One mole of ${\mathrm{A}}_2{\mathrm{B}}_4\left(\mathrm{g}\right)$ was sealed in a tube under atmospheric conditions at ${25}^{0}C$. Calculate the number of moles of  ${\mathrm{AB}}_2\left(\mathrm{gas}\right)$ present if the equilibrium  ${\mathrm{A}}_2{\mathrm{B}}_4\left(\mathrm{g}\right)\rightleftharpoons 2{\mathrm{AB}}_2\left(\mathrm{g}\right)({\mathrm{K}}_{\mathrm{c}}=16)$is reached after some time.

$A_2{B}_4\left(g\right)\rightleftharpoons 2A{B}_2\left(g\right)$

1                       0            initially

(1-X)                2X           at equilibrium

$K_c=\frac{{\left(2x\right)}^2}{(1-x)}=16$ (given), $4x^2=16-16x$,$4x^2+16x-16=0$, $x^2+4x-4=0$,

$x=\frac{-4\pm \sqrt{16+16}}{2}$   $=\frac{-4\pm 4\sqrt{2}}{2}$ $=\frac{-4\pm 4\times 1.414}{2}$ $=\frac{-4\pm 5.656}{2}=\frac{1.656}{2}$ = 0.828

The number of moles of ${\mathrm{NO}}_2=2\mathrm{x}$ = 2 x 0.828 = 1.656