Example Calculations involving Colligative Properties (Solution Properties)

Calcium Chloride (CaCl 2, Mol. Mass = g/mol, d = 2.15 g/ml) is often used as a de-icing agent for sidewalks. Given that a saturated aqueous solution of CaCl 2 is 32.0% by mass and has a density of 1.56 g/ml, determine the freezing point of this saturated solution. Note that for H 2 O, mol. mass = g/mol, k b =  C/m, k f =  C/m, d= g/ml. i.Read question carefully. What are you trying to determine?

Calcium Chloride (CaCl 2, Mol. Mass = g/mol, d = 2.15 g/ml) is often used as a de-icing agent for sidewalks. Given that a saturated aqueous solution of CaCl 2 is 32.0% by mass and has a density of 1.56 g/ml, determine the freezing point of this saturated solution. Note that for H 2 O, mol. mass = g/mol, k b =  C/m, k f =  C/m, d= g/ml. i.Read question carefully. What are you trying to determine? Freezing point ii.Identify the solute and solvent: Solute = CaCl 2, Solvent = H 2 O iii.Identify the appropriate equation: Fp depression: FP soln = FP solv –  T f where:  T f = i k f m

Calcium Chloride (CaCl 2, Mol. Mass = g/mol, d = 2.15 g/ml) is often used as a de-icing agent for sidewalks. Given that a saturated aqueous solution of CaCl 2 is 32.0% by mass and has a density of 1.56 g/ml, determine the freezing point of this saturated solution. Note that for H 2 O, mol. mass = g/mol, k b =  C/m, k f =  C/m, d= g/ml. iii.Identify the appropriate equation: Fp depression: FP soln = FP solv –  T f where:  T f = i k f m iv.Organize Information: FP H2O = 0.0  C (must know) i = 3 (Ca 2+, 2 Cl - ; 3 ions formed)

Calcium Chloride (CaCl 2, Mol. Mass = g/mol, d = 2.15 g/ml) is often used as a de-icing agent for sidewalks. Given that a saturated aqueous solution of CaCl 2 is 32.0% by mass and has a density of 1.56 g/ml, determine the freezing point of this saturated solution. Note that for H 2 O, mol. mass = g/mol, k b =  C/m, k f =  C/m, d= g/ml. iii.Identify the appropriate equation: Fp depression: FP soln = FP solv –  T f where:  T f = i k f m iv.Organize Information: FP H2O = 0.0  C (must know) i = 3 (Ca 2+, 2 Cl - ; 3 ions formed) k f =  C/m m = ????? (molality not given!!!!!)

Calcium Chloride (CaCl 2, Mol. Mass = g/mol, d = 2.15 g/ml) is often used as a de-icing agent for sidewalks. Given that a saturated aqueous solution of CaCl 2 is 32.0% by mass and has a density of 1.56 g/ml, determine the freezing point of this saturated solution. Note that for H 2 O, mol. mass = g/mol, k b =  C/m, k f =  C/m, d= g/ml. v.Must convert given concentration to molality (m): vi.Given Concentration unit?

Calcium Chloride (CaCl 2, Mol. Mass = g/mol, d = 2.15 g/ml) is often used as a de-icing agent for sidewalks. Given that a saturated aqueous solution of CaCl 2 is 32.0% by mass and has a density of 1.56 g/ml, determine the freezing point of this saturated solution. Note that for H 2 O, mol. mass = g/mol, k b =  C/m, k f =  C/m, d= g/ml. v.Must convert given concentration to molality (m) vi.Given Concentration unit? 32.0% by mass CaCl 2 vii.Use 32% by mass as the starting point 32% CaCl 2 by mass = 32 g CaCl 2 / 100 g soln so input: (1) 32 g CaCl 2 and (2) 100 g soln into the table

