# Dalton's Law

Dalton's Law of Partial Pressures
The relation between the total pressure of a mixture of gases and the pressures of the individual gases was expressed by John Dalton in 1807. This law is known as the law of partial pressures. The partial pressure of a gas in a mixture is defined as the pressure which the gas would exert if it is allowed to occupy the whole volume of the mixture at the same temperature. According to Dalton's law of partial pressures, the total pressure of a mixture of non-interacting gases is equal to the sum of the partial pressures of the constituent gases.

Let a mixture of gases have the amount n1 of the first gas, n2 of the second gas, and so on. Let the corresponding partial pressures be p1, p2, . . . . The total pressure is given by

pt = p1 + p2 + . . . (5.11)
If the gases present in the mixture behave ideally, then, it is possible to write separately for each gas,

p1V = n1RT
p2V= n2 RT ..................(5.12)

and hence, (p1 + P2 + . . . ) V = (n1 + n2 + . . .) RT

i.e., (ptotal V = ntotal RT)......................(5.13)

where (ntotal) is the total amount of gases in the mixture. Dividing eq. (5.12) by eq. (5.13), we get
(5.14, 5.15)

and so on,

The fractions n1/ntotal, n2/ntotal, etc., are called the mole fractions, of the respective gases. The mole fraction of a constituent of any mixture (gaseous, liquid or solid) is defined as the amount (or number of molecules) of that constituent divided by the total amount (or number of molecules) in the mixture. If the mole fractions are given, it is possible to calculate partial pressures.