COLLIGATIVE PROPERTIES ASSIGNMENT

  1. Calculating Mole Fraction and Molality
    The antifreeze in most automobile radiators is a mixture of equal volumes of ethylene glycol and water, with minor amounts of other additives that prevent corrosion. What are the (a) mole fraction and (b) molality of ethylene glycol, C2H4(OH)2, in a solution prepared from 2.22 × 103 g of ethylene glycol and 2.00 × 103 g of water (approximately 2 L of glycol and 2 L of water)?

Solution
(a) The mole fraction of ethylene glycol may be computed by first deriving molar amounts of both solution components and then substituting these amounts into the unit definition.



Notice that mole fraction is a dimensionless property, being the ratio of properties with identical units (moles).

(b) To find molality, we need to know the moles of the solute and the mass of the solvent (in kg).

First, use the given mass of ethylene glycol and its molar mass to find the moles of solute:

Then, convert the mass of the water from grams to kilograms:

Finally, calculate molarity per its definition:

Check Your Learning
What are the mole fraction and molality of a solution that contains 0.850 g of ammonia, NH3, dissolved in 125 g of water?

Answer:

7.14 × 10−3; 0.399 m

 

2.

Converting Mole Fraction and Molal Concentrations
Calculate the mole fraction of solute and solvent in a 3.0 m solution of sodium chloride.

Solution
Converting from one concentration unit to another is accomplished by first comparing the two unit definitions. In this case, both units have the same numerator (moles of solute) but different denominators. The provided molal concentration may be written as:

The numerator for this solution’s mole fraction is, therefore, 3.0 mol NaCl. The denominator may be computed by deriving the molar amount of water corresponding to 1.0 kg

and then substituting these molar amounts into the definition for mole fraction.

Check Your Learning
The mole fraction of iodine, I2, dissolved in dichloromethane, CH2Cl2, is 0.115. What is the molal concentration, m, of iodine in this solution?

Answer:

1.50 m

3.

Calculation of a Vapor Pressure
Compute the vapor pressure of an ideal solution containing 92.1 g of glycerin, C3H5(OH)3, and 184.4 g of ethanol, C2H5OH, at 40 °C. The vapor pressure of pure ethanol is 0.178 atm at 40 °C. Glycerin is essentially nonvolatile at this temperature.

Solution
Since the solvent is the only volatile component of this solution, its vapor pressure may be computed per Raoult’s law as:

First, calculate the molar amounts of each solution component using the provided mass data.


Next, calculate the mole fraction of the solvent (ethanol) and use Raoult’s law to compute the solution’s vapor pressure.


Check Your Learning
A solution contains 5.00 g of urea, CO(NH2)2 (a nonvolatile solute) and 0.100 kg of water. If the vapor pressure of pure water at 25 °C is 23.7 torr, what is the vapor pressure of the solution?

Answer:

23.4 torr

4.

Calculating the Boiling Point of a Solution
What is the boiling point of a 0.33 m solution of a nonvolatile solute in benzene?

Solution
Use the equation relating boiling point elevation to solute molality to solve this problem in two steps.

  1. Calculate the change in boiling point.
  2. Add the boiling point elevation to the pure solvent’s boiling point.

Check Your Learning
What is the boiling point of the antifreeze described in Example 1?

Answer:

109.2 °C

5.

The Boiling Point of an Iodine Solution
Find the boiling point of a solution of 92.1 g of iodine, I2, in 800.0 g of chloroform, CHCl3, assuming that the iodine is nonvolatile and that the solution is ideal.

Solution
We can solve this problem using four steps.

  1. Convert from grams to moles of I2using the molar mass of I2in the unit conversion factor.
    Result: 0.363 mol
  2. Determine the molality of the solution from the number of moles of solute and the mass of solvent, in kilograms.
    Result: 0.454 m
  3. Use the direct proportionality between the change in boiling point and molal concentration to determine how much the boiling point changes.
    Result: 1.65 °C
  4. Determine the new boiling point from the boiling point of the pure solvent and the change.
    Result: 62.91 °C
    Check each result as a self-assessment.

