Law of Partial Pressures

The rule that states that the total pressure exerted by a mixture of gases equals the sum of the partial pressures exerted by each individual gas in the mixture is known as Dalton’s law of partial pressures (or vice versa). The overall pressure exerted by a mixture of two gases A and B, for example, is equal to the sum of gas A and gas B’s respective partial pressures.

Formula for Dalton’s Law

Using mathematics, we can express Dalton’s law of partial pressures in the following way:

Ptotal = ∑ni= pi∑i=npi (or) Ptotal = P1 + P2 + P3 +… + Pn 

Where,

The symbol Ptotal denotes the total pressure exerted by the combination of gases.

The partial pressures of the gases 1, 2,…,n  in a mixture of ‘n’ gases are P1, P2,…, Pn.

Partial Pressures are expressed in terms of Mole Fractions.

The product of the partial pressure of a certain gas divided by the total pressure exerted by the gaseous mixture equals the mole fraction of that gas in a mixture of gases. This mole fraction can also be used to compute the total number of moles of a constituent gas when the total number of moles in the mixture is known. Furthermore, with the help of the equation provided below, it is possible to calculate the volume occupied by a specific gas in a mixture using the mole fraction.

Examples of Dalton’s Law of Partial Pressure that have been solved

Example No. 1

The walls of a container that contains a mixture of hydrogen gas and oxygen gas are subjected to a total pressure of 1.5 atm. In a mixture with a partial pressure of hydrogen equal to 1 atm, calculate the mole fraction of oxygen present.

Assume that PHydrogen = 1 atm and Ptotal = 1.5 atm

Ptotal = PHydrogen + POxygen is calculated using Dalton’s law formula.

Because of this, POxygen = 0.5 atm

Now, the mole fraction of oxygen, Oxygen = 0.5/1.5 = 0.33

As a result, the mole fraction of oxygen in the mixture is 0.33 moles/litre.

In an empty 10L container at 300 degrees Celsius, 30 litres of gas A kept under pressure of 1 atm and 15 litres of gas B kept under pressure of 2 atm are transferred from two 1 atm-pressured containers. Figure out how much total pressure is present inside the container, as well as the partial pressures of gases A and B (Assume that A and B are ideal gases).

PV = nRT is derived from the ideal gas equation.

1 mol A = (30L×1atm)/(0.08206 atm.L.mol-1) × 300K = 1.22 mol A.

1 mol B = (15 × 2atm)/(0.08206 atm.L.mol-1) × 300K = 1.22 mol B

There are 2.44 mol of moles in the gaseous mixture, which is the total number of moles in the mixture.

Total pressure inside the 10L container = Ptot = nRT/V 

Ptot = (2.44mol × 0.08206 atm) L.mol-1.K-1 × 300K)/10L = 6.006 atm (L.mol-1.K-1 × 300K)

As a result, the total pressure inside the 10 litre container is 6.006 atmospheres.

In this equation, the mole fraction of gas A equals the mole fraction of gas B = (1.22 mol/2.44 mol)=0.5.

As a result, the partial pressure of gas A = 0.5 × 6.006 = 3.003 atm, and the partial pressure of gas B = 0.5 × 6.006 = 3.003 atm.

In the resulting 10L container, the partial pressures of gases A and B are equal to 3.003 atm, indicating that both gases have equal partial pressures

Conclusion.

Partial impression is the pressure exerted by a mixture of gases when their volume is the same. In a mixture, each gas exerts some pressure. The overall pressure of an ideal gas mixture is equal to the sum of the partial pressures of the component gases.