Quantitative Ways of Expressing Solution Concentration

Back to Secs 13.4-5: Properties of Solutions

Quantitative ways of expressing solution concentration 1. Mass percentage

The mass percentage of a component in a solution is given by mass of component Mass % of component = x100 total mass of solution e.g., What is the mass per cent of solute in a solution containing 3.25 g of Ba(NO3)2 in 100 g H2O?

For work with very dilute solutions, concentrations may be expressed in parts per million (ppm) or parts per billion (ppb): A solution whose concentration is 1 ppm contains 1 g solute per 106 g solution

73 E.g., seawater contains 0.412 g of Ca2+ per kg of water. What is the concentration of Ca2+ in ppm?

2. Mole fraction, X Mol fraction of a component is defined as mol component Xcomponent = total mol all components

E.g., what is the mol fraction of CH3OH in a solution which contains 6.00 g of CH3OH dissolved in 480 g of H2O?

74 3. Molarity, M mol solute As in Ch 4, M = liters solution

4. Molality, m Defined as the number of mol of solute per kilogram of solvent: mol solute m = kg solvent

Notice that molality is defined in terms of solvent mass Note also that molarity is defined in terms of solution volume E.g., find the molality of a solution that contains 36.5 g of napthalene (C10H8) in 420 g of toluene (C7H8)

75 What other information would we need to calculate the molarity of this solution?

Colligative Properties of Solutions Depend upon the concentration but not the kind of solute particles Include: vapor-pressure reduction freeze-point lowering, boiling-point elevation osmotic pressure

Review: what is the difference between an ionic and a molecular solute?

E.g., Calculate the concentration of sodium ions in 0.135 M Na3PO4 solution.

76 1. Vapor-pressure reduction Vapor pressure over a liquid is a dynamic equilibrium (Ch 11) A nonvolatile solute added to a volatile solvent reduces the capacity of the solvent molecules to move from liquid to vapor phase (how?) BUT the rate at which solvent molecules move from vapor to liquid phase is not changed

The extent to which the vapor pressure is lowered is proportional to the solute concentration

How to calculate the vapor pressure above a solution?

Raoult's Law

77 o P = XAPA P = vapor pressure of solution

XA = mol fraction of solvent

o PA = vapor pressure of pure solvent

Ideal solutions are said to obey Raoult's Law

E.g., find the vapor pressure of H2O above a solution prepared by adding 10.00g of lactose (C12H22O11) to 100 g water at 338 K (the vapor pressure of H2O is 187.5 mm Hg)

When do solutions not obey Raoult's Law? What is responsible for deviations from ideal behavior?

78 What if both the solvent and solute are volatile? How to calculate vapor pressure?

2. Boiling-point elevation

How does the vapor pressure of a pure liquid respond to increasing temperature?

What effect does the addition of a nonvolatile solute have upon the vapor pressure of a volatile solvent?

Vapor Pressure vs Temperature curves: recall the discussion of phase diagrams from Ch. 11......

79 Since the addition of solute decreases the vapor pressure of the solvent, the boiling point of the solvent increases....

The increase in boiling point, Tb, is proportional to the concentration of solute Express in terms of molality:

Tb = Kbm

Kb = molal boiling point elevation constant m = molality of solute particles 3. Freezing point depression

Tf = Kfm

Kf = molal freeze-point depression constant m = molality of solute particles

E.g., find the freezing and boiling points of a solution of

100 g of ethylene glycol, C2H6O2, in 900 g of H2O (Kf = 1.86 o o C/m; Kb = 0.52 C/m)

80 Remember: colligative properties depend upon the total number of solute particles, independent of their nature

E.g., arrange the following aqueous solutions in order of increasing boiling point: 0.030 m glycerin; 0.020 m KBr; 0.030 m benzoic acid,

HC7H5O2

4. Osmosis

Movement of solvent through a semipermeable membrane

Solvent moves from a region of low solute concentration 81 to a region of high solute concentration

The pressure required to prevent osmosis is known as the osmotic pressure, , of the solution

The osmotic pressure  is given by the relation π  MRT Where M = molarity of solution and R = gas constant

E.g., What is the osmotic pressure of an aqueous solution containing 1.10 g of urea, (NH2)2CO, in 100 mL of solution at 20oC?

82 What is meant by a hypertonic solution? By a hypotonic solution?

Problems du Jour

The density of acetonitrile, CH3CN, is 0.876 g/mL, and the density of methanol, CH3OH, is 0.791 g/mL. A solution is made by dissolving 20.0 mL of CH3OH in 100.0 mL CH3CN.

Calculate the mol fraction of CH3OH.

83 Calculate the molality of CH3OH in the solution.

Assuming the volumes are additive, find the molarity of CH3OH.

Problems du Jour Calculate the vapor pressure of water above a solution made by adding 5.00 g sodium sulfate to 115 g H2O at 338 K (the vapor pressure of water = 187.5 torr at 338 K)

84 Calculate the freezing and boiling points of a solution made by adding 2.75 g MgCl2 to 80.0 mL of water (Kf = o o 1.86 C/m; Kb=0.52 C/m for water)

Problem du Jour

Calculate the mass of ethylene glycol, C2H6O2, that must be added to 1.00 kg of ethanol, C2H5OH, to reduce its vapor pressure by 13.2 torr at 35oC. The vapor pressure of o pure C2H5OH is 100 torr at 35 C.

85 Problem du Jour The cooling system of a car is filled with a solution formed by adding equal volumes of water (density=1.00 g/mL) and ethylene glycol (density = 1.12 g/mL). Calculate the o freezing and boiling points for the mixture. (Kf = 1.86 C/m; o Kb=0.52 C/m for water)