Check Your Learning
What is the boiling point of a solution of 1.0 g of glycerin, C3H5(OH)3, in 47.8 g of water? Assume an ideal solution.

Answer:

100.12 °C

6.

Calculation of the Freezing Point of a Solution
What is the freezing point of the 0.33 m solution of a nonvolatile nonelectrolyte solute in benzene described in Example 2?

Solution
Use the equation relating freezing point depression to solute molality to solve this problem in two steps.

  1. Calculate the change in freezing point.
  2. Subtract the freezing point change observed from the pure solvent’s freezing point.

Check Your Learning
What is the freezing point of a 1.85 m solution of a nonvolatile nonelectrolyte solute in nitrobenzene?

Answer:

−9.3 °C

7.

Calculation of Osmotic Pressure
What is the osmotic pressure (atm) of a 0.30 M solution of glucose in water that is used for intravenous infusion at body temperature, 37 °C?

Solution
We can find the osmotic pressure, Π, using the formula Π = MRT, where T is on the Kelvin scale (310 K) and the value of R is expressed in appropriate units (0.08206 L atm/mol K).

Check Your Learning
What is the osmotic pressure (atm) a solution with a volume of 0.750 L that contains 5.0 g of methanol, CH3OH, in water at 37 °C?

Answer:

5.3 atm

8.

  1. Determine the change in freezing point from the observed freezing point and the freezing point of pure benzene (Table 2).
  2. Determine the molal concentration from Kf, the freezing point depression constant for benzene (Table 2), and ΔTf.

  3. Determine the number of moles of compound in the solution from the molal concentration and the mass of solvent used to make the solution.
  4. Determine the molar mass from the mass of the solute and the number of moles in that mass.

Check Your Learning
A solution of 35.7 g of a nonelectrolyte in 220.0 g of chloroform has a boiling point of 64.5 °C. What is the molar mass of this compound?

Answer:

1.8 × 102 g/mol

9.

Determination of a Molar Mass from Osmotic Pressure
A 0.500 L sample of an aqueous solution containing 10.0 g of hemoglobin has an osmotic pressure of 5.9 torr at 22 °C. What is the molar mass of hemoglobin?

Solution
Here is one set of steps that can be used to solve the problem:

  1. Convert the osmotic pressure to atmospheres, then determine the molar concentration from the osmotic pressure.


  2. Determine the number of moles of hemoglobin in the solution from the concentration and the volume of the solution.
  3. Determine the molar mass from the mass of hemoglobin and the number of moles in that mass.

Check Your Learning
What is the molar mass of a protein if a solution of 0.02 g of the protein in 25.0 mL of solution has an osmotic pressure of 0.56 torr at 25 °C?

Answer:

2.7 × 104 g/mol

10.

The Freezing Point of a Solution of an Electrolyte
The concentration of ions in seawater is approximately the same as that in a solution containing 4.2 g of NaCl dissolved in 125 g of water. Assume that each of the ions in the NaCl solution has the same effect on the freezing point of water as a nonelectrolyte molecule, and determine the freezing temperature the solution (which is approximately equal to the freezing temperature of seawater).

Solution
We can solve this problem using the following series of steps.

  1. Convert from grams to moles of NaCl using the molar mass of NaCl in the unit conversion factor.
    Result: 0.072 mol NaCl
  2. Determine the number of moles of ions present in the solution using the number of moles of ions in 1 mole of NaCl as the conversion factor (2 mol ions/1 mol NaCl).
    Result: 0.14 mol ions
  3. Determine the molality of the ions in the solution from the number of moles of ions and the mass of solvent, in kilograms.
    Result: 1.1 m
  4. Use the direct proportionality between the change in freezing point and molal concentration to determine how much the freezing point changes.
    Result: 2.0 °C
  5. Determine the new freezing point from the freezing point of the pure solvent and the change.
    Result: −2.0 °C
    Check each result as a self-assessment.

