Properties of Gases Flashcards
Intensive property
constant through the system at equilibrium, unchaged by partitioning
Extensive property
scale with the size of the system
When do all gases follow the ideal gas law, pV=nRT
in the limit of low densities
what is the compressibility factor of a real gas
z = pv / nRT
why do some gases not follow the ideal gas law
deviations arise from intermolecular forces at high pressure
kinetic theory of gases
describes properties of a gas in terms of molecules in constant random motion
what are the assumptions of the kinetic theory of gases
- newtonian mechanics
- no intermolecular interactions
- collisions are elastic
what is pV in terms of the average kinetic energy in the x direction
pV = 2 * N * Ekin,x
what is pV in terms of the overall kinetic energy
pV = 2/3 * N * Ekin
this looks like pV = nRT if Ekin is proportional to T
what is the pressure of a pure gas in terms of the mean squared velocity
p = 2/3 * N/V
Ekin = 1/3 * N/V * mv^2
where v^2 is the mean of all the squares of the velocities
what assumptions are made when finding the pressure of a pure gas in terms of the velocities of the gas molecules
- no interparticle collisions (point particles)
- only considering particles close to the wall
- elastic collisions with wall
why do we not need to assume the wall is flat and gives reflections like a mirror
when finding the pressure of a pure gas in terms of the velocities of the gas molecules
arriving and departing distributions are the same at equilibrium
what is the equipartition theorem
each quadratic degree of freedom has the same energy as: 1/2 K T
K is boltzmann constant
what is necessary for equipartition theorem to work
only works if energies are classical - i.e. many energy levels are available
what degrees of freedom/ modes are classical at normal T
translations and rotations but not vibrations
which experiments were used to verify the maxwell-boltzmann distribution
- rotating cyclinder
- gravity experiment
- Time of Flight mass spectrometry (arrival time at detector follows MB distribution)
put the mode, median, mean, and rms of the maxwell-boltzmann distribution in order of increasing magnitude
mode < median < mean < rms
why is the mean > mode
the distribution is skewed to the right
Describe the features of effusion
- gas leaks through small hole in the wall
- molecules which hit the hole (area = A) escape
- hits are evenly spread on the wall
what is Graham’s law of effusion
effusion rate is inversely proportional to the square root of relative molecular mass
what is the collision cross-section
the effective cross-sectional area for a collision
σ = πd^2
d is the diameter of the molecule
what is the collision rate in terms of the collision cross-section
w = N/V * σ v
v is the relative velocity
N/V is the number density
σ is the collision cross-section
why is the relative velocity used in finding the collision rate in terms of the collision cross-section
to account for the fact that all of the molecules are moving
which mass is used to calculate the relative speed
reduced mass, μ
what is the mean free path
the mean distance travelled between collisions
what is the time between collisions in terms of the rate of collisions
τ = 1/w
τ is the time between collisions
w is the rate of collisions
what is the mean free path in terms of the time between collisions
λ = τ * v
v is the mean speed
τ is the time between collisions
λ is the mean free path
collision density
total rate of collisions per unit volume
what is collision density proportional to
collision density is proportional to the reaction rate for a gas reaction
what are the transport properties of a gas
- viscosity - transport of momentum down a velocity gradient
- thermal conductivity - transport of energy down a temperature gradient
- diffusion - transport of matter down a concentration gradient
what does transport property (of a gas) mean
the properties of a gas out of equilibrium, e.g. flowing
