Class 11

Chemistry

Gases & Solutions

States of Matter

Why at extremely low pressures, the real gases obey the ideal gas equation?

At low pressures, volume $V$ is very large and hence the correction term b (a constant of small value) can be neglected in comparison to the very large value of $V$. Thus the van der Waal's equation for $1$ mole of a real gas.

$(P+V_{2}a )(V−b)=RT$ may be written as $(P+V_{2}a )(V)=RT$

or $PV+Va =RT$

or $PV=RT−Va $

For large $V$ (at very low pressures) $Va $ is very small and can be ignored.

$∴$ $PV$ becomes $RT$ at very low pressures.