Check Your Learning
Assume that each of the ions in calcium chloride, CaCl2, has the same effect on the freezing point of water as a nonelectrolyte molecule. Calculate the freezing point of a solution of 0.724 g of CaCl2 in 175 g of water.

Answer:

−0.208 °C

OTHER QUESTIONS

  1. Which is/are part of the macroscopic domain of solutions and which is/are part of the microscopic domain: boiling point elevation, Henry’s law, hydrogen bond, ion-dipole attraction, molarity, nonelectrolyte, nonstoichiometric compound, osmosis, solvated ion?
  2. What is the microscopic explanation for the macroscopic behavior illustrated in Figure 7 in Chapter 11.3 Solubility?
  3. Sketch a qualitative graph of the pressure versus time for water vapor above a sample of pure water and a sugar solution, as the liquids evaporate to half their original volume.
  4. A solution of potassium nitrate, an electrolyte, and a solution of glycerin (C3H5(OH)3), a nonelectrolyte, both boil at 100.3 °C. What other physical properties of the two solutions are identical?
  5. What are the mole fractions of H3PO4 and water in a solution of 14.5 g of H3PO4in 125 g of water?

    (a) Outline the steps necessary to answer the question.

    (b) Answer the question.

  6. What are the mole fractions of HNO3 and water in a concentrated solution of nitric acid (68.0% HNO3 by mass)?

    (a) Outline the steps necessary to answer the question.

    (b) Answer the question.

  7. Calculate the mole fraction of each solute and solvent:

    (a) 583 g of H2SO4 in 1.50 kg of water—the acid solution used in an automobile battery

    (b) 0.86 g of NaCl in 1.00 × 102 g of water—a solution of sodium chloride for intravenous injection

    (c) 46.85 g of codeine, C18H21NO3, in 125.5 g of ethanol, C2H5OH

    (d) 25 g of I2 in 125 g of ethanol, C2H5OH

  8. Calculate the mole fraction of each solute and solvent:

    (a) 0.710 kg of sodium carbonate (washing soda), Na2CO3, in 10.0 kg of water—a saturated solution at 0 °C

    (b) 125 g of NH4NO3 in 275 g of water—a mixture used to make an instant ice pack

    (c) 25 g of Cl2 in 125 g of dichloromethane, CH2Cl2

    (d) 0.372 g of histamine, C5H9N, in 125 g of chloroform, CHCl3

  9. Calculate the mole fractions of methanol, CH3OH; ethanol, C2H5OH; and water in a solution that is 40% methanol, 40% ethanol, and 20% water by mass. (Assume the data are good to two significant figures.)
  10. What is the difference between a 1 M solution and a 1 m solution?
  11. What is the molality of phosphoric acid, H3PO4, in a solution of 14.5 g of H3PO4in 125 g of water?

    (a) Outline the steps necessary to answer the question.

    (b) Answer the question.

  12. What is the molality of nitric acid in a concentrated solution of nitric acid (68.0% HNO3 by mass)?

    (a) Outline the steps necessary to answer the question.

    (b) Answer the question.

  13. Calculate the molality of each of the following solutions:

    (a) 583 g of H2SO4 in 1.50 kg of water—the acid solution used in an automobile battery

    (b) 0.86 g of NaCl in 1.00 × 102 g of water—a solution of sodium chloride for intravenous injection

    (c) 46.85 g of codeine, C18H21NO3, in 125.5 g of ethanol, C2H5OH

    (d) 25 g of I2 in 125 g of ethanol, C2H5OH

  14. Calculate the molality of each of the following solutions:

    (a) 0.710 kg of sodium carbonate (washing soda), Na2CO3, in 10.0 kg of water—a saturated solution at 0°C

