Chemistry · Textbook solutions

Solutions

Every solved example, exercise, and miscellaneous question — in the order the textbook teaches them. · 57 questions

2. Solutions — worked examples

14 q

Solved Examples

Worked · 14
  1. Solved Ex.2.1
    The solubility of N2\mathrm{N_2} gas in water at 25∘C25^\circ\mathrm{C} and 1 bar is 6.85×10−46.85 \times 10^{-4} mol L−1\mathrm{mol\ L^{-1}}. Calculate (a) Henry's law constant (b) molarity of N2\mathrm{N_2} gas dissolved in water under atmospheric conditions when partial pressure of N2\mathrm{N_2} in atmosphere is 0.75 bar.
  2. Solved Ex.2.2
    The Henry's law constant of methyl bromide (CH3Br)\mathrm{(CH_3Br)}, is 0.159 mol L−1 bar−1\mathrm{mol\ L^{-1}\ bar^{-1}} at 25∘C25^\circ\mathrm{C}. What is the solubility of methyl bromide in water at 25∘C25^\circ\mathrm{C} and at pressure of 130 mmHg?
  3. Solved Ex.2.3
    The vapour pressures of pure liquids A and B are 450 mm Hg and 700 mm Hg, respectively at 350 K. Find the composition of liquid and vapour if total vapour pressure is 600 mm.
  4. Solved Ex.2.4
    A solution is prepared by dissolving 394 g of a nonvolatile solute in 622 g of water. The vapour pressure of solution is found to be 30.74 mm Hg at 30∘C30^\circ\mathrm{C}. If vapour pressure of water at 30∘C30^\circ\mathrm{C} is 31.8 mm Hg, what is the molar mass of solute?
  5. Solved Ex.2.5
    The vapour pressure of pure benzene (molar mass 78 g/mol) at a certain temperature is 640 mm Hg. A nonvolatile solute of mass 2.315 g is added to 49 g of benzene. The vapour pressure of the solution is 600 mm Hg. What is the molar mass of solute?
  6. Solved Ex.2.6
    The normal boiling point of ethyl acetate is 77.06∘C77.06^\circ\mathrm{C}. A solution of 50 g of a nonvolatile solute in 150 g of ethyl acetate boils at 84.27∘C84.27^\circ\mathrm{C}. Evaluate the molar mass of solute if Kb\mathrm{K_b} for ethyl acetate is 2.77∘C kg mol−12.77^\circ\mathrm{C\ kg\ mol^{-1}}.
  7. Solved Ex.2.7
    3.795 g of sulphur is dissolved in 100 g of carbon disulphide. This solution boils at 319.81 K. What is the molecular formula of sulphur in solution? The boiling point of the solvent is 319.45 K. (Given that KbK_b for CS2\mathrm{CS_2} = 2.42 K kg mol−1\mathrm{K\ kg\ mol^{-1}} and atomic mass of S = 32 u
  8. Solved Ex.2.8
    1.02 g of urea when dissolved in 98.5 g of certain solvent decreases its freezing point by 0.211 K. 1.609 g of unknown compound when dissolved in 86 g of the same solvent depresses the freezing point by 0.34 K. Calculate the molar mass of the unknown compound. (Molar mass of urea = 60 g mol−1\mathrm{g\ mol^{-1}})
  9. Solved Ex.2.9
    What is the molar mass of a solute if a solution prepared by dissolving 0.822 g of it in 300 mdm3\mathrm{mdm^3} of water has an osmotic pressure of 149 mm Hg at 298 K?
  10. Solved Ex.2.10
    0.2 mm aqueous solution of KCl freezes at −0.680∘C-0.680^\circ\mathrm{C}. Calculate van't Hoff factor and osmotic pressure of solution at 0∘C0^\circ\mathrm{C}. (Kf=1.86 K kg mol−1)(\mathrm{K_f} = 1.86\ \mathrm{K\ kg\ mol^{-1}})
  11. Solved Ex.2.11
    0.01m0.01m aqueous formic acid solution freezes at −0.021∘C-0.021^\circ\mathrm{C}. Calculate its degree of dissociation. Kf=1.86 K kg mol−1\mathrm{K_f} = 1.86\ \mathrm{K\ kg\ mol^{-1}}
  12. Solved Ex.2.12
    3.4 g of CaCl2\mathrm{CaCl_2} is dissolved in 2.5 L of water at 300 K. What is the osmotic pressure of the solution? van't Hoff factor for CaCl2\mathrm{CaCl_2} is 2.47.
  13. Solved Ex.2.13
    Which of following solutions will have maximum boiling point elevation and which have minimum freezing point depression assuming the complete dissociation? (a) 0.1 mm KCl (b) 0.05 mm NaCl (c) 1m1m AlPO4\mathrm{AlPO_4} (d) 0.1 mm MgSO4\mathrm{MgSO_4}
  14. Solved Ex.2.14
    Assuming complete dissociation, calculate the molality of an aqueous solution of KBr whose freezing point is −2.95∘C-2.95^\circ\mathrm{C}. Kf\mathrm{K_f} for water is 1.86 K kg mol−1\mathrm{K\ kg\ mol^{-1}}

