Chemistry - Chemical Equilibrium Question with Solution | TestHub

$2HI(g)\rightleftharpoons H_2(g)+I_2(g)$

Initial moles: $1$

Equilibrium moles: $(1-\alpha )$ $\frac{\alpha }{2}$ $\frac{\alpha }{2}$

$K_p=\frac{{\left(\frac{\alpha }{2}{P}_T\right)}^2}{((1-\alpha {)}^2{P}_T{)}^2}$ ; $\frac{\alpha }{(1-\alpha )}=2\sqrt{K_p}$

$\sqrt{K_p}=\frac{\alpha }{2(1-\alpha )}$

$2\sqrt{K_p}(1-\alpha )=\alpha$

$2\sqrt{K_p}-2\alpha \sqrt{K_p}=\alpha$

$2\sqrt{K_p}=\alpha +2\alpha \sqrt{K_p}$

$2\sqrt{K_p}=\alpha (1+2\sqrt{K_p})$

$\alpha =\frac{2\sqrt{K_p}}{1+2\sqrt{K_p}}$