    (b) 125 g of NH4NO3 in 275 g of water—a mixture used to make an instant ice pack

    (c) 25 g of Cl2 in 125 g of dichloromethane, CH2Cl2

    (d) 0.372 g of histamine, C5H9N, in 125 g of chloroform, CHCl3

  15. The concentration of glucose, C6H12O6, in normal spinal fluid is . What is the molality of the solution?
  16. A 13.0% solution of K2CO3 by mass has a density of 1.09 g/cm3. Calculate the molality of the solution.
  17. Why does 1 mol of sodium chloride depress the freezing point of 1 kg of water almost twice as much as 1 mol of glycerin?
  18. What is the boiling point of a solution of 115.0 g of sucrose, C12H22O11, in 350.0 g of water?

    (a) Outline the steps necessary to answer the question

    (b) Answer the question

  19. What is the boiling point of a solution of 9.04 g of I2 in 75.5 g of benzene, assuming the I2 is nonvolatile?

    (a) Outline the steps necessary to answer the question.

    (b) Answer the question.

  20. What is the freezing temperature of a solution of 115.0 g of sucrose, C12H22O11, in 350.0 g of water, which freezes at 0.0 °C when pure?

    (a) Outline the steps necessary to answer the question.

    (b) Answer the question.

  21. What is the freezing point of a solution of 9.04 g of I2 in 75.5 g of benzene?

    (a) Outline the steps necessary to answer the following question.

    (b) Answer the question.

  22. What is the osmotic pressure of an aqueous solution of 1.64 g of Ca(NO3)2 in water at 25 °C? The volume of the solution is 275 mL.

    (a) Outline the steps necessary to answer the question.

    (b) Answer the question.

  23. What is osmotic pressure of a solution of bovine insulin (molar mass, 5700 g mol−1) at 18 °C if 100.0 mL of the solution contains 0.103 g of the insulin?

    (a) Outline the steps necessary to answer the question.

    (b) Answer the question.

  24. What is the molar mass of a solution of 5.00 g of a compound in 25.00 g of carbon tetrachloride (bp 76.8 °C; Kb = 5.02 °C/m) that boils at 81.5 °C at 1 atm?

    (a) Outline the steps necessary to answer the question.

    (b) Solve the problem.

