Gas Law and Kinetic Molecular Theory

Kinetic-Molecular Theory of Gases

A theory that explains gas behavior based on 5 main assumptions about gas particles

Assumption 1 (KMT)

Gases consist of large numbers of tiny particles that have mass

Assumption 2 (KMT)

Gas particles are in constant, rapid, random motion and possess kinetic energy

Assumption 3 (KMT)

There are no attractive or repulsive forces between gas particles

Assumption 4 (KMT)

Collisions between gas particles and with container walls are perfectly elastic (no kinetic energy lost)

Assumption 5 (KMT)

The average kinetic energy of gas particles depends only on temperature (higher T = higher KE)

Four quantities needed to describe a gas

Volume, temperature, pressure, and number of moles (or molecules)

Volume (of a gas)

The volume of a gas is equal to the volume of its container

Standard temperature for gas laws

0 °C or 273 K

Standard pressure for gas laws

1 atm = 101.3 kPa = 760 mmHg = 760 torr

Temperature conversion (°C ↔ K)

K = °C + 273 or °C = K − 273

Pressure

Force per unit area (P = Force / Area)

Atmospheric pressure at sea level

≈ 101.3 kPa ≈ 1 atm ≈ 760 mmHg ≈ 760 torr

Effect of altitude on pressure

As altitude increases, atmospheric pressure decreases

Mercury barometer

Device that measures atmospheric pressure by balancing air pressure against the weight of a mercury column

Manometer

Device that measures pressure difference using a U-shaped tube with liquid (usually mercury)

Pressure units conversion

1 atm = 101.3 kPa = 760 mmHg = 760 torr

Boyle’s Law

At constant temperature, pressure and volume are inversely proportional (P₁V₁ = P₂V₂)

Boyle’s Law relationship

As pressure ↑, volume ↓ (inverse)

Robert Boyle

“Father of Modern Chemistry”; discovered Boyle’s Law (1627–1691)

Charles’s Law

At constant pressure, volume and temperature (in Kelvin) are directly proportional (V₁/T₁ = V₂/T₂)

Charles’s Law relationship

As temperature ↑, volume ↑ (direct)

Jacques-Alexandre Charles

French scientist who discovered Charles’s Law (1746–1823)

Gay-Lussac’s Law

At constant volume, pressure and temperature (in Kelvin) are directly proportional (P₁/T₁ = P₂/T₂)

Gay-Lussac’s Law relationship

As temperature ↑, pressure ↑ (direct)

Joseph-Louis Gay-Lussac

French chemist and physicist who discovered Gay-Lussac’s Law (1778–1850)

Combined Gas Law

Combines Boyle’s, Charles’s, and Gay-Lussac’s laws: P₁V₁/T₁ = P₂V₂/T₂

Elastic collision

A collision in which kinetic energy is conserved (gas particle collisions are elastic)

Kinetic energy of gas particles

Depends only on temperature; KE ∝ T (in Kelvin)

Why we don’t feel atmospheric pressure

Air pressure pushes equally in all directions (inside and outside our bodies)

STP

Standard Temperature and Pressure: 0 °C (273 K) and 1 atm (101.3 kPa or 760 mmHg)

Directly proportional

When one variable increases, the other increases by the same factor (y = kx)

Inversely proportional

When one variable increases, the other decreases by the same factor (y = k/x or xy = k)

Boyle’s Law formula

P₁V₁ = P₂V₂ (T and n constant)

Charles’s Law formula

V₁/T₁ = V₂/T₂ (P and n constant) ← Temperatures must be in Kelvin

Gay-Lussac’s Law formula

P₁/T₁ = P₂/T₂ (V and n constant) ← Temperatures must be in Kelvin

Combined Gas Law formula

P₁V₁/T₁ = P₂V₂/T₂ (n constant)