Ideal Gas Equation - Learn Ideal Gas Equation & Limitations

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Ideal Gas Equation

PV =nRT is considered as Ideal Gas Equation which describes the behaviour of a gas. This is also known as the General Equation of gas. This equation gives the relationship between pressure, temperature, volume and amount of gas.

Ideal Gas Equation Derivation

Boyle’s Law states that the Volume of the system is inversely proportional to the pressure of the system where the number of moles and temperature remains constant.

Charle’s Law states that the Volume of the system is directly proportional to the Temperature.

According to Avogadro’s Law the volume of the system is directly proportional to the number of moles contained in the system.

Combining all these equations we get,

R: Gas Constant

This equation is known as Ideal Gas Law. According to the Equation, Ideal gas is the one who’s Volume is proportional to the number of moles and temperature and inversely proportional to the pressure. This equation is true for only ideal gases. An ideal gas is a hypothetical condition to a gaseous substance where there are negligible intermolecular forces and molecular size is insignificant as compared to the empty spaces between molecules. The condition which can result in an ideal gas is low pressure and high temperature only.

Value of Gas Constant R

In equation PV=nRT, If P is expressed in atmosphere (atm), V in litres(L), T in kelvin(K), and n in moles(mol). Substituting it in the Ideal Gas Equation, we have

PV together as a unit of energy. So The Unit of R is J/K.mol

This Ideal Gas Equation can be used to find the value of any one of the variable if other four are known. We can also predict the final state(P, V, T, n) of the gas when its initial state(P, V, T, n) of the variables is known. Let, there be two conditions of an ideal gas: initial and final condition.

Initial condition: P_i, V_i, n_i, T_i

Final condition: P_f, V_f, n_f, T_f

Then,

This will result in

Since both are the values of R, we get

This equation is known as a general gas equation.

Standard Temperature and Pressure (STP)

T = 273.15 K (0 degree Celcius)

P= 10⁵ Pa (1 bar)

The volume of 1 mole of an ideal gas = 22.71 litres (at STP)

The volume of 1 mole of an ideal gas = 22.41 litres (at 1 atm and 0 degrees Celcius)

Limitations of Ideal Gas

An ideal gas is based on assumptions that are not true.

In reality, Ideal gas does not exist, but the ideal gas equation is very helpful to understand the behaviour of gases during reactions.
Gases at low density, low pressure and high temperature approximately behave as Ideal Gas.
Ideal gas law doesn’t work for low temperature, high density and extremely high pressures because at this condition the molecular size and intermolecular forces matters.
Ideal gas law does not apply for heavy gases(refrigerants) and gases with strong intermolecular forces(like Water Vapour).

Summarised Notes

Check the summarised notes on Ideal Gas Equation to revise quickly.

The ideal gas equation is given by:

The general gas equation is given by:

Standard temperature and pressure are taken as 273.15 K (0 degrees Celcius) and 10⁵ Pa (1 bar) respectively.

Hope this article on the Ideal gas equation has helped you understand the concepts covered here. You can put your comment below in case you have a query or doubt.