kg, calculate (a) the freezing point depression (b) the relative lowering of vapour pressure –1 (c) the osmotic pressure at 298 K and (d) the molar mass of the substance. Given : Kf (CCl4) = 31.8 K kg mol and –3  (solution) = 1.64 g cm . 10. A solution containing 0.122 kg of benzoic acid in 1 kg of benzene (b. pt. 353 K) boils at 354.5 K. Determine the apparent molar mass of benzoic acid (which dimerizes) in the solution and the degree of dimerization. –1 Given : vapH1m (benzene) = 394.57 J g . 11. A solution containing 0.011 kg of barium nitrate in 0.1 kg of water boils at 100.46°C. Calculate the degree of ionization –1 of the salt. Kb (water) = 0.52 K kg mol . 12. When 3.24 g of mercuric nitrate Hg (NO3)2 dissolved in 1 kg of water, the freezing point of the solution is found to be – 0.0558°C. When 10.84 g of mercuric chloride HgCl2 is dissolved in 1 kg of water, the freezing point of the –1 solution is –0.0744°C. Kf = 1.86 mol K kg. Will either of these dissociate into ions in an aqueous solution ? 13. To 500 cm of water 3.0 × 10 kg of acetic acid is added. If 23% of acetic acid is dissociated, what –1 –3 will be the depression of freezing point? Kf and density of water are 1.86 K kg mol and 0.997 g cm , respectively. –1 –1 3 –3 SOLUTION AND COLLIGATIVE PROPERTIES 14. A 0.01 m aqueous solution of K3[Fe(CN)6] freezes at –0.062°C. What is the apparent percentage of dissociation? [Kf for water = 1.86] 15. The degree of dissociation of Ca (NO 3) 2 in a dilute aqueous solution containing 7 g of the salt per 100 g of water at 100°C is 70%. If the vapour pressure of water at 100°C is 760 mm, calculate the vapour pressure of the solution. 16. The vapour pressure of solution containing 6.69 g of Mg(NO3)2 dissolved in 100 g of water is 747 Torr at 373 K. Calculate the degree of dissociation of the salt in the solution. 17. At 353 K, the vapour pressure of pure ethylene bromide and propylene bromide are 22.93 –2 and 16.93 k Nm , respectively, and these compounds form a nearly ideal solution. 3 mol of ethylene bromide and 2 mole of propylene bromide are equilibrated at 553 K and a total pressure of –2 20.4 k Nm . (a) What is the composition of the liquid phase? (b) What amount of each compound is present in the vapour phase? 18. The vapour pressure of two pure liquids, A and B, that form an ideal solution are 300 and 800 torr, respectively, at temperature T. A mixture of the vapour of A and B for which the amount fraction of A is 0.25 is slowly compressed at temperature T. Calculate : (a) The composition of the first drop of the condensate, (b) The total pressure when this drop is formed, (c) The composition of the solution whose normal boiling point is T. (d) The pressure when only the last bubble of vapour remains. (e) The composition of the last bubble. 19. A certain mass of a substance, when dissolved in 100 g C6H6, lowers the freezing point by 1.28°C. The same mass of solute dissolved in 100 g water lowers the freezing point by 1.40°C. If the substance has normal molecular weight in benzene and is completely ionised in water, into how many ions does it dissociate in water? Kf for H2O and –1 C6H6 are 1.86 and 5.12 K kg mol . 20. The cryoscopic constant for acetic acid is 3.6 K kg/mol. A solution of 1 g of a hydrocarbon in 100 g of acetic acid freezes at 16.14°C instead of the usual 16.60°C. The hydrocarbon contains 92.3% carbon. What is the molecular formula? 21. A radiator was filled with 10 L of water to which 2.5 L of methanol (density = 0.8 g.mL ) were added. At 9 : 00 pm, the vehicle is parked outdoors where the temperature is 0°C. The temperature is decreasing at a uniform rate of –1 0.5°C / min. Upto what time will there be no danger to the radiator of the car. Kf (water) = 1.86 kg.mol K. Assume methanol to be non-volatile. 22. Sea water is found to contain 5.85% NaCl and 9.50% MgCl2 by weight of solution. Calculate its normal boiling point –1 assuming 80% ionisation for NaCl and 50% ionisation of MgCl2 [Kb (H2O) = 0.51 kg mol K]. 23. Find the freezing point of a glucose solution whose osmotic pressure at 25°C is found to be 30 atm. –1 Kf (water) = 1.86 kg.mol . K. 24. The latent heat of fusion of ice is 80 calories per gram at 0°C. What is the freezing point of a solution of KC in water containing 7.45 grams of solute 500 grams of water, assuming that the salt is dissociated to the extent of 95%? 25. At 300 K, two solutions of glucose in water of concentration 0.01 M and 0.001 M are separated by semipermeable membrane. Pressure needs to be applied on which solution, to prevent osmosis? Calculate the magnitude of this applied pressure? 