Kinetic-Molecular Theory
 Theory developed to explain gas behavior.
 Theory of moving molecules.
 Assumptions:
1. Gases consist of a large number of molecules in constant random motion.
2. The volume of individual molecules is negligible compared to the volume of the container.
3. Intermolecular forces (forces between gas molecules) are negligible.
4. Energy can be transferred between molecules, but total kinetic energy is constant at constant temperature.
5. The average kinetic energy of molecules is proportional to temperature.
 Kinetic molecular theory gives us an understanding of pressure and temperature on the molecular level.
 The pressure of a gas results from the number of collisions per unit time on the walls of container.
 The magnitude of pressure is given by how often and how hard the molecules strike.

 Gas molecules have an average kinetic energy.
 Each molecule has a different energy.
 There is a spread of individual energies of gas molecules in any sample of gas. Fig. 10.15
 As the temperature increases, the average kinetic energy of the gas molecules increases.
 As kinetic energy increases, the velocity of the gas molecules increases.
 Root mean square speed (rms), u, is the speed of a gas molecule having average kinetic energy.
 Average kinetic energy, e , is related to root mean square speed: e = 0.5mu²
 

Molecular Effusion and Diffusion
 Average kinetic energy of a gas is related to its mass:
e = 0.5mu²
 Consider two gases at the same temperature: the lighter gas has a higher rms (Root mean square speed) than the heavier gas.
 Mathematically: u = (3RT/M)^0.5
 The lower the molar mass, M, the higher the rms for that gas at a constant temperature.

Graham's Law of Effusion
 Effusion is the escape of a gas through a tiny hole (a balloon will deflate over time due to effusion).
 The rate of effusion can be quantified.
 Consider two gases with molar masses M₁ and M₂, the relative rate of effusion is given by
 r₁/r₂ = (M₂/M₁)^0.5 = u₁/u₂
 Only those molecules that hit the small hole will escape through it.
 Therefore, the higher the rms, the more likelihood of a gas molecule hitting the hole.

Diffusion and Mean Free Path
 Diffusion of a gas is the spread of the gas through space.
 Diffusion is faster for light gas molecules.
 Diffusion is significantly slower than rms (consider someone opening a perfume bottle: it takes while to detect the odor but rms at 25^oC is about 1150 mi/hr!).
 Diffusion is slowed by gas molecules colliding with each other.
 Average distance of a gas molecule between collisions is called mean free path.
 At sea level, mean free path is about 6 x 10^-6 cm.

Real Gases: Deviations from Ideal Behavior
 From the ideal gas equation,
PV/RT = n
 For 1 mol of gas, PV/RT = 1 for all pressures.
 In a real gas, PV/RT varies from 1 significantly. see fig. 10.20
 The higher the pressure, the more the deviation from ideal behavior.

 As temperature increases, the gases behave more ideally. fig. 10.21
 The assumptions in kinetic molecular theory show where ideal gas behavior breaks down:
1. the molecules of a gas have finite volume;
2. molecules of a gas do attract each other.

As the pressure increases, molecules are forced closer together and the volume of the container gets smaller.
Relatively more gas molecules are present per unit space.
Therefore, the higher the pressure, the less the gas resembles an ideal gas.

 As the gas molecules get closer together, the smaller the intermolecular distance.
 The smaller the distance between gas molecules, the more likely attractive forces will develop between the molecules.
 Therefore, the less the gas resembles ideal gas.
 As temperature increases, the gas molecules move faster and further apart.
 Also, higher temperatures mean more energy available to break intermolecular forces.
 Therefore, the higher the temperature, the more ideal the gas.

The van der Waals Equation
Add two terms to the ideal gas equation to correct for volume of molecules (V - nb) and molecular attractions n²a/V²
 The correction terms generate the van der Waals equation:
{P + n²a/V²}(V-nb) = nRT
 where a and b are empirical constants.
 To understand the effect of intermolecular forces on pressure, consider a molecule that is about to strike the wall of the container: the striking molecule is attracted by neighboring molecules.  Therefore, the impact on the wall is lessened.

CHAPTER 11 INTERMOLECULAR FORCES, SOLIDS AND LIQUIDS.
A Molecular Comparison of Liquids and Solids

 Gases are highly compressible, assume shape and volume of container:
 gas molecules are far apart and do not interact much with each other.
Liquids are almost incompressible, assume the shape but not the volume of container:
 liquid molecules are held closer together than gas molecules, but not so rigidly that the molecules cannot slide past each other.
 Solids are incompressible and have a definite shape and volume:
 solid molecules are packed closely together.  The molecules are so rigidly packed that they cannot easily slide past each other.
 Converting a gas into a liquid or solid requires the molecules to get closer to each other:
 cool or compress.
 Converting a solid into a liquid or gas requires the molecules to move further apart:
 heat or reduce pressure.
 The forces holding solids and liquids together are called intermolecular forces.

Intermolecular Forces
 The covalent bond holding a molecule together is an intramolecular force.
 The attraction between molecules is an intermolecular force. (attractions between ions is strictly an ionic bond, but is considered an intermolecular force even though no molecules are involved.)
 Intermolecular forces are much weaker than intramolecular forces (e.g., 16 kJ/mol vs. 431 kJ/mol for HCl).
 When a substance melts or boils, the intermolecular forces are broken (not the covalent bonds).
 When a substance condenses, intermolecular forces are formed.
The strengths of these forces determine things like boiling points and melting points.

Ion-Dipole Forces
 Interaction between an ion (e.g., Na⁺) and a dipole (e.g., water).
 Strongest of all intermolecular forces:
F = kQ₁Q₂/d²
* Since Q₁ is a full charge and Q₂ is a partial charge, F is comparatively large.
 F increases as Q increases and as d decreases:
 the larger the charge and smaller the ion, the larger the ion-dipole attraction.

Dipole-Dipole Forces
 Dipole-dipole forces exist between neutral polar molecules.
 Polar molecules need to be close together.
 Weaker than ion-dipole forces:
 Q₁ and Q₂ are partial charges.
 There is a mix of attractive and repulsive dipole-dipole forces as the molecules tumble.
If two molecules have about the same mass and size, then dipole-dipole forces increase with increasing polarity.
see table 11.2 and compare the molecules shown. Acetonitrile CH₃CN has the highest boiling point b/c it has the strongest intermolecular forces. (i.e. larger dipole!)

London Dispersion Forces
 Weakest of all intermolecular forces.
 It is possible for two adjacent neutral molecules to affect each other.
 The nucleus of one molecule (or atom) attracts the electrons of the adjacent molecule (or atom).
 For an instant, the electron clouds become distorted.
 In that instant, a dipole is formed (called an instantaneous dipole).
 One instantaneous dipole can induce another instantaneous dipole in an adjacent molecule (or atom).
 Instantaneous dipoles are called London Dispersion Forces.
 Polarizability is the ease with which an electron cloud can be deformed.
 The larger the molecule (the greater the number of electrons) the more polarizable.
 London dispersion forces increase as molecular weight increases.
 they exist between all molecules.
they also depend on the shape of the molecule.
 The greater the surface area available for contact, the greater the dispersion forces.
THUS... London dispersion forces between spherical molecules are lower than those between sausage-like molecules.