One mole of ${\mathrm{N}}_2{\mathrm{O}}_{4\left(\mathrm{g}\right)}$ at 300 K is kept in a closed container under one atmosphere. It is heated to 600 K to decompose to ${\mathrm{NO}}_{2\left(\mathrm{g}\right)}$. If the resultant pressure at equilibrium is 2.4 atm, then which is correct?

${\mathrm{P}}_1=1 \mathrm{atm}$

${\mathrm{T}}_1=300\mathrm{k}$

${\mathrm{n}}_1=1$

${\mathrm{P}}_2=2.4 \mathrm{atm}$

${\mathrm{T}}_2=600\mathrm{k}$

${\mathrm{n}}_2=?$

$\frac{{\mathrm{P}}_1}{{\mathrm{P}}_2}=\frac{n_1{T}_1}{n_2{T}_2}$

$\frac{1}{2.4}=\frac{1\times 300}{n_2\times 600}$

${\mathrm{n}}_2=1.2$

${\mathrm{N}}_2{\mathrm{O}}_4\rightleftharpoons 2{\mathrm{NO}}_2$

1 mole           0 

1 − x               2x 

1 − x + 2x = 1.2, x= 0.2

1-0.2 $\left(20\% \mathrm{dissociated}\right)$

0.8                     0.4 

P = 2.4 atm 

1.6 atm           0.8 atm

${\mathrm{K}}_{\mathrm{p}}=\frac{0.8\times 0.8}{1.6}=0.4 \mathrm{atm}$