Chapter Twelve

Physical Properties

Of Solutions

Outline of the Chapter

• The fundamental properties of Solutions

• Working with solutions– Concentration Units

• Saturated Solutions and Equilibrium

• Colligative Properties– Freezing point depression– Boiling point elevation

Some Types Of Solutions

Solution Concentration

• Molarity is the moles of solute per liter of solution.

moles of solute (mol)Molarity (M) = _____________________________

volume of solution (L)

• Molarity is the most frequently used concentration in chemical situations. Needed in many calculations to determine how many moles are present in a certain volume of solution:

moles of solute = volume of solution x molarity

More Concentration Units

amount of solute (g)

Percent by mass = ____________________________ x 100%

amount of solution (g)

volume of solute (L)

Percent by volume = ____________________________ x 100%

volume of solution (L)

amount of solute (g)

Mass/volume percent = ___________________________ x 100%

volume of solution (L)

Solutions By “Parts”

• Parts per million is the number of particles of solute per one-million particles of solution. Fluoridated drinking water contains ~ 1 ppm of fluoride ion.

1 ppm = 1 mg/L (10-3)• Parts per billion is the number of particles of

solute per one-billion particles of solution.

1 ppb = 1 µg/L (10-6)• Parts per trillion is the number of particles of

solute per one-trillion particles of solution.

1 ppt = 1 ng/L (10-9)

Molality

• Molarity varies with temperature due to the expansion or contraction in the volume of the solution.

• To be independent of temperature, a concentration unit must be based on mass only, not volume.

• Molality (m) is the number of moles of solute per one kilogram of solvent (not solution!). Molality does not vary with temperature.

(kg)solventofmass

soluteofmolesm

moles of solute (mol)M = _____________________________

volume of solution (L)

How many milliliters of water (d = 0.998 g/mL) are required to dissolve 25.0 g of urea and thereby produce a 1.65 m solution of urea, CO(NH2)2?

An Example

Mole Fraction And Mole Percent

• The mole fraction (xi) of a solution component i is the fraction of all the molecules in the solution that are molecules of i.

amount of component i (mol)

xi = = ni / ntotal total amount of solution components (mol)

xi < 1; x1 + x2 + x3 + … = 1

• The mole percent of a solution component is its mole fraction multiplied by 100%.

An Example

Example 12.6 (p.516)

An aqueous solution of ethylene glycol used as an automobile engine coolant is 40.0% HOCH2CH2OH by mass and has a density of 1.05 g/mL. What are the

(a) molarity, (b) molality, and mole fraction of HOCH2CH2OH.

Formation Of Solution

Consider two important factors in solution formation:• Enthalpy of solution• Intermolecular forces in mixtures

Enthalpy Of Solution

• Solution formation can be considered to take place in three steps:

– Move the molecules of solvent apart to make room for the solute molecules. H1 > 0

– Separate the molecules of solute to the distances found between them in the solution. H2 > 0

– Allow the separated solute and solvent molecules to mix randomly. H3 < 0

Hsoln = H1 + H2 + H3

Illustrating enthalpy

terms when solute

dissolves in solvent

Intermolecular Forces In Solution Formation

• If all intermolecular forces are of comparable strength, this type of solution is called an ideal solution and Hsoln = 0.

• If the intermolecular forces between solute and solvent molecules are stronger than other intermolecular forces,

H3 > H1 + H2, Hsoln < 0 - exothermic.

• If the intermolecular forces between solute and solvent molecules are weaker than other intermolecular forces,

H3 < H1 + H2, Hsoln > 0 – endothermic.

• If the intermolecular forces between solute and solvent are much weaker than other intermolecular forces, the solute does not dissolve in the solvent. The compound is described as relatively insoluble in the solvent.

Intermolecular Forces In Solution

Aqueous Solutions Of Ionic Compounds

• Two forces

- inter-ionic attractions that hold ions together

in crystal

- ion-dipole forces, the attraction of water

dipoles for cations and anions, that cause

an ionic solid to dissolve in water • The extent to which an ionic solid dissolves in

water is determined largely by the competition between inter-ionic attractions and the ion-dipole attractions.

Ion-Dipole Forces in Dissolution

An Example

Example 12.8

Predict whether each of the following is likely to be a

solution or a heterogeneous mixture.

a. ethanol, CH3OH, and water, HOH

b. Pentane, CH3(CH2)3CH3, and octane, CH3(CH2)6CH3

c. Sodium chloride, NaCl, and carbon tetrachloride, CCl4

d. 1-decanol, CH3(CH2)8CH2OH, and water, HOH

Formation of a Saturated Solution

Dynamic equilibrium: rate of crystallization = rate of dissolving

Some Solubility Terms

• Liquids that mix in all proportions are called miscible.

