Calculations Involving Colligative Properties

Introduction We now understand colligative properties. To use this knowledge, we need to be able to predict these colligative properties. Freezing Point Depression Boiling Point Elevation

Introduction We also need to use a different kind of concentration determination. Instead of molarity, we will use molality, m mole fraction, X

Molality Molarity - we measure the number of mols of solute in the volume of the solution. M solution = n solute /V solution Molality - we measure the number of mols of solute in the mass of solvent. m solution = n solute /m solvent

Molality m solution = n solute /m solvent The mass of the solvent is measured in kilograms, kg. 1 mole of solute in 1,000 g of solvent gives a 1 m solution.

Molality Example 1 Find the molality of g of sodium chloride dissolved in kg of water. m NaCl = g m H2O = kg M NaCl = g/mol m = n NaCl /m H2O n NaCl = m NaCl /M NaCl =87.66 g/58.44 g/mol n NaCl = mol =1.500 mol/2.500 kg m = mol/kg

Molality How many grams of potassium iodide must be dissolved in g of water to produce a molal KI solution? m solution = m m H2O = g = kg M KI = g/mol m = n KI /m H2O =n KI = m x m H2O n KI = mol (0.060)(0.5000) mol m KI = n KI x M KI =(0.030)(166.0) g= 5.0 g Example 2

Mole Fraction Mole Fraction is the ratio of number of mols of the solute to the total number of mols of the solute plus the solvent. We use the symbol X to represent the mole fraction. X solute = n solute n solute + n solvent

Mole Fraction Example 3 Ethylene glycol, C 2 H 6 O 2, is added to automobile cooling systems to protect against cold weather. What is the mole fraction of each component in a solution containing 1.25 mols of ethylene glycol (EG) and 4.00 mol of water? n EG = 1.25 mol n H2O = 4.00 mol X EG = n EG n EG + n H2O = 1.25 mol 1.25 mol mol =0.238 X H2O = n H2O n EG + n H2O = 4.00 mol 1.25 mol mol =0.762

Colligative Calculations The magnitudes of freezing point depression (∆T f ) and boiling point elevation (∆T b ) are directly proportional to the molal concentration of the solute, if the solute is molecular and not ionic.

Colligative Calculations The magnitudes of freezing point depression (∆T f ) and boiling point elevation (∆T b ) are directly proportional to the molal concentration of all ions in solution, if the solute is ionic.

Colligative Calculations ∆T f = K f x m where ∆T f is the freezing point depression of the solution K f is the molal freezing point constant for the solvent. m is the molal concentration of the solution

Colligative Calculations ∆T b = K b x m where ∆T b is the boiling point elevation of the solution K b is the molal boiling point constant for the solvent. m is the molal concentration of the solution

Example 4 What is the freezing point depression of a benzene (C 6 H 6, BZ) solution containing 400 g of benzene and 200 g of the compound acetone (C 3 H 6 O, AC). K f for benzene is 5.12°C/m. m BZ = 400 g = kg m AC = 200 g M AC = 58.0 g/mol K f = 5.12°C/m n AC = m AC M AC = 200 g 58.0 g/mol 3.45 mol m = n AC m BZ = 3.45 mol kg =8.62 m Colligative Calculations n AC = ∆T f = K f x m= (5.12°C/m)(8.62 m) = 44.1°C

NaCl produces 2 mols of particles for each mol of salt added; m = 2(1.50 m) = 3.00 m Example 5 What is the boiling point of a 1.50 m NaCl solution? m = 1.50 m K b = 0.512°C/m T b = 100.0°C Colligative Calculations ∆T b = K b x m= (0.512°C/m)(3.00 m) = 1.54°C T = T b + ∆T b = 100.0°C °C = 101.5°C

Summary Molality - we measure the number of mols of solute in the mass of solvent. m solution = n solute /m solvent The mass of the solvent is measured in kilograms, kg.

Mole Fraction is the ratio of number of mols of the solute to the total number of mols of the solute plus the solvent. We use the symbol X to represent the mole fraction. X solute = n solute n solute + n solvent Summary

∆T f = K f x m; ∆T f is the freezing point depression of the solution, K f is the molal freezing point constant for the solute, and m is the molal concentration of the solution. ∆T b = K b x m; ∆T b is the boiling point elevation of the solution, K b is the molal boiling point constant for the solute, and m is the molal concentration of the solution. Summary