Chemistry

Problem

A certain gas

A

polymerises to a small extent at a given temperature and pressure :

nA \rightleftharpoons (A)_n

. Show that the gas obeys the approximate equation :

\frac{PV}{RT} = \left[ 1 - \frac{(n-1)K_C}{V^{n-1}} \right].

where

K_C = \frac{[A_n]}{[A]^n}

and

V

is the volume of the container. Assume initially one mole of

A

was taken in the container.