Graham’s law

Graham’s law states that the rate of diffusion or effusion

of a gas is inversely proportional to the square root of its
molar mass:

Diffusion is the mixing of gases as the result of random motion and

frequent collisions

Diffusion is the mixing of gases. (a) Two different gases in separate

containers. (b) When the stopcock is opened, the gases mix by diffusion.

Effusion is the escape of gas molecules from a container to a

region of vacuum

Effusion is the escape of a gas into a vacuum

The Kinetic Molecular Theory of Gases
• A gas is composed of particles that are separated by relatively large distances.
The volume occupied by individual molecules is negligible.
• Gas molecules are constantly in random motion, moving in straight paths,
colliding with the walls of their container and with one another in perfectly
elastic collisions.
• Gas molecules show no forces of attraction or replusion.
• No energy is lost in collision of molecules, the collision is completely elastic.

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Gases that behave as though these assumptions were strictly true are said to
exhibit ideal behavior. Many gases do exhibit ideal or nearly ideal behavior
under ordinary conditions.

Under the conditions of high pressure and low temperature, the behavior
of a real gas deviates from ideal.
At high pressures, gas molecules are relatively close together. We can assume
that gas molecules occupy no volume only when the distances between
molecules are large. When the distances between molecules are reduced, the
volume occupied by each individual molecule becomes more significant.

At low temperatures, gas molecules are moving more slowly. We can assume
that there are no intermolecular forces between gas molecules, either
attractive or repulsive, when the gas molecules are moving very fast and the
magnitude of their kinetic energies is much larger than the magnitude of any
intermolecular forces. When molecules move more slowly, they have lower
kinetic energies and the magnitude of the forces between them becomes
more significant.
Van der Waals Equation
Ideal gas PV=nRT
Incorporating both corrections into the ideal
gas equation gives us the van der Waals
equation, with which we can analyze gases
under conditions where ideal behavior is not
expected.

a indicates how strongly molecules of

a particular type of gas attract one another.
b is related to molecular (or atomic) size,
although the relationship is not a simple one.
 Solutions are homogeneous mixtures of two or
more pure substances.
 In solution, the solute is dispersed uniformly
throughout the solvent.
 Intermolecular forces

The dipole–dipole force exists between all molecules that are polar.
Polar molecules have electron-rich regions (which have a partial
negative charge) and electron-deficient regions (which have a partial
positive charge).

Hydrogen Bonding. Polar molecules containing hydrogen atoms

bonded directly to small electronegative atoms—most importantly
fluorine, oxygen, or nitrogen—exhibit an intermolecular force called
hydrogen bonding. HF, NH3, and H2O, for example, all exhibit
hydrogen bonding.

The ion–dipole force occurs when an ionic compound is mixed with a polar
compound; it is especially important in aqueous solutions of ionic compounds.
For example, when sodium chloride is mixed with water, the sodium and
chloride ions interact with water molecules via ion–dipole forces. The positive
sodium ions interact with the negative poles of water molecules, while the
negative chloride ions interact with the positive poles.
 Solvent–solute interactions >
Solvent-solvent and solute-
solute interactions (Solution
forms

A solute’s ability to dissolve in a solvent depends largely upon:

(1) How strong the intermolecular forces are that bind the solute molecules to
each other. The stronger they are, the more difficult it is for the solvent to break
them apart.
(2) How strong the intermolecular forces are between the solute and the solvent.
The stronger these are, the easier it is for the solvent to dissolve the solute.
 Energetic of Solution Formation
Separating the solute into its constituent
particles. This step is always endothermic
(positive ΔH) because energy is required to
overcome the forces that hold the solute
particles together.

Separating the solvent particles from

each other to make room for the solute
particles.
This step is also endothermic because
energy is required to overcome the
intermolecular
forces among the solvent particles.
Mixing the solute particles with the
solvent particles.
This step is exothermic because energy is
released as the solute particles interact
(through intermolecular forces) with the
solvent particles.
The solution process, has three DH components:
1- The DH of separating the solute particles from each other (DHsolute)
2- The DH of separating solvent particles from each other (DHsolvent)
3- The entire DH for the whole dissolving process (which we’ll call DHsoln)

Hess’s law, the overall enthalpy change upon solution formation,

called the enthalpy of solution (𝚫Hsoln) and can be defined as
the sum of the changes in enthalpy for each step:
DHsoln = DHsolute + DHsolvent + DHmix
endothermic (+) endothermic (+) exothermic (-)

An enthalpy change (DH) is approximately equal to the difference between the

energy used to break bonds in a chemical reaction and the energy gained by the
formation of new chemical bonds in the reaction. It describes the energy change
of a system at constant pressure.
Energetics of Solution Process:
(a) When ΔHmix is greater in magnitude than the sum of ΔHsolute and ΔHsolvent, the
heat of solution is negative (exothermic).
(b) When ΔHmix is smaller in magnitude than the sum of ΔHsolute and ΔHsolvent, the
heat of solution is positive (endothermic).
Molecular Compounds in water
 Solubility
We can measure how easily a solute will dissolve in a certain solvent. This measurement is
called solubility.
Solubility is defined as the maximum amount of solute that dissolves in a specific
amount of solvent.
High Solubility: The solute dissolves quickly & easily (e.g. salt in water)
Low Solubility: The solute does not dissolve easily (e.g. sand in water)

