Ideal Gas Laws

The ideal gas law is also called the general gas law. As the name suggests, the law applies under ideal conditions, but not to real gases. The ideal gas law correlates pressure, volume, temperature and amount of gas. It was formulated in 1824 by French physicist Émile Clapeyron.

The ideal gas law determines the product of the pressure and volume of one (1) gram of molecule of an ideal gas is the same as the product of absolute temperature of gas and the universal gas constant.

Ideal Gas Equation

The ideal gas equation comprises Boyle’s law, Charle’s Law and Avogadro’s law.

The ideal gas equation is given as

PV=nRT

Here,

P = pressure

V = volume

R = ideal gas constant

T = temperature

n = amount of substance

Ideal Gas Law Units

When the gas constant R is used as 0.082 L.atm/K.mol then the unit of pressure must be in atmospheric atm, unit of volume must be in litres L and the temperature should be in kelvin K.

If we use the gas constant as R = 8.31J/K.mol, we need to insert the P-pressure into the Pa units, the volume must be in the m3 units and the temperature T in the Kelvin-K units.

Ideal Gas Equation Derivation

The ideal gas equation consists of three laws which are Boyle’s law, Charle’s Law and Avogadro’s law.

Boyle’s Law

Boyle’s law establishes the relationship between volume and pressure at a constant temperature and a constant mass. Robert Boyle conducted an experiment on gases to study the variation in their behaviour under changing physical conditions.

According to Boyle’s law, at constant temperature if the pressure of gases increases then the volume of decreases. In simple words, Boyle’s law states that the volume of gas is inversely proportional to pressure if the temperature as well as the number of molecules are constant.

According to the Boyle’s law

P∝ 1/V

————- (1)

P=k1 x1/V

Here, 

k1= proportionality constant

Now,

k1 =PV

Here, k is constant. Therefore, for final volume and final pressure and the initial volume and initial pressure is given as

P1/P2=V2/V1

Here, 

P1= initial pressure

P2= final pressure 

V1= initial volume 

V2= final volume

Charle’s Law

In 1787 Jacques Charles analyzed the effect or influence of temperature on the volume of a gaseous element at constant pressure. He performed this analysis to understand the fact behind hot air balloon flight. According to his analysis, the volume of a gas is directly proportional to the temperature at constant pressure and mass.

It means when the temperature increases, the volume also increases and when the temperature decreases, then also the volume decreases. 

According to Charles Law

V∝T————- (2)

Therefore,

V=k2T

Avagadro’s Law

In 1811 Amedeo Avogadro combined the Dalton’s atomic theory and Gay Lussac’s law to derive another important gas law which is called Avogadro’s law. According to Avogadro’s law, at constant temperature and pressure, the volume of all gases consists of an equal number of molecules. In simple words, at constant temperature and pressure, the volume of a gas is directly proportional to the number of molecules present in that gas.

According to Avagadro’s Law

V∝n —————– (3)

Therefore,

 V=k3n

Now, for ideal gas equation, combine the equations (1), (2) and (3), hence we get 

V∝ nT/P 

When we remove the proportionality constant then we get 

V=nRT/P

Here,

R = gas constant 

And also

PV=nRT ———- (4)

Equation (4) is the ideal gas equation.

Ideal Gas

An ideal gas is a theoretical gas which is made from a set of point particles which moves randomly and that interact through elastic collisions.

In the ideal gas, the molecules of gas move freely in every direction, and the collision between them is considered as perfectly elastic, which means there is no loss of kinetic energy due to collision.

Although there is no such thing as an ideal gas, all real gases approach this property if the density is low enough. This is possible because the gas molecules are so far apart that they don’t interact with each other. The ideal gas concept helps us to study the real gases.

Forms of Ideal Gas Laws

Molar volume

The ideal gas equation in molar form is given as

Vm=V/n=RT/P

Therefore, 

PVm=RT

Here,

Vm= molar volume

Density and specific Volume 

⍴=m/V=nMw/V=PMw/RT

Now, we know, 

R/Mw=Rsp

Therefore, 

⍴=P/RspT

Here,

Rsp= specific gas constant

⍴= density 

Mw= molecular weight

Limitations of Ideal Gas Law

There are some limitations of ideal gas which are given here

1. The ideal gas law PV=nRT only applies to ideal gases. It is a good approximation to real gases at low pressure and/or high temperature. 
2. At high pressure and low temperature, the ideal law equation deviates from the behaviour of real gases. This is explained by the increasing intermolecular repulsive forces under these conditions.

Conclusion

An ideal gas is a theoretical gas which is made from a set of point particles which move randomly and that interact through elastic collisions.

The ideal gas law determines the product of the pressure and volume of one (1) gram of molecule of an ideal gas is the same as the product of absolute temperature of gas and the universal gas constant.

The ideal gas equation is given as

PV=nRT

The ideal gas equation consists of three laws which are Boyle’s law, Charle’s Law and Avogadro’s law.

According to Boyle’s Law

P∝1/V

According to Charles Law

V∝T

According to Avagadro’s Law

V∝n