Dalton’s Law of Partial Pressure

Introduction

According to this law the total pressure exerted by a mixture of gases is equal to the sum of the partial pressures exerted by an individual gas. As for example the total pressure exerted by two gases A and B is equal to the sum of partial pressures exerted by gas A and gas B. 

Partial pressure

The pressure exerted by an individual gas present in a mixture of gases is known as the Partial Pressure. As for example if a container contains a mixture of two gases namely oxygen and nitrogen then the pressure exerted individually by oxygen and nitrogen on the walls of the container is referred to as their partial pressure. The pressure exerted by a mixture of these gases is known as the total pressure.

This Partial Pressure of gas is the measure of its thermodynamic activity. Partial pressure tells us about the reactivity of a gas in a fixed volume, based on the partial pressures various types of gases diffuse and dissolve. Thus this property of gases helps us to know about the chemical reactions of the gases. It is denoted by ‘ P ‘ along with the symbol of the gas in subscript e.g. PN2 , PO2 .

Formula for Dalton’s Law of Partial Pressure

As for example in a mixture of gases like oxygen, hydrogen and nitrogen then the total pressure exerted by the ideal gas mixture. It can be written as : 

P total = PO2  + PN2 +  PH2

Here, Ptotal refers to the total pressure of mixture of gases

PO2 refers to the partial pressure of oxygen gas

PN2 refers to the partial pressure of nitrogen

PH2  refers to the partial pressure of hydrogen

Relation between mole fraction and partial pressure

Mole fraction refers to the ratio of a particular gas present in a mixture to the total number of moles of  individual gases in the mixture.

Mole fraction: x I = no of moles of an individual gas / total no of moles of the mixture

Mole fraction is also known as the amount of fraction.

Mole fraction also helps in the calculation of the volume which is occupied by a specific gas in the mixture with the help of the below given formula:

Xi = Pi / Ptotal  =  Vi / Vtotal  = ni / ntotal 

Xi refers to the mole fraction, P refers to the pressure, V is volume and n is the number of moles.

Applications of Dalton’s Law

This law can be used in the calculation of different quantities such as:

  • Mole fraction of a gas in a mixture of gases which is equal to the partial pressure of the gas to the total pressure of the mixture.

  • In percentage calculation of a gas in a mixture.

  • Used in calculating the aqueous tension (i.e. the partial pressure of water vapours).

  • Dalton’s law is widely used in the calculation of partial pressures of gases like oxygen and carbon dioxide inside our body, thus it is widely used in biology.

Limitations of Dalton’s Law 

  • It is only applicable if the component gases in a mixture do not react with each other.

  • This law is not applicable to gases that react chemically.

Solved Examples

Q1. A mixture of gases contains 4.76 mol of Nitrogen, 0.74 mole of Oxygen and 2.5 mole of Hydrogen. Calculate the partial pressure of gases, if the total pressure is 2 atm. at a fixed temperature.

Ans. PN2 = xN2 PTotal = 0.595 × 2 = 1.19 atm.

 PO2 = xO2 PTotal = 0.093 × 2 = 0.186 atm.

 PH2 = xH2 PTotal = 0.312 × 2 = 0.624 atm.

Q2. A container holds three gases: oxygen, carbon dioxide, and helium. The partial pressures of the three gases are 2.00 atm, 3.00 atm, and 4.00 atm, respectively. What is the total pressure inside the container?

Ans. Dalton’s Law of Partial Pressures: 

Ptot = PO2 + PCO2 + PHe

The sum of all the partial pressures in the container gives us the total pressure:

Ptot = 2.00 atm + 3.00 atm + 4.00 atm = 9.00 atm

Q3. 80.0 liters of oxygen is collected over water at 50.0 °C. The atmospheric pressure in the room is 96.00 kPa. What is the partial pressure of the oxygen?

Ans. Ptot = PO2 + PH2O

96.00 kPa = PO2 + 12.344 kPa

PO2 = 83.66 kPa

Conclusion

Here our topic coverage ends hope you were able to grasp some knowledge about the Dalton’s Laws of partial pressure, mole fraction, partial pressures and many more.

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