The ideal gas equation pV = nRT applies to mixtures just as to pure gases. It was in fact with a gas mixture, ordinary air, that Boyle, Gay-Lussac and Charles did their early experiments. The only new concept we need in order to deal with gas mixtures is partial pressure.
The pressure exerted by a gas depends on the force exerted by each molecular collision with the walls of the container and on the number of such collisions in a unit area per unit time. If a gas contains two types of molecules, each species will engage in such collisions and thus, make a contribution to the total pressure, in exact proportion to its abundance in the mixture. The contribution that each species makes to the total pressure of gas is known as the “partial pressure” of the species. Therefore, in other words, “partial pressure of a component gas, in a gaseous mixture, is the pressure that would have been exerted, had the said component occupied the entire volume alone under identical conditions of temperature.”
The statement of Dalton’s Law is “The total pressure of a mixture of non-reacting gases is equal to the sum of their partial pressures”.
Let a mixture of gases have 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
ptotal = p1 + p2 + ….
If the gases present in the mixture behave ideally, then, it is possible to write separately for each gas,
p1V = n1 RT (a)
p2V = n2RT (b)
Hence (p1 + p2 + …) V = (n1 + n2 + …) RT
i.e., ptotal V = ntotalRT (c)
where ntotal is the total moles of gases in the mixture. Dividing Eqs (a) and (b) by Eq. (c), We get
x1 , x2, and so on are the mole fraction of each gas respectively Partial Pressure of a gas = Mole fraction of the gas × Total Pressure of the gaseous mixture
Dalton’s Law of Partial pressure is applicable only for non – reacting gases.
Q1. Calculate partial pressure of nitrogen and oxygen in air assuming it to be composed of mostly nitrogen and oxygen. Volume percentage of oxygen and nitrogen in air are 20 and 80 respectively, and atmospheric pressure to be 1.0.
Ans: Mole fraction of N2(g) = 0.8 and Mole fraction of O2(g) = 0.2
Partial pressure of N2(g) = 0.8 1 = 0.8 atm
Partial pressure of O2(g) = 0.2 1 = 0.2 atm
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