Dr. Saidane
Chem 200
Lecture Notes
Chapter 13
Properties of Solutions
SOLUTIONS
A solution is a homogeneous mixture of two or more substances in a single phase. In a
solution, atoms, molecules, or ions are thoroughly mixed, resulting in a mixture that has
the same composition and properties throughout.
Components of Solutions
The dissolving medium in a solution is called a solvent and the substance dissolved in a
solution is called the solute.
Types of Solutions
Solutions can be solids, liquids, or gases.

Examples of solid solutions are alloys.

Any mixture of gas is a gaseous solution.

Liquid solutions can be aqueous or organic. An example of aqueous solution is saltwater; an example of organic solution is gasoline, which is a mixture of
hydrocarbons.
In this chapter, we will focus largely on aqueous solutions, but must of this material
apply to non-aqueous solutions.
Molecular Nature of Dissolving

Solids dissolve in water when individual molecules or ions are attracted to water
molecules and break away from the solid.

When dissolved, the molecules are surrounded by water and held in suspension by
dipole-dipole interactions, whereas the ions are held by ion-dipole interactions.
Solubility

A given quantity of solvent can dissolve only so much solute. A solution is saturated
when the solvent has dissolved all the solute it can and some undissolved solute
remains.
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
The concentration of solid solute in a saturated solution has reached its greatest value
and no more can dissolve. In other words, a saturated solution represents the limit of
a solute’s ability to dissolve in a given quantity of solvent. The molar solubility of a
substance is its molar concentration in a saturated solution.

A saturated solution is one in which the dissolved and undissolved solute are in
dynamic equilibrium with one another.

A solution that contains less solute than a saturated solution under the existing
conditions is an unsaturated solution.

A supersaturated solution is a solution that contains more dissolved solute than a
saturated solution under the same conditions. A supersaturated solution may remain
unchanged for a long time if it is not disturbed, but once it is disturbed, crystals start
to form until the solution becomes saturated.
WHY DOES ANYTHING DISSOLVE?
Heats of Solutions

The formation of a solution is accompanied by an energy change. Solvent and solute
particles experience changes in their intermolecular interactions.

The amount of heat energy change when a specific amount of solute dissolves in a
solvent is the enthalpy of solution. Depending on the solute, the enthalpy of solution
can be exothermic or endothermic.

The enthalpy of solution, Hsol, is the sum of the enthalpy changes required to
separate the molecules or ions of the solute (the lattice enthalpy, HL) and the
enthalpy change accompanying their hydration, Hhyd  Hsol = HL + Hhyd. In
some cases Hsol is exothermic, and in others it is endothermic.

In the gaseous state, molecules are so far apart that there are virtually no
intermolecular forces between molecules. Therefore, the solute-solute interaction has
little effect on the enthalpy of a solution of gases  Hsol = 0.

Hsol < 0 when a gas dissolves in a liquid because the interaction between gas solute
and solvent molecules outweighs the energy needed to separate solvent molecules.
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Solubility and Disorder
Energy and matter tend to disperse.

Matter has a natural tendency to disperse in a disorderly way. The reverse process in
unnatural and has no tendency to occur. The dispersal of matter accounts for the
expansion of gases and the spreading of matter through the environment, and
contributes to the tendency of solids to dissolve.

Many substances dissolve to give a system with more disorder than was present
initially.

When a polar solute is dissolved in water, the water molecules may become organized
around it. As a result, the disorder of the solvent is reduced when the solution is
formed. The solution is more stable and therefore loses some of its energy to the
surroundings, which now becomes less organized because it gained energy. In this
process the overall disorder of the solute, solvent and their surrounding must increase.

Dissolving depends on the balance between the dispersal of matter in the solution and
the dispersal of energy in the surroundings.
FACTORS AFFECTING SOLUBILITY
The solubility of a substance in a given solvent depends on a number of factors. The
solubility of a gas depends on its partial pressure, and the solubilities of all substances,
including gases, vary with temperature.
Solute-Solvent Interactions

The solubility of a substance depends on the choice of solvent as well as on the
substance itself.
The interactions between solute molecules and the interactions
between solvent molecules must be replaced by solute-solvent interactions when a
solution forms. If the new interactions are similar to those replaced, very little energy
is required for the solution to form and the dissolution is favorable.

When the main cohesive forces in a solute are hydrogen bonds, the solute is more
likely to dissolve in a hydrogen-bonded solvent than in other solvent, because the new
interactions solute-solvent have similar energies than solute-solute or solvent-solvent
interactions.
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
If the principal cohesive forces between solute molecules are London forces, than the
best solvent is likely to be one held together by the same kind of forces.

