# Derivation of Ideal Gas Equation

According to the Ideal Gas equation-

The product of Pressure & Volume of a gas bears a constant relation with the product of Universal gas constant and the temperature.

i.e. $pv = nRT$

Derivation of the Ideal Gas Equation-

Let us consider the pressure exerted by the gas to be ‘p,

Volume of the gas be – ‘v

Temperature be – T

n – be the number of moles of gas

Universal gas constant – R

According to Boyle’s Law,

At constant n & T, the volume bears an inverse relation with the pressure exerted by a gas.

i.e. $v \propto \frac{1}{p}$ ………………………………(i)

According to the Charles’ Law,

When p & n are constant, the volume of a gas bears a direct relation with the Temperature.

i.e. $v \propto T$ ………………………………(ii)

When p & T are constant, then the volume of a gas bears a direct relation with the number of moles of gas.

i.e. $v \propto n$ ………………………………(iii)

Combining all the three equations, we have-

$v \propto \frac{nT}{p}$

or $pv = nRT$

where R is the Universal gas constant, which has a value of 8.314 J/mol-K

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