A-Level Physics Gas Laws: Units, Laws, and Molecular Theory

SI unit of pressure

The Pascal (Pa), equivalent to N/m².

SI unit of volume

Cubic metre (m³).

SI unit of temperature in gas laws

Kelvin (K).

0°C in Kelvin

273 K.

Symbol R in the ideal gas law

The ideal gas constant, 8.31 J/mol·K.

Boyle's Law

At constant temperature, pressure is inversely proportional to volume: pV = constant.

Charles's Law

At constant pressure, volume is directly proportional to absolute temperature: V ∝ T.

Pressure Law

At constant volume, pressure is directly proportional to absolute temperature: P ∝ T.

Ideal gas equation

pV = nRT.

Value of R, the ideal gas constant

8.31 J/mol·K.

Rearranging the ideal gas law to find number of moles

n = pV / RT.

Converting degrees Celsius to Kelvin

Add 273 to the Celsius temperature.

Assumptions of an ideal gas

No intermolecular forces, elastic collisions, random motion, negligible volume, obey Newton's laws.

When real gases deviate from ideal gas behaviour

At high pressure and low temperature.

Avogadro's constant

6.022 × 10²³ particles/mol.

Calculating number of molecules from moles

N = n × N_A.

Definition of one mole of gas

The amount of substance that contains as many particles as there are atoms in 12 g of carbon-12.

Graph of pressure vs volume for Boyle's Law

A downward curve showing inverse proportionality.

Graph of volume vs temperature for Charles's Law

A straight line showing direct proportionality starting from absolute zero.

Graph of pressure vs temperature for the Pressure Law

A straight line starting from absolute zero showing direct proportionality.

Why temperature must be in Kelvin for gas laws

Because Kelvin is proportional to the average kinetic energy of gas particles.

Absolute zero

0 K, the temperature at which all particle motion theoretically stops.

Why gas particles exert pressure

They collide with the walls of the container, exerting force.

What causes pressure in a gas

The collisions of gas molecules with the walls of the container.

Collisions of gas molecules

The collisions of gas molecules with the walls of the container.

Formula for converting cm³ to m³

Divide by 1,000,000.

Formula for converting dm³ to m³

Divide by 1,000.

Area under a p-V graph

The work done by or on the gas.

Pressure in an ideal gas

The frequency and momentum of particle collisions with the container walls.

Why do particles in a gas exert pressure?

Because they collide with the container walls, changing momentum and exerting force.

Elastic collisions in ideal gases

Collisions where kinetic energy is conserved.

Effect of temperature on particle speed

The average speed increases due to increased kinetic energy.

Gases deviate from ideal behaviour at high pressures

Because particle volume and intermolecular forces become significant.

Internal energy of an ideal gas

Because ideal gases are assumed to have no intermolecular forces.

Relationship between pressure and average kinetic energy

Pressure is proportional to the average kinetic energy of molecules.

Molar gas constant

The constant R in pV = nRT; 8.31 J mol⁻¹ K⁻¹.

Absolute temperature

A temperature scale where 0 K is the point of zero particle energy.

Standard temperature and pressure (STP)

0°C (273 K) and 1 atm (1.01 × 10⁵ Pa).

Effect of doubling temperature (in K) on pressure

Pressure doubles.

Effect of tripling pressure at constant T on volume

Volume becomes one-third.

Shape of a V-T graph at constant pressure

Straight line through the origin (Kelvin scale).

Kinetic theory equation for pressure

pV = 1/3 Nm⟨c²⟩, where ⟨c²⟩ is mean square speed.

Average kinetic energy of a gas particle

KE_avg = (3/2)kT.

Boltzmann constant (k)

Relates temperature to average kinetic energy; k = R/N_A.

Terms in pV = nRT

p = pressure, V = volume, n = moles, R = gas constant, T = temperature.

Terms in pV = 1/3 Nm⟨c²⟩

N = number of molecules, m = mass per molecule, ⟨c²⟩ = mean square speed.

Difference between Celsius and Kelvin

They have the same scale, but 0 K = -273°C.

Why is Kelvin scale used in gas laws?

Because gas laws are proportional to absolute temperature, not relative.

Mean square speed

The average of the squares of the speeds of the gas molecules.