Calcium Chloride (CaCl 2, Mol. Mass = g/mol, d = 2.15 g/ml) is often used as a de-icing agent for sidewalks. Given that a saturated aqueous solution of CaCl 2 is 32.0% by mass and has a density of 1.56 g/ml, determine the freezing point of this saturated solution. Note that for H 2 O, mol. mass = g/mol, k b =  C/m, k f =  C/m, d= g/ml. Input: (1) 32 g CaCl 2 and (2) 100 g soln into the appropriate cells! CaCl 2 H2OH2OSoln mole gram ml

Calcium Chloride (CaCl 2, Mol. Mass = g/mol, d = 2.15 g/ml) is often used as a de-icing agent for sidewalks. Given that a saturated aqueous solution of CaCl 2 is 32.0% by mass and has a density of 1.56 g/ml, determine the freezing point of this saturated solution. Note that for H 2 O, mol. mass = g/mol, k b =  C/m, k f =  C/m, d= g/ml. input: (1) 32 g CaCl 2 and (2) 100 g soln into the appropriate cells! CaCl 2 H2OH2OSoln mole gram 32 g ml

Calcium Chloride (CaCl 2, Mol. Mass = g/mol, d = 2.15 g/ml) is often used as a de-icing agent for sidewalks. Given that a saturated aqueous solution of CaCl 2 is 32.0% by mass and has a density of 1.56 g/ml, determine the freezing point of this saturated solution. Note that for H 2 O, mol. mass = g/mol, k b =  C/m, k f =  C/m, d= g/ml. input: (1) 32 g CaCl 2 and (2) 100 g soln into the appropriate cells! CaCl 2 H2OH2OSoln mole gram 32 g100 g ml

Calcium Chloride (CaCl 2, Mol. Mass = g/mol, d = 2.15 g/ml) is often used as a de-icing agent for sidewalks. Given that a saturated aqueous solution of CaCl 2 is 32.0% by mass and has a density of 1.56 g/ml, determine the freezing point of this saturated solution. Note that for H 2 O, mol. mass = g/mol, k b =  C/m, k f =  C/m, d= g/ml. Now use the definition of molality (m) to find what’s needed: m = mol CaCl 2 / Kg H 2 O We want the following boxes: (1) mol CaCl 2 and (2) Kg H 2 O CaCl 2 H2OH2OSoln mole gram 32 g100 g ml

Calcium Chloride (CaCl 2, Mol. Mass = g/mol, d = 2.15 g/ml) is often used as a de-icing agent for sidewalks. Given that a saturated aqueous solution of CaCl 2 is 32.0% by mass and has a density of 1.56 g/ml, determine the freezing point of this saturated solution. Note that for H 2 O, mol. mass = g/mol, k b =  C/m, k f =  C/m, d= g/ml. Now use the definition of molality (m) to find what’s needed: m = mol CaCl 2 / Kg H 2 O We want the following boxes: (1) mol CaCl 2 and (2) Kg H 2 O CaCl 2 H2OH2OSoln mole ??? gram 32 g???100 g ml

Calcium Chloride (CaCl 2, Mol. Mass = g/mol, d = 2.15 g/ml) is often used as a de-icing agent for sidewalks. Given that a saturated aqueous solution of CaCl 2 is 32.0% by mass and has a density of 1.56 g/ml, determine the freezing point of this saturated solution. Note that for H 2 O, mol. mass = g/mol, k b =  C/m, k f =  C/m, d= g/ml. Use CaCl 2 molar mass to convert g CaCl 2 to mol CaCl 2 32 g CaCl 2 (1 mol CaCl 2 / g CaCl 2 ) = mol CaCl 2 CaCl 2 H2OH2OSoln mole ??? gram 32 g100 g ml