Soaps and detergents are a practical application of the like-dissolves-like rule. Soaps
are the sodium salts with anions of a carboxylic acid. Soaps have a polar carboxylate
(-CO2) group, called the head group, at one end of a long nonpolar hydrocarbon
chain.
Because of its polar character, the head group is hydrophilic, or water
attracting, whereas the nonpolar hydrocarbon tail is hydrophobic, or water repelling.
The hydrophobic tails dissolve in grease (London forces), leaving the hydrophilic
head dissolved in water (dipole-dipole or hydrogen bonds). As a result, the whole
soap with the grease trapped in it dissolves in water and is washed away when rinsed.
Solubility of Ionic Compounds

We can predict whether a given ionic solid is likely to dissolve in water by using the
solubility rules (Chapter 4, table 4.1, p. 11).

In order to dissolve an ionic compound, the ion-dipole interaction must be greater
than the ion-ion interaction. This happens when ionic compounds are formed from
large anions with low charges. Ionic compounds with large anions with low charges
are often soluble.
Pressure and Solubility: Henry’s Law

The solubility of a gas is directly proportional to its partial pressure, because an
increase in pressure corresponds to an increase in the rate at which gas molecules
strike the surface of the solvent.

The molar solubility of a gas is denoted by Cg, and Henry’s law is written: Cg = kH x
P, where kH, which is called Henry’s constant, depends on the gas, the solvent, and
the temperature. The law implies that at constant temperature, doubling the partial
pressure of a gas doubles its solubility.
Temperature and Solubility

The variation of solubility with temperature is difficult to predict, except in the case
of gases, where raising the temperature nearly always lowers the solubility.

Most ionic and molecular compounds are more soluble in hot water than in cold.
However, a few solids, such as lithium sulfate, are less soluble at high temperatures
than at low. A smaller number of compounds show a mixed behavior.
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EXPRESSING CONCENTRATION
The amount of solute in a solvent, also called concentration, can be expressed in different
ways as shown in the following table:
Concentration
Definition
Units
Molarity
Moles of solutes per liter of solution
mol/L or M
Molality
Moles of solute per kilograms of solvent
mol/kg, or m
Volume percentage
Volume of solute expressed as a percentage
%
of the total volume
Mass percentage
Mass of solute expressed as a percentage of
%
a total mass
Mole Fraction (X)
Number of moles of solute expressed as a
-
fraction of the total number of moles in the
solution.
Parts per million
Parts per billion
Volume of solute in mL per kL of solution.
ppm (by volume)
Mass of solute in mg per kg of solution
ppm (by mass)
Volume of solute in L per kL of solution.
ppb (by volume)
Mass of solute in g per kg of solution
ppb (by mass)
Solution Stoichiometry
Molarity
The molarity, M, of a solution is the number of moles of solute molecules or
formula units divided by the volume of the solution (in liters).
Molarity = number of moles of solute / volume of solution (liters)
Molarity can be used to calculate the number of moles, n, of a solute in a solution or the
volume, V, of a solution.
n=MxV
or
V=n/M
Dilution
Diluting a solution is the reduction of the molarity from an initial value by adding
more solvent. When a solution is diluted, the same number of solute molecules occupies
a larger volume.
The amount of solute in the final solution is the same as the amount of solute in the initial
volume of solution.
ninitial = nfinal  Minitial x Vinitial = Mfinal x V final
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Titrations
Titrations are used to determine the amount of an acid or base, or the amount of
oxidizing or reducing agent is a solution. The solution being titrated is called the analyte.
A known volume of the analyte is transferred into a flask to which an indicator was
added. Then a solution called titrant is added to the analyte until the indicator change
color. The change of color of the indicator corresponds to the stoichiometric point. At
the stoichiometric point the solution contains an equal amount of titrant and analyte.
n titrant = nanalyte  Mtitrant x Vtitrant = Manalyte x V analyte
This allows to determine the stoichiometric relation between analyte and titrant species.
COLLIGATIVE PROPERTIES
The presence of a solute affects the physical properties of the solvent. Four physical
properties are affected in the same way by solutes regardless of the identity of the solute.
Properties that depend on the number of solute molecules and not on their chemical
identity are called colligative properties.
Vapor-Pressure Lowering

The vapor pressure of a solvent is lowered by a nonvolatile solute. For example, the
vapor pressure of pure water at 40C is 55 Torr but that of 0.1 m NaCl(aq) solution is
only 44 Torr at the same temperature. A nonvolatile solute particle can block the
escape of solvent molecule but has no effect on the rate of return of the solvent
particles from the vapor to the solution.

Raoult’s Law: The vapor pressure of a solvent in the presence of a nonvolatile solute
is proportional to the mole fraction. P = Xsolvent Ppure. Where Ppure is the vapor
pressure of the pure solvent, Xsolvent is the mole fraction of the solvent in the solution.
Freezing Point Depression

The freezing point of the solvent is lowered by the presence of a solute.

