Law of Partial Pressure

Dalton’s law of partial pressure states that in a mixture of non-reacting gases, the total pressure exerted equals the sum of partial pressure of an individual gas. Therefore, the pressure imposed by a single gas in a mixture of gases is known as its partial pressure. For example, if a container contains a combination of three gases, oxygen, nitrogen, and carbon dioxide, the pressure imposed by oxygen on the container’s walls is its partial pressure, just as the pressure exerted by nitrogen and carbon dioxide separately is their respective partial pressures. Therefore, the pressure exerted (total) on the container walls by the mixture of the gases equals the sum of partial pressures of gases in a mixture (oxygen, nitrogen, and carbon dioxide).

Dalton’s law of Partial pressure

The pressure applied by the individual gas in a mixture is called the partial pressure of that gas. Let us assume that we have a mixture of ideal gases, and we could use the ideal gas theory to resolve the problems of the gases in the mixture. Dalton’s law of the partial pressures says that the total pressure of a mixture of the gases is equivalent to the sum of partial pressures of component gases:

PT = P1 + P2 +P3 +P4 …………..Pn

Demonstrating the Partial Pressures in terms of The Mole Fraction

The ratio of a gas’s partial pressure to the overall pressure exerted by a gaseous form of the mixture is the mole fraction of that gas in a mixture of gases. When a total number of the moles in a mixture is known, that mole fraction could be used to determine the total no. of the moles of components of the gas. With the help of the equation below, you can calculate the volume taken by certain gas in the mixture using that mole fraction.

Here, Xi represents the mole fraction of gas.

• symbol ‘i’ represents a mixture of ‘n’ gases
• symbol ‘n’ represents a number of moles,
• symbol ‘P’ represents a pressure
• ‘V’ represents a volume.

Derivation from Dalton’s law

The ideal gas law is Dalton’s law. For real gases, it is simply a rough approximation. With increased pressure, the divergence from the Law rises. Compared to the open space between particles, the volume occupied by a gas becomes large at high pressure. At high pressure, the Intermolecular forces between particles increase.

Dalton’s law of Partial Pressure Assumptions

Gases are assumed to behave as ideal gases in Dalton’s law:

• A single given mixture of gases exerts a gas’s partial pressure.
• A single given mixture of gases exerts a gas’s partial pressure. The kinetic theory of gases governs gas molecules. In other words, they behave like point masses with minimal volume that are far separated from one another, neither are attracted nor repelled by others and collide with each other & container walls inelastic collisions.
• Dalton’s law accurately predicts gas behaviour, although real gases depart as pressure rises. 

As there is less space among gas molecules at high pressure, interactions become more important.

Avogadro Law of Partial pressure

Avogadro’s Law asserts that equal volumes of all gases contain the same number of molecules at the same temperature and pressure. Amedeo Avogadro, an Italian scientist, and physicist, first described the Law in 1811. This gas law, which is a mathematical relationship, can be written in a few different ways.

It might be stated as follows:

k = V/n

Here, 

k =constant of proportionality

V= volume of gas

n= number of moles in the gas

Because Avogadro’s law states that the ideal gas constant is the same for all gases,

constant,k = P1V1/T1n1 = P2V2/T2n2

V1/n1 = V2/n2

V1n2 = V2n1

Here, 

P = pressure of a gas

V =volume

T = temperature

n=number of moles

Conclusion

In the above notes, we have studied the Law of partial pressure, which was proposed by John Dalton. John Dalton, an English chemist, physicist, and meteorologist, proposed the law of partial pressure in 1802. The overall pressure of the mixture of gases equals the sum of partial pressures of the constituent gases. For an ideal gas mixture, Dalton’s law holds perfectly. Because the molecules in an ideal gas are so far apart, they do not react. With minor variations, the combination of real gases follows Dalton’s law.