Exercises

43 q

1. Choose the most correct option

Practice · 12
  1. Choose the most correct option.
    Ex Q.1 (i)
    The vapour pressure of a solution containing 2 moles of a solute in 2 moles of water (vapour pressure of pure water = 24 mm Hg) is
    1. A.
      24 mm Hg
    2. B.
      32 mm Hg
    3. C.
      48 mm Hg
    4. D.
      12 mm Hg
  2. Ex Q.1 (ii)
    The colligative property of a solution is
    1. A.
      vapour pressure
    2. B.
      boiling point
    3. C.
      osmotic pressure
    4. D.
      freezing point
  3. Ex Q.1 (iii)
    In calculating osmotic pressure the concentration of solute is expressed in
    1. A.
      molarity
    2. B.
      molality
    3. C.
      mole fraction
    4. D.
      mass percent
  4. Ex Q.1 (iv)
    Ebullioscopic constant is the boiling point elevation when the concentration of solution is
    1. A.
      1m
    2. B.
      1M
    3. C.
      1 mass%
    4. D.
      1 mole fraction of solute.
  5. Ex Q.1 (v)
    Cryoscopic constant depends on
    1. A.
      nature of solvent
    2. B.
      nature of solute
    3. C.
      nature of solution
    4. D.
      number of solvent molecules
  6. Ex Q.1 (vi)
    Identify the correct statement
    1. A.
      vapour pressure of solution is higher than that of pure solvent.
    2. B.
      boiling point of solvent is lower than that of solution
    3. C.
      osmotic pressure of solution is lower than that of solvent
    4. D.
      osmosis is a colligative property.
  7. Ex Q.1 (vii)
    A living cell contains a solution which is isotonic with 0.3 M sugar solution. What osmotic pressure develops when the cell is placed in 0.1 M KCl solution at body temperature?
    1. A.
      5.08 atm
    2. B.
      2.54 atm
    3. C.
      4.92 atm
    4. D.
      2.46 atm
  8. Ex Q.1 (viii)
    The osmotic pressure of blood is 7.65 atm at 310 K. An aqueous solution of glucose isotonic with blood has the percentage (by volume)
    1. A.
      5.41 %
    2. B.
      3.54 %
    3. C.
      4.53 %
    4. D.
      53.4 %
  9. Ex Q.1 (ix)
    Vapour pressure of a solution is
    1. A.
      directly proportional to the mole fraction of the solute
    2. B.
      inversely proportional to the mole fraction of the solute
    3. C.
      inversely proportional to the mole fraction of the solvent
    4. D.
      directly proportional to the mole fraction of the solvent
  10. Ex Q.1 (x)
    Pressure cooker reduces cooking time for food because
    1. A.
      boiling point of water involved in cooking is increased
    2. B.
      heat is more evenly distributed in the cooking space
    3. C.
      the higher pressure inside the cooker crushes the food material
    4. D.
      cooking involves chemical changes helped by a rise in temperature.
  11. Ex Q.1 (xi)
    Henry's law constant for a gas CH3Br\mathrm{CH_3Br} is 0.159 mol dm−3\mathrm{mol\,dm^{-3}} atm at 25∘C25^\circ\mathrm{C}. What is the solubility of CH3Br\mathrm{CH_3Br} in water at 25∘C25^\circ\mathrm{C} and a partial pressure of 0.164 atm?
    1. A.
      0.0159 mol L−1\mathrm{mol\ L^{-1}}
    2. B.
      0.164 mol L−1\mathrm{mol\ L^{-1}}
    3. C.
      0.026 M
    4. D.
      0.042 M
  12. Ex Q.1 (xii)
    Which of the following statement is NOT correct for 0.1 M urea solution and 0.05 M sucrose solution?
    1. A.
      osmotic pressure exhibited by urea solution is higher than that exhibited by sucrose solution
    2. B.
      urea solution is hypertonic to sucrose solution
    3. C.
      they are isotonic solutions
    4. D.
      sucrose solution is hypotonic to urea solution

2. Answer the following in one or two sentences

Practice · 10
  1. Answer the following in one or two sentences
    Ex Q.2 (i)
    What is osmotic pressure?
  2. Ex Q.2 (ii)
    A solution concentration is expressed in molarity and not in molality while considering osmotic pressure. Why?
  3. Ex Q.2 (iii)
    Write the equation relating boiling point elevation to the concentration of solution.
  4. Ex Q.2 (iv)
    A 0.1 mm solution of K2SO4\mathrm{K_2SO_4} in water has freezing point of −4.3∘C-4.3^\circ\mathrm{C}. What is the value of van't Hoff factor if KfK_f for water is 1.86 K kg mol−1\mathrm{K\ kg\ mol^{-1}}?
  5. Ex Q.2 (v)
    What is van't Hoff factor?
  6. Ex Q.2 (vi)
    How is van't Hoff factor related to degree of ionization?
  7. Ex Q.2 (vii)
    Which of the following solutions will have higher freezing point depression and why ? a. 0.1 mm NaCl b. 0.05 mm Al2(SO4)3\mathrm{Al_2(SO_4)_3}
  8. Ex Q.2 (viii)
    State Raoult's law for a solution containing a nonvolatile solute
  9. Ex Q.2 (ix)
    What is the effect on the boiling point of water if 1 mole of methyl alcohol is added to 1 dm3\mathrm{dm^3} of water? Why?
  10. Ex Q.2 (x)
    Which of the four colligative properties is most often used for molecular mass determination? Why?

