Chem 105 Unit Three

Kinetic Molecular Theory Assumptions

Assumes gas molecules:

1. Have tiny volumes compared with their container’s volume

2. Move randomly and constantly

3. Collide elastically with the walls of a container and other gas molecules

4. Have no intermolecular interactions

5. Average kinetic energy is proportional to temperature

Kinetic Energy for Gases

At a given temperature, all gases have the same average kinetic energy - but, they don’t have the same speed!

u_rms trends

u_rms = √((3RT)/M)

As temperature increases, the most probable speed (u_rms) increases and the distribution of speeds gets wider (because T is in the numerator) - as mass increases, u_rms decreases (because M is in the denominator)

Effusion

Gas escaping from its container through a tiny hole into a region of lower concentration - heavier gases effuse more slowly

Diffusion

Spreading of gas through other gases - heavier gases diffuse more slowly

Graham’s Law

Rate of diffusion and effusion is inversely proportional to density and inversely proportional to √M

(Rate_A)/(Rate_B) = √((M_B)/(M_A))

Pressure

The amount of force applied to an area - can be measured with a barometer

P = force/area

Parameters Affecting Gases

• Pressure (P) in atm, Pa, or mmHg

• Volume (V) in L or m³

• Temperature (T) in K

• # of Moles (n)

Boyle’s Law

V goes down as P goes up - decreasing the volume increases the number of collisions per area, so pressure increases - P is proportional to 1/V, so P₁V₁ = P₂V₂

Charles’s Law

V decreases as T increases - V is proportional to T, so V₁/T₁ = V₂/T₂

Avogadro’s Law

V increases as n increases - V is proportional to n, so V₁/n₁ = V₂/n₂

Amonton’s Law

P increases as T increases - P is proportional to T, so P₁/T₁ = P₂/T₂

Ideal Gas Law

PV = nRT

Combines all four laws (Boyle, Charles, Avogadro, Amonton) - “ideal” because we’re assuming KMT assumptions are valid

STP

Standard temperature and pressure for gases

• Standard temp is 273.15 K

• Standard pressure is 1 bar

• 1 mol of gas at STP = 22.7 L in molar volume

Molar Mass Law

M = m/n (grams/mole), so you combine it with the ideal gas law to make M = (mRT/PV)

Density Equation

d = PM/RT

Density of gases increases when the molar mass of the gas increases

Buoyancy

Depends on differences in gas density which arise from:

• Molar Masses (smaller M = lower d)

• Temperature (higher T = lower d)

So, hot air balloons can float!

Dalton’s Law of Partial Pressures

Total Pressure = the sum of pressures each gas would exert if it were alone in the same volume (“partial” pressures) - TP depends on the number of moles of gas present, not their identities

P_total = (n_totalRT)/V

Mole Fraction

Ratio between moles of one component and the total moles present

X₁ = n₁/n_total so… P₁ = X₁P_total

Van der Waals Force

Any interaction between neutral atoms/molecules, including hydrogen bonds, dipole-dipole interactions, and london dispersion forces - NOT chemical bonds, just electrostatic interactions

London Dispersion Forces

An intermolecular force between atoms/molecules caused by the presence of temporary dipoles - temporary dipoles are based on the polarizability of the atom/molecule - present between all atoms/molecules

Polarizability

The tendency of an electron cloud to distort - the bigger the atom, the larger the polarizability - larger polarizability = larger london dispersion forces

Dipole-Dipole Interactions

An attraction between regions of polar molecules that have partial charges of opposite sign

Hydrogen Bonds

A strong dipole-dipole interaction which occurs between a hydrogen bonded to an N, O, or F atom and another N, O, or F atom

Ion-Dipole Interactions

An attractive force between an ion and a molecule that has a permanent dipole

Four Types of Intermolecular Forces (weakest → strongest)

1. London Dispersion Forces

2. Dipole-Dipole Interactions

3. Hydrogen Bonds

4. Ion-Dipole Interactions

Real Life Gases (violations of ideal gas law)

Particle volume is not negligible at high pressure (violates KMT) - intermolecular attractions are significant at low temperatures (violates KMT) - so, ideal gas behavior must be corrected when at high pressure and/or low temperature (Van der Waals Equation)

Van der Waals Equation

Law for real gases when attractive forces and/or volume of particles are not negligible - a and b are specific to each gas - (n²a)/V² corrects for attraction forces and (nb) corrects for the volume of particles

(P+(n²a)/V²)(V-nb) = nRT

Boiling Point of Gases

Boiling point increases with polarizability as the number of electrons and the electron-cloud radius increases - more surface area = greater LDFs