Comprehensive Gas Laws and Kinetic Theory for Chemistry

Boyle’s Law

Pressure and volume are inversely related (P₁V₁ = P₂V₂) when temperature is constant.

Charles’s Law

Volume and temperature are directly related (V₁/T₁ = V₂/T₂) when pressure is constant.

Gay-Lussac’s Law

Pressure and temperature are directly related (P₁/T₁ = P₂/T₂) when volume is constant.

Avogadro’s Law

Volume is directly proportional to the number of moles of gas (V₁/n₁ = V₂/n₂).

Combined Gas Law

Combines Boyle’s

Ideal Gas Law

PV = nRT

Ideal Gas Constant (R)

0.0821 L·atm/mol·K or 62.4 L·mmHg/mol·K.

STP (Standard Temperature and Pressure)

273 K (0°C) and 1 atm; 1 mol gas = 22.4 L.

Kinetic-Molecular Theory (KMT)

Gases consist of tiny particles in random motion; no forces; elastic collisions; kinetic energy ∝ temperature.

Average Kinetic Energy (KE)

Directly proportional to temperature in Kelvin.

Why gases exert pressure

Because gas particles collide with the container walls.

Relationship between temperature and kinetic energy

Higher temperature → faster-moving particles → greater kinetic energy.

Graham’s Law of Effusion

r₁/r₂ = √(M₂/M₁); lighter gases diffuse and effuse faster.

Effusion vs Diffusion

Effusion = gas escapes through a hole; Diffusion = gas spreads through space.

Dalton’s Law of Partial Pressures

P_total = P₁ + P₂ + P₃ + …; each gas exerts pressure independently.

Gas collected over water

Pgas = Patm – P_H₂O.

Gas density formula

d = (PM)/(RT).

Molar mass from gas data

M = (dRT)/P.

Real Gas Behavior

Deviates from ideal at low temperature or high pressure.

Ideal Gas Conditions

Low pressure and high temperature (particles far apart

Deviations from Ideal Behavior

Caused by molecular volume and intermolecular attractions.

van der Waals equation

(P + a(n/V)²)(V – nb) = nRT; corrects for attraction (a) and volume (b).

At constant temperature

If pressure increases

At constant pressure

If temperature increases

At constant volume

If temperature increases

Main component of air

Nitrogen (≈78%).

Characteristics of gases

Highly compressible

Conditions for most ideal gas

High temperature

Real gases deviate most

At low temperature and high pressure.

Root-mean-square (rms) speed

u = √(3RT/M); lighter gases move faster.

Heavier vs lighter gases

Lighter gases have higher average speed and faster effusion rates.

Kinetic energy equality rule

All gases at the same temperature have the same average kinetic energy.

Temperature scale for gas laws

Always use Kelvin (K = °C + 273).

Cold zero volume

Volume = 0 at –273°C = 0 K (absolute zero).

Density and temperature

Gas density decreases as temperature increases (at constant pressure).

Density and pressure

Gas density increases with increasing pressure (at constant temperature).

Collecting gas over water

Equalize water levels inside and outside the tube before measuring gas volume.

Greenhouse gases

CO₂

Gas with rotten egg smell

H₂S (hydrogen sulfide).