${\mathrm{A}}_{\left(\mathrm{g}\right)}+3{\mathrm{B}}_{\left(\mathrm{g}\right)}\underset{ }{\rightleftharpoons }4{\mathrm{C}}_{\left(\mathrm{g}\right)}$ . Initial concentration of A is equal to that of B. The equilibrium concentration of A and C are equal. ${\mathrm{K}}_{\mathrm{C}}$ is equal to :

$\text{A\hspace{0.17em}\hspace{0.17em}+\hspace{0.17em}\hspace{0.17em}3B\hspace{0.17em}}\underset{ }{\rightleftharpoons }\text{\hspace{0.17em}4C}$

Initial :   1      1           0
Equilib  : 1-x  1-3x     4x

[A] = [C]
1 – x = 4x   x = 0.2
[A] = 1-0.2 = 0.8
[B] = 1- 3x : 1 – 0.6 = 0.4, [C] = 4x = 0.8

${\text{K}}_{\text{C}}\text{=}\frac{{\left[\text{C}\right]}^{\text{4}}}{\left[\text{A}\right]{\left[\text{B}\right]}^{\text{3}}}\text{=\hspace{0.17em}}\frac{{\left[\text{0.8}\right]}^{\text{4}}}{\left[\text{0.8}\right]{\left[\text{0.4}\right]}^3}\text{=8}$