26. At 10°C, the osmotic pressure of urea solution is 500 mm. The solution is diluted and the temperature is raised to 25°C, when the osmotic pressure is found to be 105.3 mm. Determine extent of dilution. –1 27. When cells of the skeletal vacuole of a frog were placed in a series of NaCl solutions of different concentration at 25°C, it was observed microscopically that they remained unchanged in 0.7% NaCl solution, shrank in more cocentrated solutions, and swelled in more dilute solutions. Water freezes from the 0.7% salt solution at –0.406°C. What is the osmotic pressure of the cell cytoplasm at 25°C ? –1 Kf = 1.86 kg mol K. 28. An ideal solution of two volatile liquid A and B has a vapour pressure of 402.5 mmHg, the mole fraction of A in vapour & liquid state being 0.35 & 0.65 respectively. What are the vapour pressure of the two liquid at this temperature. 29. Dry air was drawn through bulbs containing a solution of 40 grams of urea in 300 grams of water, then through bulbs containing pure water at the same temperature and finally through a tube in which pumice moistened with strong H2SO4 was kept. The water bulbs lost 0.0870 grams and the sulphuric acid tube gained 2.036 grams. Calculate the molecular weight of urea. 30. A 0.1 M solution of potassium ferrocyanide is 46% dissociated at 18°C. What will be its osmotic pressure? 31. At 100°C, benzene & toluene have vapour pressure of 1375 & 558 Torr respectively. Assuming these two form an ideal binary solution that boils at 1 atm & 100°C. What is the composition of vapour issuing at these conditions? 32. Two beaker A and B present in a closed vessel. Beaker A contains 152.4 g aqueous solution of urea, containing 12 g of urea. Beaker B contains 196.2 g glucose solution, containing 18 g of glucose. Both solutions allowed to attain the equilibrium. Determine wt. % of glucose in it's solution at equilibrium : 33. The vapour pressure of two pure liquids A and B, that form an ideal solution are 100 and 900 mm Hg respectively at temperature T. This liquid solution of A and B is composed of 1 mole of A and 1 mole of B. What will be the pressure, when 1 mole of mixture has been vaporized ? 34. The addition of 3 g of substance to 100 g CCl4 (M = 154 g mol–1) raises the boiling point of CCl4 by 0.60°C of Kb (CCl4) is 5.03 kg mol–1 K. Calculate : (a) the freezing point depression (b) the relative lowering of vapour pressure (c) the osmotic pressure at 298 K (d) the molar mass of the substance Given Kf(CCl4) = 31.8 kg mol–1 K and  (density) of solution = 1.64 g/cm3. 35. A one litre solution is prepared by dissolving some solid lead-nitrate in water. The solution was found to boil at 100.15°C. To the resulting solution 0.2 mole NaCl was added. The resulting solution was found to freeze at –0.83°C. Determine solubility product of PbCl2. Given Kb= 0.5 and Kf = 1.86. Assume molality to be equal to molarity in all case. 36. A protein has been isolated as sodium salt with their molecular formula NaxP (this notation means that xNa+ ions are associated with a negatively charged protein P –x). A solution of this salt was prepared by dissolving 0.25 g of this sodium salt of protein in 10 g of water and ebulliscopic analysis revealed that solution boils at temperature 5.93 × 10–3 °C higher than the normal boiling point of pure water. Kb of water 0.52 kg mol–1. Also elemental analysis revealed that the salt contain 1% sodium metal by weight. Deduce molecular formula and determine molecular weight of acidic form of protein HxP. SOLUTION AND COLLIGATIVE PROPERTIES 37. The vapour pressure of two miscible liquids (A) and (B) are 300 and 500 mm of Hg respectively. In a flask 10 mole of (A) is mixed with 12 mole of (B). However, as soon as (B) is added, (A) starts polymerising into a completely insoluble solid. The polymerisation follows first-order kinetics. After 100 minute, 0.525 mole of a solute is dissolved which arrests the polymerisation completely. The final vapour pressure of the solution is 400 mm of Hg. Estimate the rate constant of the polymerisation reaction. Assume negligible volume change on mixing and polymerisation, and ideal behaviour for the final solution. 38. If 20 mL of ethanol (density = 0.7893 g/mL) is mixed with 40 mL water (density = 0.9971 g/mL) at 25°C, the final solution has density of 0.9571 g/mL. Calculate the percentage change in total volume of mixing. Also calculate the molality of alcohol in the final solution. 39. Mixture of two liquids A and B is placed in cylinder containing piston. Piston is pulled out isothermally so that volume of liquid decreases but that of vapour increases. When negligibly small amount of liquid was remaining, the mole fraction of A in vapour is 0.4. Given P°A = 0.4 atm and P°B = 1.2 atm at the experimental temperature. Calculate the total pressure at which the liquid has almost evaporated. (Assume ideal behaviour) 40. 