Gas Laws, Kinetic Molecular Theory, Deviation from Ideal Gas Law

Boyle’s Law

P₁V₁=P₂V₂

• Pressure and Volume are Inversely Related

Charles’ Law

V₁/T₁=V₂/T₂

• Volume and Temperature are directly related

Gay-Lussac’s Law

P₁/T₁=P₂/T₂

• Pressure and Temperature are directly proportional

Avagadro’s Law

V₁/n₁=V₂/n₂

• Volume and number of moles are directly related

Ideal Gas Law

PV=nRT

Combined Gas Law

P₁V₁/n₁T₁=P₂V₂/n₂T₂

Derivation Ideal Gas Law

MM = DRT/P

D = MMP/RT

Mole Fraction

X_A = n_A / n_A+n_B

Partial Pressure

P_gas=X_gas(P_total)

Kinetic Molecular Theory

1. The particles are so small compared with the distance between them that the volume of individual particles can be assume to be negligible

2. Particles are in constant, random motion

3. Particles are assumed to exert no force on each other; they are assumed neither to attract nor to repel each other

4. Average kinetic energy of gas particles is assumed to be directly proportional to the Kelvin temperature of the gas

Kinetic Energy

KE = 1/2mv²

• Kinetic energy is the energy that objects possess due to their motion

• Gases at the same temperature have the same average kinetic energy

Partial Pressure

P_total = P₁ + P₂ + P₃ + …

Diffusion

The spread of one substance throughout a space or throughout a second substance

Effusion

The escape of gas molecules through a tiny hole into an evacuated space

Rate of effusion depends on the mass of the gas

Graham’s Law

V₁/V₂ = sqrt(m₂/m₁)

Correct for non-ideal gas behavior when..

• Pressure of the gas is high →actual observed pressure of the gas is lower than expected pressure due to intermolecular attractions

• Temperature is low →Actual observed volume of the gas particles is higher than expected due to gas particles actually taking up space

van der Waals Equation

(P + an²/V²)(V - nb) = nRT