Kinetic Molecular Theory (KMT) Assumptions

Number 1

Gas particles are in continuous, random motion. This assumption is always true.

This means as particles are always moving in unpredictable directions

Number 2

The distance between the particles is much greater than their size, in other words the volume
occupied by the particles is infinitesimally small compared to the unoccupied space in the vessel. This assumption is never perfectly true since the particles take up some space. It is truest
at low pressures when very few particles are present.

Most of a gas’s volume is empty space

Number 3

Particle exert no force upon one another. This assumption is never completely true since all particles with electrons are subject to London dispersion forces, which are attractive. Polar
molecules are subject to dipole-dipole forces, which are stronger than London forces. This assumption is truest for small particles with relatively few electrons and no dipoles.

The ideal gas model assumes no attractions or repulsions between particles

Number 4

The kinetic energy associated with the motion of gas particles is directly proportional to absolute temperature. The KE doesn’t depend on any other parameters. This assumption is
always true.

Higher temperature means greater average KE

Number 5

Collisions, either between particles or with the walls of the vessel are elastic, i.e. they occur with loss of kinetic energy associated with motion. This assumption is true for atoms, but is less true for molecules since the bonds in molecules act like springs absorbing some of the energy during collisions.

KE is transferred during collisions but the total KE is not lost

Temperature and particle motion

• Higher temperature → higher average KE → faster particle motion

• Lower temperature → lower average KE

• At the same temperature, all gases have the same average KE, but different average speeds

• Lighter gas particles move faster than heavier ones at the same temperature

Gas pressure

• Pressure = force per unit area

• Gas pressure comes from particles colliding with container walls

• More particles → more collisions → higher pressure

• Smaller volume → more frequent wall collisions → higher pressure

Changes that increase pressure (assuming other variables stay constant)

• Number of gas particles increases → pressure increases

• Temperature increases → pressure increases

• Volume decreases → pressure increases

Ideal vs. real gases

• Ideal gas = perfectly follows all 5 KMT assumptions

• Real gases have particle volume and intermolecular forces

• Real gases behave most ideally at

-Low pressure (particles are farther apart)

-Higher temperature (attractions matter less)

• No real gas is perfectly ideal

Diffusion vs. Effusion

• Diffusion = random spreading and mixing of gas articles

• Effusion = gas particles escaping through a tiny opening

• Both are driven by entropy (more dispersal)

• Diffusion continues until particles become evenly distributed

• Lighter gases diffuse and effuse faster than heavier gases

Graham’s law

• Grahams law compares the rates of diffusion or effusion of two gases

• Lighter gases move faster than heavier gases at the same temperature

• The rate is inversely related to the square root of molar mass

• A gas with a smaller molar mass travels farther in the same amount of time

• Lower molar mass = faster gas

• Higher molar mass = slower gas

• If one gas is four times as heavy, it moves at half the rate

KE and gas velocity

• Gases at the same temperature have the same average KE

• Different gases at the same temperatures can have different average speeds

• Lighter molecules move faster

• Heavier molecules move slower

• Temperature determines average KE while molar mass affects speed

Entropy and gas behavior

• Entropy is associated with randomness or dispersal of energy and matter

• Diffusion and effusion increase the dispersal of gas particles

• Spontaneous processes tend toward increased total entropy

• Gases spreading out into a larger space general increases entropy

• More spreading out = generally greater entropy

Ideal gas law

• The ideal gas law describes the relationship between pressure, volume, moles and temperature

• Increasing the number of gas particles increases pressure if volume and temperature stay constant

• Increasing temperature increases pressure if volume and number of particles stay constant

• Increasing volume decreases pressure if temperature and number of particles stay constant

• Temperature must be in kelvin

Ideal gas law and molar mass

• The ideal gas law is PV = nRT

• Calculate pressure, volume, temperature, or moles of a gas

• Temperature must be in kelvin

• Pressure and volume units much match the units of R

• Molar mass is divided by moles. MM = g/mol

• Use ideal gas law to determine the molar mass of an unknown gas

Gas stoichiometry

• Balanced chemical equations tell you the mole ratios between reactants and products

• Coefficients represent moles, not grams

• When a reaction produces a gas, you can use stoichiometry to calculate hoe many moles of gas are produced

• You can then use PV = nRT to calculate the gas pressure or volume

Gas laws and combining volumes

• Gas volumes are proportional to the number of moles when temperature and pressure are constant'

• The coefficients in a balanced equation give the volume ratios of reacting gases when they are at the same temperature and pressure

• This only applies when comparing gases under the same temperature an pressure conditions