Calcium Chloride (CaCl 2, Mol. Mass = g/mol, d = 2.15 g/ml) is often used as a de-icing agent for sidewalks. Given that a saturated aqueous solution of CaCl 2 is 32.0% by mass and has a density of 1.56 g/ml, determine the freezing point of this saturated solution. Note that for H 2 O, mol. mass = g/mol, k b =  C/m, k f =  C/m, d= g/ml. Use CaCl 2 molar mass to convert g CaCl 2 to mol CaCl 2 32 g CaCl 2 (1 mol CaCl 2 / g CaCl 2 ) = mol CaCl 2 CaCl 2 H2OH2OSoln mole mol gram 32 g100 g ml

Calcium Chloride (CaCl 2, Mol. Mass = g/mol, d = 2.15 g/ml) is often used as a de-icing agent for sidewalks. Given that a saturated aqueous solution of CaCl 2 is 32.0% by mass and has a density of 1.56 g/ml, determine the freezing point of this saturated solution. Note that for H 2 O, mol. mass = g/mol, k b =  C/m, k f =  C/m, d= g/ml. Now find Kg H 2 O by subtracting the mass of soln and solute 100 g soln – 32 g CaCl 2 = 68 g or Kg H 2 O CaCl 2 H2OH2OSoln mole mol gram 32 g???100 g ml

Calcium Chloride (CaCl 2, Mol. Mass = g/mol, d = 2.15 g/ml) is often used as a de-icing agent for sidewalks. Given that a saturated aqueous solution of CaCl 2 is 32.0% by mass and has a density of 1.56 g/ml, determine the freezing point of this saturated solution. Note that for H 2 O, mol. mass = g/mol, k b =  C/m, k f =  C/m, d= g/ml. Now find Kg H 2 O by subtracting the mass of soln and solute 100 g soln – 32 g CaCl 2 = 68 g or Kg H 2 O CaCl 2 H2OH2OSoln mole mol gram 32 g68 g100 g ml

Calcium Chloride (CaCl 2, Mol. Mass = g/mol, d = 2.15 g/ml) is often used as a de-icing agent for sidewalks. Given that a saturated aqueous solution of CaCl 2 is 32.0% by mass and has a density of 1.56 g/ml, determine the freezing point of this saturated solution. Note that for H 2 O, mol. mass = g/mol, k b =  C/m, k f =  C/m, d= g/ml. We can now calculate molarity (m) m = mol CaCl 2 / Kg H2O = mol /.068 Kg = m CaCl 2 H2OH2OSoln mole mol gram 32 g68 g100 g ml

Calcium Chloride (CaCl 2, Mol. Mass = g/mol, d = 2.15 g/ml) is often used as a de-icing agent for sidewalks. Given that a saturated aqueous solution of CaCl 2 is 32.0% by mass and has a density of 1.56 g/ml, determine the freezing point of this saturated solution. Note that for H 2 O, mol. mass = g/mol, k b =  C/m, k f =  C/m, d= g/ml. iii.Identify the appropriate equation: Fp depression: FP soln = FP solv –  T f where:  T f = i k f m iv.Organize Information: FP H2O = 0.0  C (must know) i = 3 (Ca 2+, 2 Cl - ; 3 ions formed) k f =  C/m m = m viii.Plug in numbers and calculate (Plug and Chug!)

Calcium Chloride (CaCl 2, Mol. Mass = g/mol, d = 2.15 g/ml) is often used as a de-icing agent for sidewalks. Given that a saturated aqueous solution of CaCl 2 is 32.0% by mass and has a density of 1.56 g/ml, determine the freezing point of this saturated solution. Note that for H 2 O, mol. mass = g/mol, k b =  C/m, k f =  C/m, d= g/ml. ix.FP H2O = 0.0  C (must know) i = 3 (Ca 2+, 2 Cl - ; 3 ions formed) k f =  C/m m = m x.  T f = i k f m :  T f = 3 (1.858  C/m ) ( m) =  C xi.FP soln = FP H20 –  T f : FP soln = 0.0  C –  C =  C (FINISHED!)