1.5 g of monobasic acid when dissolved in 150 g of water lowers the freezing point by 0.165°C. 0.5 g of the same acid when titrated, after dissolution in water, requires 37.5 mL of N/10 alkali. Calculate the degree of dissociation of the acid (Kf for water = 1.86° C mol–1). 41. 30 mL of CH3OH (d = 0.7980 g cm–3) and 70 mL of H2O (d = 0.9984 g cm–3) are mixed at 25°C to form a solution of density 0.9575 g cm–3. Calculate the freezing point of the solution. Kf(H2O) is 1.86 kg mol–1 K. Also calculate its molarity. 42. Vapour pressure of C6H6 and C7H8 mixture at 50°C is given by P (mm Hg) = 179 XB + 92, where XB is the mole fraction of C6H6 . A solution is prepared by mixing 936 g benzene and 736 g toluene and if the vapours over this solution are removed and condensed into liquid and again brought to the temperature of 50°C, what would be mole fraction of C6H6 in the vapour state ? 43. When the mixture of two immiscible liquids (water and nitrobenzene) boils at 372 K and the vapour pressure at this temperature are 97.7 kPa (H2O) and 3.6 kPa (C6H5NO2). Calculate the weight % of nitrobenzene in the vapour. 44. The molar volume of liquid benzene (density = 0.877 g mL–1) increase by a factor of 2750 as it vaporizes at 20°C and that of liquid toluene (density = 0.867 g mL–1) increases by a factor of 7720 at 20°C solution has a vapour pressure of 46.0 torr. Find the mole fraction of benzene in the vapour above the solution. 45. Calculate the boiling point of a solution containing 0.61 g of benzoic acid in 50 g of carbon disulphide assuming 84% dimerization of the acid. The boiling point and Kb of CS2 are 46.2°C and 2.3 K kg mol–1, respectively. 46. At 25°C, 1 mol of A having a vapour pressure of 100 torr and 1 mol of B having a vapour pressure of 300 torr were mixed. The vapour at equilibrium is removed, condensed and the condensate is heated back to 25°C. The vapour now formed are again removed, recondensed and analyzed. What is the mole fraction of A in this condensate ? 47. The vapour pressure of a certain liquid is given by the equation : Log10P = 3.54595 – 313.7 + 1.40655 log10 T where P is the vapour pressure in mm and T = Kelvin Temperature. T Determine the molar latent heat of vaporisation as a function of temperature. Calculate the its value at 80 K. 48. A very dilute saturated solution of a sparingly soluble salt A3B4 has a vapour pressure of 20 mm of Hg at temperature T, while pure water exerts a pressure of 20.0126 mm Hg at the same temperature. Calculate the solubility product constant of A3B4 at the same temperature. 49. The molar volume of liquid benzene (density = 0.877 g mL–1) increases by a factor of 2750 as it vaporises at 20°C while in equilibrium with liquid benzene. At 27°C when a non - volatile solute (that does not dissociate) is dissolved in 54.6 cm3 of benzene vapour pressure of this solution, is found to be 98.88 mm Hg. Calculate the freezing point of the solution. Given : Enthalpy of vaporization of benzene (l) = 394.57 J/g Molal depression constant for benzene = 5.12 K kg. mol–1 Freezing point of benzene = 278.5 K. 50. The freezing point of 0.02 mol fraction solution of acetic acid (A) in benzene (B) is 277.4 K. Acetic acid exists partly as a dimer 2A = A2. Calculate equilibrium constant for the dimerisation. Freezing point of benzene is 278.4 K and its heat of fusion Hf is 10.042 kJ mol–1. 51. Tritium, T (an isotope of H) combines with fluorine to form weak acid TF, which ionizes to give T +. Tritium is radioactive and is a -emitter. A freshly prepared aqueous solution of TF has pT (equivalent of pH) of 1.5 and freezes at –0.372°C. If 600 mL of freshly prepared solution were allowed to stand for 24.8 years, calculate (i) ionization constant of TF. (ii) Number of -particles emitted. (Given : Kf for water = 1.86 kg mol K–1, t1/2 for tritium = 12.4 years.) 52. An ideal solution was prepared by dissolving some amount of cane sugar (non-volatile) in 0.9 moles of water. The solution was then cooled just below its freezing temperature (271 K), where some ice get separated out. The remaining aqueous solution registered a vapour pressure of 700 torr at 373 K. Calculate the mass of ice separated out, if the molar heat of fusion of water is 96 kJ. 53. The freezing point depression of a 0.109 M aq. solution of formic acid is –0.21°C. Calculate the equilibrium constant for the reaction, +  HCOOH (aq) ‡ˆ ˆˆ ˆ† ˆˆ H (aq) + HCOO (aq) Kf for water = 1.86 kg mol–1 K 54. 10 g of NH4Cl (mol. weight = 53.5) when dissolved in 1000 g of water lowered the freezing point by 0.637°C. Calculate the degree of hydrolysis of the salt if its degree of dissociation of 0.75. The molal depression constant of water is 1.86 kg mol–1 K.