• When there is a dynamic equilibrium between an undissolved solute and a solution, the solution is saturated.

• The concentration of the solute in a saturated solution is the solubility of the solute.

• A solution which contains less solute than can be held at equilibrium is unsaturated.

Solubility As A Function of Temperature

• About 95% of all ionic compounds have aqueous solubilities that increase significantly with increasing temperature.

• Most of the remainder have solubilities that change little with temperature.

• A very few have solubilities that decrease with increasing temperature.

• A supersaturated solution is created when a warm, saturated solution is allowed to cool without the precipitation of the excess solute.

Some Solubility Curves

A Supersaturated Solution

Selective Crystallization

When KNO3(s) is crystallized from an aqueous solution of KNO3 containing CuSO4 as an impurity,

CuSO4 remains in the solution.

The Solubilities Of Gases

The solubilities of gases depend on temperature and pressure.

• Most gases become less soluble in liquids as the temperature increases.

• At a constant temperature, the solubility (S) of a gas is directly proportional to the pressure of the gas (Pgas) in equilibrium with the solution.

S = k Pgas (k > 1)

The value of k depends on the particular gas and the solvent.

• The effect of pressure on the solubility of a gas is known as Henry’s Law.

Effect of Temperature on Solubility of Gases

Effect of Pressure on Solubility of Gases

As a gas is compressed into a smaller volume, increasing the number of molecules per unit volume, the number of dissolved molecules per unit volume – the concentration of the solution – also increases.

Aqueous Solubility As AFunction Of Gas Pressure

Vapor Pressures of Solutions

• Raoult’s law states that the vapor pressure of the solvent above a solution (Psolv) is the product of the vapor pressure of the pure solvent (Po

solv) and the mole fraction of the solvent in the solution (xsolv):

Psolv = xsolv . Posolv

• The vapor in equilibrium with an ideal solution of two volatile components has a higher mole fraction of the more volatile component than is found in the liquid.

Fractional Distillation

An Interesting Phenomenon

Two different aqueous solutions in a closed container. After a time, the levels are unequal. Explain why this spontaneous change occurred.

Colligative Properties

Colligative Properties – physical properties of solutions that depend on the number of solute particles present but not on the identity of the solute.

• Freezing point depression• Boiling point elevation

Freezing Point Depressionand Boiling Point Elevation

• Consider solutions with- a volatile solvent

- a solute: nonvolatile, nonelectrolytic, and soluble in liquid solvent but not frozen solvent

• The vapor pressure of the solution is that of the solvent in the solution, and at all temperatures this vapor pressure is lower than that of the pure solvent.

• The presence of the solute lowers (depresses) the freezing point of the solvent (Tf) and increases (elevates) the boiling point of the solvent (Tb).

In a solution, the vapor pressure of

the solvent is lowered

and

the fusion curve is displaced to lower

temperatures

(red curves)

Vapor Pressure LoweringBy A Nonvolatile Solute

Equations for FPD, BPE

Tf = Tf, solution– Tf, solvent = – Kf x m

Tf = Tb, solution– Tb, solvent = Kb x m

Tf – fusion temperature (melting)

Tb – boiling temperaturem – molality of solute

Kf, Kb – constants

FPD And BPE Constants

An Example

What mass of sucrose, C12H22O11, should be added to 75.0 g H2O to raise the boiling point to 100.35 0C?

Summary

• Molarity is expressed as moles per liter and molality is expressed as moles of solute per kilogram of solvent.

• Units used for very dilute concentrations of solutes include parts per million (ppm), parts per billion (ppb), and parts per trillion (ppt).

• The type and magnitude of intermolecular forces are important in solution composition.

• The solubility of a solute is its concentration in a saturated solution.

Summary (continued)

• Solubility of solids vs. gasses

• Solubility of ionic solids increases with increasing temperature

• Solubility of gasses decreases with increasing temperature

• Solubility of gases in solutions:•decreases with an increase in temperature •increases linearly with pressure – Henry’s Law

•Solubility (S) Pgas S = k P (as long as T is constant)

Summary (continued)

• Vapor pressure of solutions vs. pure solvents

• Raoult’s Law:•Vapor pressure of solvent above solution is equal to the product of the mole fraction of solvent and the vapor pressure of pure solvent:

Psolution = xsolvent Psolvent

Summary (continued)

• Colligative properties depend on the particular solvent and the number of solute particles present.

• The presence of solutes lowers the vapor pressure of the solution and causes both a freezing point depression and a boiling point elevation of the solvent.