# Physical Chemistry Equations

Ideal Gas Law
pV = nRT

pVm = RT
pV = NKbT

Boyle’s Law
p ∝ 1/V
Charles’ Law
p∝T
Change in momentum per collision
2m (x)
Collision volume
A(x)∆t
Number of molecules colliding with a wall in a time ∆t
[A(x)∆t*n*Na] / 2V
– where A is the area of the wall, divide by 2V bc only half of the molecules are traveling towards the wall
Force
F = ∆p/∆t (momentum)
F = [n*M*A(x)]/V
– where x is the average velocity
Pressure per unit area
p = (n*M*x)/V (divide both sides by A to get F/A)
– where A is the area of the wall
Pressure x Volume
pV = 1/3(nMc^2)
– where c^2 is the mean square speed of gas molecules
Root mean square speed (rms)
c = (3RT/M)^1/2 = ()^1/2
Total kinetic energy
(3/2)nRT
(3/2)KbT for one molecule
Most probable speed
s* = (2RT/M)^1/2
Mean relative speed
s-rel = (√2)*
Collision frequency
Za = σ*√2**(p/KbT)
Za = σ*√2**Na*(RT/p)
– where σ is the cross-sectional area of the collision tube
Mean free path
λ = RT/(Na*√2*σ*p)
λ = mean speed (s)/Za
Total number of collisions
Zaa = Za (N/2V)
Zaa = Za (p/2KbT)
Fraction of molecules with E > ℇ
exp(-ℇ/KT)
Rate of effusion
(p*A*Na) / [(2piMRT)]^1/2
– where A is the area of the hole
Graham’s law of effusion
rate ∝ (1/√M)

The rate of effusion of a gas is inversely proportional to the square root of its molar mass:

Rate gas A/Rate gas B = (MgasB/MgasA)^1/2

Vapour pressure
(∆m/A∆t) * [(2piRT/M)]^1/2
– where A is the area of the hole
The van der Waals’ equation
p = (RT/Vm-b) – (a/Vm^2)
Lennard-Jones potential (energy of interaction of 2 molecules)
V(R) = 4ℇ*[(σ^12/R^12)-(σ^6-R^6)]
The Clapeyron Equation
∆p/∆T = ∆H/T∆V
– Describes the slope of the coexistence line
– If ∆V = (+), the liquid is less dense than its solid phase & vv –> gradient = (+) & vv
Mean speed
= (8RT/Pi*M)^1/2
Mean square speed
() = (3RT/M) = c^2
Critical Temperature
The highest temperature at which the liquid phase can form by compression of the gas
– Tc
Phase
A form of matter that is uniform throughout in chemical composition and physical state
– temperature, pressure, composition considered
Coexistence lines
The temperature and pressure conditions at which two phases can coexist in equilibrium
Triple point
The temperature and pressure conditions in which the three phases can coexist
Critical point
The temperature and pressure conditions above which there is no distinction between a liquid and a gas

The point at which the density of the vapour matches the density of the liquid

– This is where a supercritical fluid exists
– Marks the highest temperature at which the liquid phase can exist

Ideal solution
A homogeneous mixture whose physical properties are the same / directly related to the properties of the individual components of the mixture
Latent heat of fusion
The amount of energy required to go from solid to liquid at the same temperature (per mol)
Equilibrium vapour pressure
The pressure of the vapour required by the coexistence line
Metastable phases
Thermodynamically unstable phases that exist if the transition to another phase is kinetically hindered
– barriers to structural rearrangement (large Ea)
– slow diffusion in the solid state
– stability = related to Gibbs
Vapour vs Gas
Vapour: The gaseous phase of a substance below the critical temperature (can still be liquified by the compression of a gas)
Gas: The gaseous phase of a substance above the critical temperature
Supercritical fluid
A substance above its critical point that has no distinction between a liquid and a gas
Categories: Physical Chemistry