  25. A sample of an organic compound (a nonelectrolyte) weighing 1.35 g lowered the freezing point of 10.0 g of benzene by 3.66 °C. Calculate the molar mass of the compound.
  26. A 1.0 m solution of HCl in benzene has a freezing point of 0.4 °C. Is HCl an electrolyte in benzene? Explain.
  27. A solution contains 5.00 g of urea, CO(NH2)2, a nonvolatile compound, dissolved in 0.100 kg of water. If the vapor pressure of pure water at 25 °C is 23.7 torr, what is the vapor pressure of the solution?
  28. A 12.0-g sample of a nonelectrolyte is dissolved in 80.0 g of water. The solution freezes at −1.94 °C. Calculate the molar mass of the substance.
  29. Arrange the following solutions in order by their decreasing freezing points: 0.1 mNa3PO4, 0.1 m C2H5OH, 0.01 m CO2, 0.15 m NaCl, and 0.2 m CaCl2.
  30. Calculate the boiling point elevation of 0.100 kg of water containing 0.010 mol of NaCl, 0.020 mol of Na2SO4, and 0.030 mol of MgCl2, assuming complete dissociation of these electrolytes.
  31. How could you prepare a 3.08 m aqueous solution of glycerin, C3H8O3? What is the freezing point of this solution?
  32. A sample of sulfur weighing 0.210 g was dissolved in 17.8 g of carbon disulfide, CS2 (Kb = 2.43 °C/m). If the boiling point elevation was 0.107 °C, what is the formula of a sulfur molecule in carbon disulfide?
  33. In a significant experiment performed many years ago, 5.6977 g of cadmium iodide in 44.69 g of water raised the boiling point 0.181 °C. What does this suggest about the nature of a solution of CdI2?
  34. Lysozyme is an enzyme that cleaves cell walls. A 0.100-L sample of a solution of lysozyme that contains 0.0750 g of the enzyme exhibits an osmotic pressure of 1.32 × 10−3 atm at 25 °C. What is the molar mass of lysozyme?
  35. The osmotic pressure of a solution containing 7.0 g of insulin per liter is 23 torr at 25 °C. What is the molar mass of insulin?
  36. The osmotic pressure of human blood is 7.6 atm at 37 °C. What mass of glucose, C6H12O6, is required to make 1.00 L of aqueous solution for intravenous feeding if the solution must have the same osmotic pressure as blood at body temperature, 37 °C?
  37. What is the freezing point of a solution of dibromobenzene, C6H4Br2, in 0.250 kg of benzene, if the solution boils at 83.5 °C?
  38. What is the boiling point of a solution of NaCl in water if the solution freezes at −0.93 °C?
  39. The sugar fructose contains 40.0% C, 6.7% H, and 53.3% O by mass. A solution of 11.7 g of fructose in 325 g of ethanol has a boiling point of 78.59 °C. The boiling point of ethanol is 78.35 °C, and Kb for ethanol is 1.20 °C/m. What is the molecular formula of fructose?
  40. The vapor pressure of methanol, CH3OH, is 94 torr at 20 °C. The vapor pressure of ethanol, C2H5OH, is 44 torr at the same temperature.

    (a) Calculate the mole fraction of methanol and of ethanol in a solution of 50.0 g of methanol and 50.0 g of ethanol.

    (b) Ethanol and methanol form a solution that behaves like an ideal solution. Calculate the vapor pressure of methanol and of ethanol above the solution at 20 °C.

    (c) Calculate the mole fraction of methanol and of ethanol in the vapor above the solution.

  41. The triple point of air-free water is defined as 273.15 K. Why is it important that the water be free of air?
  42. Meat can be classified as fresh (not frozen) even though it is stored at −1 °C. Why wouldn’t meat freeze at this temperature?
  43. An organic compound has a composition of 93.46% C and 6.54% H by mass. A solution of 0.090 g of this compound in 1.10 g of camphor melts at 158.4 °C. The melting point of pure camphor is 178.4 °C. Kf for camphor is 37.7 °C/m. What is the molecular formula of the solute? Show your calculations.
  44. A sample of HgCl2 weighing 9.41 g is dissolved in 32.75 g of ethanol, C2H5OH (Kb = 1.20 °C/m). The boiling point elevation of the solution is 1.27 °C. Is HgCl2an electrolyte in ethanol? Show your calculations.
  45. A salt is known to be an alkali metal fluoride. A quick approximate determination of freezing point indicates that 4 g of the salt dissolved in 100 g of water produces a solution that freezes at about −1.4 °C. What is the formula of the salt? Show your calculations.
  46. Answers to Chemistry End of Chapter Exercises

    2. The strength of the bonds between like molecules is stronger than the strength between unlike molecules. Therefore, some regions will exist in which the water molecules will exclude oil molecules and other regions will exist in which oil molecules will exclude water molecules, forming a heterogeneous region.

    4. Both form homogeneous solutions; their boiling point elevations are the same, as are their lowering of vapor pressures. Osmotic pressure and the lowering of the freezing point are also the same for both solutions.

    6. (a) Find number of moles of HNO3 and H2O in 100 g of the solution. Find the mole fractions for the components.

    (b) The mole fraction of HNO3 is 0.378. The mole fraction of H2O is 0.622.

    8. (a) ; ; (b) ; ; (c) ; ; (d) ; 

    10. In a 1 M solution, the mole is contained in exactly 1 L of solution. In a 1 m solution, the mole is contained in exactly 1 kg of solvent.

