# Dalton’s law of partial pressure || Numeric Example

## Dalton's law of partial pressure :

When a gas is placed in a vessel, it exerts pressure on the walls of the vessel. If 2 – 3 gases are put together in the vessel, then all these together will exert pressure.

Dalton discovered in 1802, that if two or more gases that do not react chemically with each other are kept in a vessel at a certain temperature, then each gas exerts the same pressure as it does at the same temperature in that vessel. But put it alone. The pressure exerted by a gas present in the mixture alone is called partial pressure.

The total pressure of a mixture of gases is equal to the sum of the partial pressures of its constituent gases. On the basis of this, Dalton presented the following rules related to gases –

When two or more gases that do not react chemically with each other are kept in a vessel at a certain temperature, the pressure of the mixture is equal to the sum of the partial pressures of those gases at the same temperature.

This law is called dalton’s law of partial pressure after its discoverer.

Let there be four different gases A, B, C and D in a mixture of a gas. If their partial pressures are p1 , p2 , p3 and p4 respectively, then the absolute pressure P of a mixture of gases can be expressed by the following equation:

P = p1 + p2 + p3 + p4

Example :- Let us assume that the pressure of a certain amount of air and water vapor in a vessel of 1000 ml volume at 25°C is 95 mm and 25 mm respectively. If the quantities of these two are closed together in the same vessel at the same temperature, then the pressure of the mixture will be 95 + 25 i.e. 120 mm.

This law is used in the volume calculations of gases to find the pressure of dry gas. Often the gases are collected over the water, due to which some water vapor is also mixed with them. The pressure of the moist gas thus obtained is the sum of the pressure of the dry gas and the pressure of the water vapor. The pressure exerted by water vapor at a given temperature is called aquous tension.

Therefore, to find the pressure of the dry gas, the pressure obtained at that temperature is subtracted from the pressure of the gas obtained in the experiment.

Pressure of gas obtained in experiment = pressure of dry gas + vapor pressure

Hence, pressure of dry gas = pressure of gas obtained in experiment + vapor pressure

Example :- The partial pressure of oxygen, hydrogen and nitrogen gas at 25 C is 135, 145 and 225 mm respectively. What will be the total pressure of the mixture of these gases at the same temperature?

Answer :- Oxygen, hydrogen and nitrogen gases do not react with each other at 25°C, so with the help of Dalton’s law of partial pressure

P = p1 + p2 + p3

Whereas P is the absolute pressure of the mixture.

p1 , p2 and p3 are the partial pressures of the constituent gases.

p1 = 135 mm p2 = 145 mm and p3 = 255

so that

P = 135 + 145 + 255

= 535 mm

Hence, the total pressure of the mixture = 535 mm

Example :- Two different gases are filled in two letters. Their pressures are 750 mm and 600 mm respectively. If these two vessels are connected keeping the temperature constant, what will be the pressure of the mixture?

Answer :- Pressure of mixture P = p1 + p2

= 750 + 600

=1350 mm

Pressure of mixture = 1350 mm

## Gaseous Diffusion :

In whatever space is available to the gases, they spread evenly. This property of gases is called the property of diffusion and this phenomenon is called diffusion.

The mixing of two or more substances into a homogeneous mixture by itself is called diffusion.

Example :- After placing a jar full of ammonia gas upside down on a jar filled with air, in some time both the air and ammonia gases spread equally in both the jars.