A vessel at $1000 \mathrm{K}$ contains ${\mathrm{CO}}_2$ at $0.5 \mathrm{atm}$. If certain amount of ${\mathrm{CO}}_2$ is converted into $\mathrm{CO}$ by the addition of graphite, the following equilibrium is established ${\mathrm{CO}}_2+\mathrm{C}\rightleftharpoons 2\mathrm{CO}$, at a pressure of $0.8$ atm, then equilibrium constant is ....... atm.

The reaction is, ${\mathrm{CO}}_2+\mathrm{C}\to 2\mathrm{CO}$

Initial pressure - $0.5 \mathrm{atm}0 \mathrm{atm}$

Final pressure - $(0.5-\mathrm{x})atm2\mathrm{x}$atm

Total pressure at equilibrium $=$ Partial pressures of ${\mathrm{CO}}_2$ and $\mathrm{CO}$

$=(0.5-\mathrm{x})+2\mathrm{x}=0.8 \mathrm{atm}\text{ (given) }$

$\therefore {\mathrm{K}}_{\mathrm{p}}=\frac{{\mathrm{p}}_{\mathrm{CO}}^2}{{\mathrm{p}}_{{\mathrm{CO}}_2}}=\frac{(0.6{)}^2}{0.2}=1.8 \mathrm{atm}$

Hence the correct answer is (A) 1.8