For the gaseous reaction $3{\mathrm{H}}_2+{\mathrm{N}}_2\iff 2{\mathrm{NH}}_3,$the equilibrium pressures of ${\mathrm{H}}_2 \mathrm{and} {\mathrm{N}}_2$ are 0.4 atm and 0.8 atm respectively. The total pressure of the equilibrium system is 2.8 atm. The value of ${\mathrm{K}}_{\mathrm{p}}$ is 

The equilibrium reaction is

${\mathrm{N}}_2+3{\mathrm{H}}_2\rightleftharpoons 2{\mathrm{NH}}_3$

At, equilibrium,${\mathrm{P}}_{{\mathrm{H}}_2}=0.4 \mathrm{atm}$

${\mathrm{P}}_{{\mathrm{N}}_2}=0.8 \mathrm{atm}$

According to Daltion’s law of partial pressure.

${\mathrm{P}}_{\mathrm{T}}={\mathrm{P}}_{{\mathrm{N}}_2}+{\mathrm{P}}_{{\mathrm{H}}_2}+{\mathrm{P}}_{{\mathrm{NH}}_3}$

$2.8=0.8+0.4+{\mathrm{P}}_{{\mathrm{NH}}_3}$

${\mathrm{P}}_{{\mathrm{NH}}_3}=(2.8-1.2) \mathrm{atm}=1.6 \mathrm{atm}$

${\mathrm{K}}_{\mathrm{p}}=\frac{{\left({\mathrm{P}}_{{\mathrm{NH}}_3}\right)}^2}{{\mathrm{P}}_{{\mathrm{N}}_2}.{\left({\mathrm{P}}_{{\mathrm{H}}_2}\right)}^3}$

${\mathrm{K}}_{\mathrm{p}}=\frac{{\left(1.6\right)}^2}{\left(0.8\right).{\left(0.4\right)}^3}$

$\therefore {\mathrm{K}}_{\mathrm{p}}=50$