How does Dalton’s law of partial pressures describe a gas mixture?

Dalton’s law describes a mixture of gases by stating that the total pressure exerted by the mixture is equal to the sum of the partial pressures of its individual component gases.12

A partial pressure is defined as the pressure that a specific gas would exert if it alone occupied the entire volume of the mixture at the same temperature. Mathematically, if a mixture contains several species, the total pressure $p$ is expressed as:12

$$p=p_1+p_2+\dots$$

where $p_1,p_2,\dots$ represent the partial pressures of each component.3

Formulated by John Dalton in 1801, this empirical relation is derived from the kinetic theory of gases under the assumption that the components behave as ideal gases and do not chemically interact with one another. While it is strictly accurate for ideal gases, it remains a reliable approximation for real gases at high temperatures and low pressures.1