A vessel at 1000 K contains ${\mathrm{CO}}_2$with a pressure of 0.5 atm. Some of CO2 is converted into CO on addtion of graphite. The value of 'K' at equilibrium when total pressure is 0.8 atm will be

The balanced equation is

${\mathrm{CO}}_2\left(\mathrm{g}\right)+\mathrm{C}\left(\mathrm{s}\right)\rightleftharpoons 2\mathrm{CO}\left(\mathrm{g}\right)$

Initial(atm):     0.5         0 

Change(atm): x            2x

Equilib(atm): 0.5- x      2x

Total pressure = 0.8

$0.5+\mathrm{x}=0.8\Rightarrow \mathrm{x}=0.3$

Equilibrium: 0.5- 0.3   2$\times$0.3

                      =0.2               0.6

${\mathrm{K}}_{\mathrm{P}}=\frac{{\mathrm{P}}_{{\mathrm{CO}}_2}}{{\mathrm{P}}_{{\mathrm{CO}}_2}}=\frac{{}^3\cancel{0.6}\times 0.6}{\cancel{0.2}}$

=1.8 atm