#"Dalton's law of partial pressures"#, which was established by experiment, holds that in a gaseous mixture, the pressure exerted by an individual component gas is the same as the pressure it would exert if it alone occupied the container.
And so, #P_"Total"=P_A+P_B+P_C.........#, where #A, B, C, etc# are the individual, component gases.
But if we assume ideality, #P_A=(n_ART)/V#, where #n_A# is the number of moles of #"component gas A"#.
And so, #P_"Total"=(n_ART)/V+(n_BRT)/V+(n_CRT)/V.........#,
Equivalently, #P_"Total"=(RT)/V{n_A+n_B+n_C.....}#.
And thus the partial pressure, #P_A#, is proportional to the mole fraction:
#P_A=(RT)/Vxxn_A/(n_A+n_B+n_C.....)#, the constant of proportionality is of course #(RT)/V#
