3.3 Kinetic Theory Flashcards
What is an ideal gas?
A gas that strickly obeys the equation of state pV = nRT. With the exception of very high densities, a real gas approximates well to an ideal gas
What is a mole?
The mole is the S.I. unit of an ‘amount of substance’. It is the amount containing as many particles (e.g. molecules) as there are atoms in 12g of carbon-12
What are the 4 assumptions for an ideal gas?
1) No intermolecular forces- particles only have kinetic energy
2) The size of the particles is negligible compared to the volume of the gas
3) The collisions between particles are perfectly elastic
4) The motion of the particles is purely random
What are the 5 assumptions of kinetic theory?
1) The time taken for a collision is negligible
2) The molecules move with constant velocity between collisions
3) The number of molecules is large, with a large number of collisions
4) The motion of the molecules is evenly distributed in all directions
5) There is a random distribution of energy among the particles
What is the ideal gas equation and the names of each value?
pV = nRT
pV = NkT
p = pressure
V = Volume
n = number of moles
N = number of particles
R = molar gas constant (8.31)
k = Boltzmann constant (1.38 x 10^-23)
T = Temperature (k)
What is number of particles, N, equal to?
n(Na)
Number of moles x Avagadro’s Number
What is the Molar gas constant, R, equal to?
NaK =Avagadro’s Number x Boltzmann constant
What is the relative molecular mass?
Mass of a molecule relative to the mass of 1/12thcarbon-12
How do you find the mass of a particle then use it to find the mass of a mole?
Atomic mass of particles x u (average mass of a proton or neutron)
E.g. carbon-12 has Atomic number 12.
So it’s mass is 12u
mass of mole = 12u x Avogadro’s number
What is the formula for pressure that includes the mean squared speed?
p = 1/3p’c² = 1/3 N/V mc²
p = Pressure
p’ = density
c² = Mean Squared speed
N=number of particles
V = Volume
m = mass of each particle
What is the molar mass?
M = Mr/1000
Mr = Relative atomic mass (big number in periodic table)
It is the mass of one mole of a substance
How do you derive the formula for pressure?
Imagine a cube with equal side lengths
1) Calculate the change in momentum (-mc-mc = -2mc)
2) Calculate the number of collisions per second by the molecule on the wall : Time = d/c = 2L/c
3) Calculate the force exerted by a molecule on the wall: F = Δp/Δt F = 2mc/(2L/c) = -mc²/L (Due to Newtons 3rd law: F = mc²/L)
4) Calculate the pressure for N molecules: pressure = NF/A = Nmc²/L/(L²) = Nmc²/L³ = Nmc²/V
5) Account for 3D: c² = cx² + cy² + cz².
cx² = cy² = cz²….We only want 1 direction so cx² = 1/3c²
6) Finally : p = 1/3Nm<c²>/V
How do you derive the formula for internal kinetic energy, U.
We know that: pV = nRT and p=1/3Nmc²/V
therefore: nRT = 1/3Nmc²
Multiply by 3/2 to get: 3/2nRT = N1/2mc²
1/2mc² = KE of particle | N is number of particles so N1/2mc² is the total kinetic energy.
Gp is negligible so U = 3/2nRT
Why do gasses with greater masses have smaller RMS speeds?
Because 1/2mc² =3/2kT all gasses at the same termp have the same mean translational kenetic energy. This implies that for gasses with greater masses, the rms speed will be smaller.
