Ideal gas law

(source: commons.wikimedia.org)
ideal gas law (or general gas equation)	$P V = n RT$
Boyle’s law	$P \propto \frac{1}{V}$
Charles’s law (or law of volumes)	$V \propto T$
combined gas law	$P V \propto T$
Avogadro’s law	$V \propto n$
Gay-Lussac’s law	$P \propto T$

$P$ is the pressure
$V$ is the volume
$n$ is the amount of substance of the gas (in $mol$ )
$T$ is the absolute temperature
$R$ is the gas constant (also universal, ideal or molar gas constant)
- $R = 8.3145 J \cdot K^{- 1} \cdot mo l^{- 1}$ .
- $R = 0.0821 L \cdot atm \cdot K^{- 1} \cdot mo l^{- 1}$
- $R = N_{A} k_{B}$
- $R$ must be expressed in units consistent with those chosen for pressure, volume and temperature.
other forms:
- $\frac{P V}{TN} = k_{b}$
  - $N$ is the total number of particles (atoms or molecules) in the gas.
  - $k_{b} = 1.380649 \times 1 0^{- 23} J \cdot K^{- 1}$ is the Boltzmann constant
  - ( $k_{b} T$ is sometimes called “thermal energy”)
- $ρ = \frac{PM}{RT}$ , where: $ρ$ is the density and $M$ is the molar mass

Dalton’s law

Dalton’s law (of partial pressures) $χ_{i} = \frac{n _{i}}{n} = \frac{p _{i}}{p}$
- total pressure $p = \sum_{i = 1}^{n} p_{i}$
- partial pressure $p_{i}$
- $χ_{i} = \frac{n _{i}}{n}$ is the mole fraction