# JEE Main & Advanced Chemistry States of Matter The Critical State

The Critical State

Category : JEE Main & Advanced

(1) A state for every substance at which the vapour and liquid states are indistinguishable is known as critical state. It is defined by critical temperature and critical pressure.

(2) Critical temperature $\mathbf{(}{{\mathbf{T}}_{\mathbf{c}}}\mathbf{)}$ of a gas is that temperature above which the gas cannot be liquified however large pressure is applied. It is given by, ${{T}_{c}}=\frac{8a}{27Rb}$

(3) Critical pressure $\mathbf{(}{{\mathbf{P}}_{\mathbf{c}}}\mathbf{)}$ is the minimum pressure which must be applied to a gas to liquify it at its critical temperature. It is given by, ${{P}_{c}}=\frac{a}{27{{b}^{2}}}$

(4) Critical volume $\mathbf{(}{{\mathbf{V}}_{\mathbf{c}}}\mathbf{)}$ is the volume occupied by one mole of the substance at its critical temperature and critical pressure. It is given by, ${{V}_{c}}=3b$

(5) Critical compressibility factor $\mathbf{(}{{\mathbf{Z}}_{\mathbf{c}}}\mathbf{)}$ is given by, ${{Z}_{c}}=\frac{{{P}_{c}}{{V}_{c}}}{R{{T}_{c}}}=\frac{3}{8}=0.375$

A gas behaves as a Vander Waal’s gas if its critical compressibility factor $({{Z}_{c}})$ is equal to 0.375. A substance is the gaseous state below ${{T}_{c}}$is called vapour and above ${{T}_{c}}$is called gas.

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