3. Answer the following

Practice · 9
  1. Answer the following.
    Ex Q.3 (i)
    How vapour pressure lowering is related to a rise in boiling point of solution?
  2. Ex Q.3 (ii)
    What are isotonic and hypertonic solutions?
  3. Ex Q.3 (iii)
    A solvent and its solution containing a nonvolatile solute are separated by a semipermable membrane. Does the flow of solvent occur in both directions? Comment giving reason.
  4. Ex Q.3 (iv)
    The osmotic pressure of CaCl2\mathrm{CaCl_2} and urea solutions of the same concentration at the same temperature are respectively 0.605 atm and 0.245 atm. Calculate van't Hoff factor for CaCl2\mathrm{CaCl_2}
  5. Ex Q.3 (v)
    Explain reverse osmosis.
  6. Ex Q.3 (vi)
    How molar mass of a solute is determined by osmotic pressure measurement?
  7. Ex Q.3 (vii)
    Why vapour pressure of a solvent is lowered by dissolving a nonvolatile solute into it?
  8. Ex Q.3 (viii)
    Using Raoult's law, how will you show that ΔP=P10x2\Delta P = P_1^0 x_2 ? Where x2x_2 is the mole fraction of solute in the solution and P10P_1^0 vapour pressure of pure solvent.
  9. Ex Q.3 (ix)
    While considering boiling point elevation and freezing point depression a solution concentration is expressed in molality and not in molarity. Why?

4 - 15. Answer the following

Practice · 12
  1. Ex Q.4
    Derive the relationship between degree of dissociation of an electrolyte and van't Hoff factor.
  2. Ex Q.5
    What is effect of temperature on solubility of solids in water? Give examples.
  3. Ex Q.6
    Obtain the relationship between freezing point depression of a solution containing nonvolatile nonelctrolyte and its molar mass.
  4. Ex Q.7
    Explain with diagram the boiling point elevation in terms of vapour pressure lowering.
  5. Ex Q.8
    Fish generally needs O2\mathrm{O_2} concentration in water at least 3.8 mg/L for survival. What partial pressure of O2\mathrm{O_2} above the water is needed for the survival of fish? Given the solubility of O2\mathrm{O_2} in water at 0∘C0^\circ\mathrm{C} and 1 atm partial pressure is 2.2×10−32.2 \times 10^{-3} mol/L
  6. Ex Q.9
    The vapour pressure of water at 20∘C20^\circ\mathrm{C} is 17 mm Hg. What is the vapour pressure of solution containing 2.8 g urea in 50 g of water?
  7. Ex Q.10
    A 5% aqueous solution (by mass) of cane sugar (molar mass 342 g/mol) has freezing point of 271K. Calculate the freezing point of 5% aqueous glucose solution.
  8. Ex Q.11
    A solution of citric acid C6H8O7\mathrm{C_6H_8O_7} in 50 g of acetic acid has a boiling point elevation of 1.76 K. If KbK_b for acetic acid is 3.07 K kg mol−1\mathrm{K\ kg\ mol^{-1}}, what is the molality of solution?
  9. Ex Q.12
    An aqueous solution of a certain organic compound has a density of 1.063 gmL−1\mathrm{gmL^{-1}}, an osmotic pressure of 12.16 atm at 25∘C25^\circ\mathrm{C} and a freezing point of −1.03∘C-1.03^\circ\mathrm{C}. What is the molar mass of the compound?
  10. Ex Q.13
    A mixture of benzene and toluene contains 30% by mass of toluene. At 30∘C30^\circ\mathrm{C}, vapour pressure of pure toluene is 36.7 mm Hg and that of pure benzene is 118.2 mm Hg. Assuming that the two liquids form ideal solutions, calculate the total pressure and partial pressure of each constituent above the solution at 30∘C30^\circ\mathrm{C}.
  11. Ex Q.14
    At 25∘C25^\circ\mathrm{C} a 0.1 molal solution of CH3COOH\mathrm{CH_3COOH} is 1.35 % dissociated in an aqueous solution. Calculate freezing point and osmotic pressure of the solution assuming molality and molarity to be identical.
  12. Ex Q.15
    A 0.15 mm aqueous solution of KCl freezes at −0.510∘C-0.510^\circ\mathrm{C}. Calculate ii and osmotic pressure at 0∘C0^\circ\mathrm{C}. Assume volume of solution equal to that of water