At the freezing point of a solution, the solute particles get in the way of the solvent
and inhibit the solid formation, freezing, (or melting). Only if the temperature is
lowered will that flow be stopped and the freezing (melting) will occur.

The freezing point of an ideal solution is proportional to the molality of the solute.

For a non-electrolyte solution (solute is molecular),
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Freezing point depression = kf x molality.
Where kf is the molal freezing point constant of the solvent (in K.kg/mol).

For an electrolyte solution (ionic solution), each formula unit contributes two or more
ions. In a dilute solution, the cations and anions move independently and contribute
nearly independently in lowering the freezing point. But in more concentrated
solutions, the ions do not move independently and the freezing point depression is
different from that of a dilute solution.
Freezing point depression = i xkf x molality.
Where i is the van’t Hoff factor. It is determined experimentally and depends on
both the concentration and the type ions in the solution.

Freezing point depression can be used to measure the molar mass of the solute.
Boiling Point Elevation

The presence of a solute raises the boiling point of the solvent. Thus the boiling point
of a solution is higher than the boiling point of the solvent.

For all solutions, we have: Boiling point elevation = kf x molality. where kf is
the molal boiling point constant of the solvent (in K.kg/mol).

The boiling point elevation can be used to determine the molar mass of the solute.
Osmosis

Osmosis occurs whenever a semipermeable membrane separates two solutions of
different concentrations.

Semipermeable membranes allow the movement of some particles while blocking the
movement of others.

Osmosis is the flow of solvent through a semipermeable membrane from the side of
the lower solute concentration to the side of the higher solute concentration. The
presence of solute particles on one side of the membrane hinders solvent molecules
from passing into the side containing pure solvent.

Osmotic pressure is the external pressure that must be applied to stop the flow of the
solvent.

The osmotic pressure is related to the molarity of the solute by the van’t Hoff
equation:  = R T x molarity.
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
Van’t Hoff equation is used to determine the molar masses of polymers and natural
macromolecules.

Osmosis help the transport the nutrients in living cells.

In reverse osmosis, a pressure greater than the osmotic pressure is applied to the
solution side of the semipermeable membrane. This application of pressure increases
the rate at which solvent molecules leave the solution, and thus reverses the flow of
solvent. Reverse osmosis is used to remove salts and other impurities in water.
COLLOIDS

A colloidal dispersion is formed when large particles are dispersed in a solvent.

Many colloids appear homogeneous because their particles cannot be seen. The
particles are, however large enough to scatter light.

The distinctive properties of solutions, colloids, and suspensions are summarized in
the following table.
Solutions
Colloids
Suspensions
Homogeneous
Heterogeneous
Heterogeneous
Particle sizes: 0.01-1 nm
Particle sizes: 1-1000 nm
Particle sizes: over 1000 nm
Do not separate on standing
Do not separate on standing Particles settle out
Cannot be separated by
Cannot be separated by
Can be separated by
filtration
filtration
filtration
Do not scatter light
Scatter light
May scatter light

There are several classes of colloids as indicated in the following table:
Class of colloid
Phase
Sol
Solid dispersed in liquid
Gel
Solid network extending throughout liquid
Liquid emulsion
Liquid dispersed in a liquid
Foam
Gas dispersed in liquid
Aerosol
Solid dispersed in gas
Smoke
Solid dispersed in gas
Fog
Liquid dispersed in gas
Smog
Solid and liquid dispersed in gas
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Solid emulsion
Liquid dispersed in solid
Skills you should have mastered
Conceptual
1. Explain the basis for the like-dissolves-like rule.
2. Explain how solutions result from the tendency of matter and energy to disperse.
3. Explain how diluting a solution affects the concentration of a solute.
4. Explain the significance of the stoichiometric point (equivalence) of a titration.
5. Explain how nonvolatile solute lowers the vapor pressure, raises the boiling point,
and lowers the freezing point of a solvent.
6. Explain the different properties of solutions and colloids.
Problem-solving
1. Calculate the molarity of a solute in a solution, volume of solution, and mass of
solute, given the other two quantities.
2. Determine the volume of solution needed to prepare a dilute solution of a given
molarity.
3. Calculate the volume of solution required for a reaction, given the corresponding
balanced chemical equation and the reactant concentration.
4. Calculate the molar concentration (molarity) of a solute from titration data.
5. Calculate the solubility of a gas at a given pressure, given its Henry’s constant.
6. Predict the relative enthalpies of two ions.
7. Calculate the mole fraction and molality of a solute, given the masses or mass
percentages of solute and solvent.
8. Calculate the amount of solute present in a given mass of solvent from the
molality.
9. Convert between molality and mole fraction or molarity.
10. Calculate the vapor pressure of a solvent by using Raoult’s law.
11. Find the molar mass of a substance from its freezing point depression, boiling
point elevation, or its osmotic pressure in a solution.
Descriptive
1. Describe the purpose and procedure of a titration.
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