Hemoglobin (HG) is the oxygen transport protein in humans. An aqueous solution of HG was prepared by dissolving 8.75 g HG into enough water to prepare ml of solution (d soln = 1.05 g/ml). The osmotic pressure of this solution was measured at 25.0 C and determined to be 10.0 torr. Determine the molar mass of Hemoglobin (HG). Note that for H 2 O, mol. mass = g/mol, k b =  C/m, k f =  C/m, d= g/ml. i.Read the question carefully. What are you trying to determine?

Hemoglobin (HG) is the oxygen transport protein in humans. An aqueous solution of HG was prepared by dissolving 8.75 g HG into enough water to prepare ml of solution (d soln = 1.05 g/ml). The osmotic pressure of this solution was measured at 25.0 C and determined to be 10.0 torr. Determine the molar mass of Hemoglobin (HG). Note that for H 2 O, mol. mass = g/mol, k b =  C/m, k f =  C/m, d= g/ml. i.Read the question carefully. What are you trying to determine? Molar mass of HG ii.Identify the solute and solvent: Solute = HG, Solvent = H 2 O iii.Identify the appropriate solution property given and equation:

Hemoglobin (HG) is the oxygen transport protein in humans. An aqueous solution of HG was prepared by dissolving 8.75 g HG into enough water to prepare ml of solution (d soln = 1.05 g/ml). The osmotic pressure of this solution was measured at 25.0 C and determined to be 10.0 torr. Determine the molar mass of Hemoglobin (HG). Note that for H 2 O, mol. mass = g/mol, k b =  C/m, k f =  C/m, d= g/ml. i.Read the question carefully. What are you trying to determine? Molar mass of HG ii.Identify the solute and solvent: Solute = HG, Solvent = H 2 O iii.Identify the appropriate solution property given and equation: Osmotic Pressure  = i R T M

Hemoglobin (HG) is the oxygen transport protein in humans. An aqueous solution of HG was prepared by dissolving 8.75 g HG into enough water to prepare ml of solution (d soln = 1.05 g/ml). The osmotic pressure of this solution was measured at 25.0 C and determined to be 10.0 torr. Determine the molar mass of Hemoglobin (HG). Note that for H 2 O, mol. mass = g/mol, k b =  C/m, k f =  C/m, d= g/ml. iv.Organize information:  = i R T M  = 10 torr (1 atm / 760 torr) = atm (must be atm) i = 1 (proteins are extremely large molecules) R = (L atm/mol K) (gas constant) T = 25.0 C = K (Temp must be kelvin) v.Solve for concentration M: M =  / (i R T) M = / (1   ) = x M

Hemoglobin (HG) is the oxygen transport protein in humans. An aqueous solution of HG was prepared by dissolving 8.75 g HG into enough water to prepare ml of solution (d soln = 1.05 g/ml). The osmotic pressure of this solution was measured at 25.0 C and determined to be 10.0 torr. Determine the molar mass of Hemoglobin (HG). Note that for H 2 O, mol. mass = g/mol, k b =  C/m, k f =  C/m, d= g/ml. iv.Use the concentration now to find moles HG: M = mol HG / L soln where M = x10 -4 mol / L (calc) and L soln = L (given) Solving for mol HG mol HG = M (L soln) = x mol/L (0.25 L) = x mol

Hemoglobin (HG) is the oxygen transport protein in humans. An aqueous solution of HG was prepared by dissolving 8.75 g HG into enough water to prepare ml of solution (d soln = 1.05 g/ml). The osmotic pressure of this solution was measured at 25.0 C and determined to be 10.0 torr. Determine the molar mass of Hemoglobin (HG). Note that for H 2 O, mol. mass = g/mol, k b =  C/m, k f =  C/m, d= g/ml. v.Finally use the mol Hg and g HG to find molar mass: Molar mass HG = g HG / mol HG g HG = 8.75 g (given above) mol HG = x mol Mol. Mass HG = 8.75 g / x mol = g/mol FINISHED!