# Ideal Gas Equation

To study the property of gasses we need to have a standard gas to study, but which gas should it be? Hydrogen, oxygen, helium, nitrogen, carbon dioxide to name a few, and there are thousands of other gasses we could study, but researchers have found that no matter what gas you study, if you take 1 mole sample of that gas and put it in the same container and maintain a constant temperature, the pressure is almost the same, and at lower densities even those tiny differences in the measurements also disappear. Thus, at really low densities, all the real gases tend to obey one universal law,

This law is described by an equation known as the Ideal gas equation,

$PV$ = $nRT$

In which P is the absolute pressure, n is the number of moles of gas present, and T is the temperature in degree Kelvin, the symbol R is a constant called as the Gas constant, and this gas constant is same for all the gasses which is equal to 8.31 J/mol.K.

This equation is sometimes also called as the ideal gas equation; this equation holds well as long as the density is kept low, this equation is applicable for a single gas or even mixture of multiple gasses where n will stand for the total moles of gas particles in the given mixture.

We can even rewrite the above ideal gas equation in terms of the Boltzmann constant k, which is defined as

$k$ = $\frac{R}{N_A}$ = $\frac{8.31 J⁄mol.K}{6.02 \times 10^{23} mol^{-1}}$ = $1.38 \times 10^{-23} J⁄K$

Therefore using the above equation we get,

$nR$ = $Nk$

Substituting this in the ideal gas equation we get,

$PV$ = $NkTs$

Where N is the number of molecules of gas present in the sample, you can find this number by multiplying the moles with the Avogadro’s number.

The only difference between the two expressions is that the first involves the use of moles and the later involves the use of molecules to calculate the required parameters. There is no ideal gas, but all real gas tend to approach that property when the density gets low enough, this is possible because the molecules of the gas are so far apart from one another that they do not interact with each other. Thus, the ideal gas concept helps us in studying the real gases.

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#### Practise This Question

The intercept of the line drawn for log P (P in atm) and log1V (V in the litre) for 1 mole of an ideal gas at  27 C is equal to