IB Physics HL: The Gas Laws

Chapter 9:

The Gas Laws


Term Definition equation units
Mole One mole of any substance contains as If a substance contains N particles n/a
many particles as 6.02214076 ⋅ 1023 then the number of moles n is 𝑛 =
𝑁
𝑁𝐴
Molar mass The mass, in grams of 1 mole of a The number of moles in a quantity 𝑔 𝑚𝑜𝑙 −1
substance m gram of a substance with molar
𝑚
mass 𝜇 is 𝑛 = 𝜇
Pressure The normal force applied per unit area 𝑁 𝑚−2
(pascals)




Boyles Law The pressure and volume are inversely 𝑝 ∝
1
or PV is constant N/ a
𝑉
proportionate. As volume increases,
pressure increases because the
molecules collide more frequently, and
vice versa
Charles law The volume of a gas is directly 𝑉
= Constant n/a
𝑇
proportional to its absolute 𝑉 𝑉
temperature in kelvin Use 𝑇1 = 𝑇2
1 2
Gay-Lussac's The pressure of a gas is directly PT = constant
law proportional to its absolute 𝑃1 𝑃2
=
temperature when the gasses mass and 𝑇1 𝑇2
volume are kept constant (T in kelvin)
The ideal For a specific amount of gas, the 𝑃𝑉 = 𝑛𝑅𝑇 (𝑅 = 8.31 𝐽 𝐾 −1 𝑚𝑜𝑙 −1)
gas law product of pressure and volume are When a gas changes values, use
directly proportional to the absolute 𝑃1 𝑉1 𝑃2 𝑉2
temperature =
𝑛1 𝑇1 𝑛2 𝑇2
Using the Boltzmann constant:
𝑃𝑉 = 𝑁𝑘𝐵 𝑇
The Pressure is related to the rms speed 1 pascals
𝑃 = 𝜌𝑐 2
Boltzmann and the density of the gas 3
equation Where P is the pressure, c is the
root mean square speed, and 𝜌 is
the density