## Precedents of the ideal gas law

Under moderate pressure and temperature, most gases follow several empirical laws about their state variables:

- Boyle's Law: $P \propto \frac{1}{V}$
- Charles' Law: $V \propto T$
- Gay-Lussac's Law: $P \propto T$
- Avogadro's Law: $V \propto n$

All four laws combine into the Ideal Gas Law:
$$pV = nRT$$
with a proportionality constant R, named the universal gas constant.
Alternatively, the Boltzmann constant can be used, given $k_B = \frac{R}{N_A}$.

Ideal gas neglects intermolecular effects.
The equation of state for an ideal gas can be derived from kinetic theory.
Expressed as a constitutive relation, it is $p = k_B \rho_N T$.
[Another constitutive relation relates p, T and entropy density.]

## Other gas laws

The following empirical laws also applies to ideal gas and ideal solution.

Dalton's Law:
In a mixture of non-reacting gases, the total pressure exerted is equal to the sum of the partial pressures of the individual gases.

$$P = \sum_{i=1} ^ n {p_i}$$

Raoult's law:
For an ideal mixture of liquids, the partial vapor pressure of each component is equal to the vapor pressure of the pure component multiplied by its mole fraction in the mixture.

$$p_i = p^{\star}_i x_i$$

Henry's law:
At constant temperature, in a given type and volume of liquid solvent, the amount of a given gas dissolved is proportional to its partial pressure in the gas phase.

$$p = K_H c_{\rm aq}$$

🏷 Category=Physics