Question

What is general gas equation or perfect gas equation? How will you derive it?

Answer 1

Let the pressure exerted by the gas = p

The volume of the gas = v

Temperature = T

Number of moles of gas= n

Universal gas constant – R

According to Boyle’s Law,

At constant n & T, the volume is inversely proportional to the pressure exerted by a gas.

i.e.

V∝ $\frac{1}{p}$ ……………………………… (i)

According to Charles’ Law,

When p & n are constant, the volume of a gas is directly proportional to the Temperature.

i.e.

V∝T ………………………………(ii)

According to Avogadro’s Law,

When p & T are constant, then the volume of a gas is directly proportional to the number of moles of gas.

i.e.

V∝ n ………………………………(iii)

Combining all the three equations, we have-

General gas equation or perfect gas equation-

V= $\frac{nT}{p}$

$\mathrm{PV}=\mathrm{nRT}$

where R is the Universal gas constant.