Saturated solution: maximum amount of solute is

dissolved in solvent. Trying to dissolve more results in
undissolved solute in container.
Unsaturated solution: less than max. amount of solute
is dissolved in solvent.
Supersaturation = more solute in solution than
normally allowed; we call this a supersaturated
solution.
 FACTORS AFFECTING SOLUBILITY

This rule can be used to predict whether or not certain substances will dissolve, or be
miscible, in each other. All we have to do is ask ourselves: “are the two items in question
polar or nonpolar? If they are both polar, or both nonpolar, then they will be soluble
(miscible)

The stronger the intermolecular attractions between solute and solvent, the more
likely the solute will dissolve
This rule can be used to predict whether or not
certain substances will dissolve, or be miscible, in
each other. All we have to do is ask ourselves:
“are the two items in question polar or nonpolar?
If they are both polar, or both nonpolar, then they
will be soluble (miscible)
The Temperature Dependence of the Solubility of Solids
The solubility of solids in water can be highly dependent on temperature.
Although exceptions exist, the solubility of most solids in water increases with
increasing temperature.
Solubility and temperature The solubility of most solids increases with
increasing temperature.

Factors Affecting the Solubility of Gases in Water

Solutions of gases dissolved in water are common. Club soda, for example, is a solution
of carbon dioxide and water, and most liquids exposed to air contain dissolved gases from
air. Fish and other aquatic animals depend on the oxygen dissolved in lake or ocean water
for life, and our blood contains dissolved nitrogen, oxygen, and carbon dioxide. Even tap
water contains dissolved gases. The solubility of a gas in a liquid is affected by both
temperature and pressure.

The Effect of Temperature

Unlike solids, the solubility of gases in water

decreases with increasing temperature.

In general, the solubility of gases in water

increases with increasing mass.
The solubility of gases decreases with an increase in the temperature

Q. Why do fish die in water that is too warm?

Because O2 gas is less soluble in warm water, fish cannot
obtain the amount of O2 required for their survival.
 Effect of pressure
• Pressure has little effect on the solubility of a liquid or solid, but has
dramatic effect on gas solubility in a liquid.
• Gases can dissolve in solvents. For example, carbon dioxide
dissolves in water, to a certain extent. Carbonated drinks contain
CO2 dissolved in water. When their lids are removed, sodas’ CO2
molecules begin to escape.

In a sealed container, the solubility

of a gas in a liquid is directly related
to the pressure of that gas above
the liquid.
This is summarized by the following
equation, known as Henry’s Law
Ways to express the Concentration of Solutions

Molarity (M) The moles of solute divided by

the volume of the solution in liter.

Molality (m) The moles of solute divided

by kilograms of solvent

Mole Fraction The moles of one component

divided by total moles of components in solution

Parts per million (ppm)

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DILUTING SOLUTIONS
 Colligative Properties
• Freezing point depression
• Elevation in boiling point
• Lowering of vapor pressure
• Osmotic Pressure

Vapor Pressure Lowering

When placed in sealed containers, volatile solvents exert a vapor
pressure, and they eventually reach a state of Equilibrium, like this;

When a nonvolatile (non-evaporating) solute is added, it

stabilizes the liquid solvent, which decreases its rate of
evaporation, like this

Once equilibrium is reestablished, the new vapor pressure

is now lower than the old one;
Freezing Point Depression in Solutions
The freezing point of pure water is 0 ◦C, but that melting point can be depressed by the
adding of a solvent such as a salt. The use of ordinary salt (sodium chloride, NaCl) on icy
roads in winter helps to melt the ice. A solution typically has a measurable lower melting
point than the than the pure solvent.
The treatment of freezing point depression is given by Ebbing. The freezing point
depression DTf, is a colligative property and defined as the difference between the
freezing points of the pure solvent and a solution of a nonelectrolyte in that solvent, and it
is directly proportional to the molal concentration m of the solution: DTf = Kf m b
where Kf is called the freezing-point-depression constant

Boiling Point Elevation

The boiling point of pure water is 100 ◦C, but the boiling point can be elevated by the
adding of a solute such as a salt. A solution typically has a measure higher boiling point
than the pure solvent.
A treatment of boiling point elevation is given by Ebbing. The boiling point elevation DTb is
a colligative property and defined as the difference between the boiling points of the
pure solvent and a solution of a nonelectrolyte in that solvent, and it is directly proportional
to the molal concentration cm of the solution: DTb = Kb m
where Kb is called the Molal boiling point constant.