    12. (a) Determine the molar mass of HNO3. Determine the number of moles of acid in the solution. From the number of moles and the mass of solvent, determine the molality. (b) 33.7 m

    14. (a) 6.70 × 10−1m; (b) 5.67 m; (c) 2.8 m; (d) 0.0358 m

    16. 1.08 m

    18. (a) Determine the molar mass of sucrose; determine the number of moles of sucrose in the solution; convert the mass of solvent to units of kilograms; from the number of moles and the mass of solvent, determine the molality; determine the difference between the boiling point of water and the boiling point of the solution; determine the new boiling point. (b) 100.5 °C

    20. (a) Determine the molar mass of sucrose; determine the number of moles of sucrose in the solution; convert the mass of solvent to units of kilograms; from the number of moles and the mass of solvent, determine the molality; determine the difference between the freezing temperature of water and the freezing temperature of the solution; determine the new freezing temperature. (b) −1.8 °C

    22. (a) Determine the molar mass of Ca(NO3)2; determine the number of moles of Ca(NO3)2 in the solution; determine the number of moles of ions in the solution; determine the molarity of ions, then the osmotic pressure. (b) 2.67 atm

    24. (a) Determine the molal concentration from the change in boiling point and Kb; determine the moles of solute in the solution from the molal concentration and mass of solvent; determine the molar mass from the number of moles and the mass of solute. (b) 2.1 × 102 g mol−1

    26. No. Pure benzene freezes at 5.5 °C, and so the observed freezing point of this solution is depressed by ΔTf = 5.5 − 0.4 = 5.1 °C. The value computed, assuming no ionization of HCl, is ΔTf = (1.0 m)(5.14 °C/m) = 5.1 °C. Agreement of these values supports the assumption that HCl is not ionized.

    28. 144 g mol−1

    30. 0.870 °C

    32. S8

    34. 1.39 × 104 g mol−1

    36. 54 g

    38. 100.26 °C

    40. (a) ; ; (b) Vapor pressures are: CH3OH: 55 torr; C2H5OH: 18 torr; (c) CH3OH: 0.75; C2H5OH: 0.25

    42. The ions and compounds present in the water in the beef lower the freezing point of the beef below −1 °C.

    44. 

    The observed change equals the theoretical change; therefore, no dissociation occurs.

Mugisa Geofrey and SOLOMON TATWEBWA

Mugisa Geofrey Zziwa is a learning facilitator with Ultimate MultiMedia Consult. With knowledge of the following topics:  Digital Pedagogy training or digital teaching skills, how to integrate ICT in teaching.  Journalism and the Internet/Computers (How internet helps journalism)  Basic web design & CMS and Multimedia Content publishing  Digital security and safety basics for journalists  Best practices for ensuring safety online  Data Mashups  Collaborative digital content development tools  Live streaming and Live reporting  Immersive Storytelling tools and practices  Among others I have conducted a number of trainings which include: • Multimedia Journalism and Digital Safety training for university Students held in Makerere University, Kampala International University and Cavendish University and sponsored by the American Embassy Uganda. • Digital Pedagogy training for Science Technology Engineering and Mathematics (STEM) Teachers held in Iganga Girls SSS in Iganga District for Eastern region Uganda, St. Maria Gorretti in MPigi District for Central region Uganda, and Teso College ALOET for the Karamoja region Uganda. Sponsored by Forum for African Women Educationalists Uganda (FAWEU) Training Teachers on integration of ICT in teaching and delivering lessons to students. • Digital Pedagogy at American Center for Teachers by Teachers In Need (TIN) Uganda. • Facilitator on Digital Pedagogy with ICT Teachers Association Uganda (ITAU) at American Center, Kyebambe Girls SSS in FortPortal for western region Uganda, Dr. Obote College Boro Boro Lira for Nothern Region Uganda.

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