Question

The $K_c$ for the reaction $A+B\iff C$ is $4$ and $K_c$ for $2A+D\iff C$ is $6$ the value of $K_c$ for $C+D\iff 2B$ is:

Answer 1

$\left(i\right)A+B\rightleftharpoons C$

$K_{c_1}=\frac{\left[C\right]}{\left[A\right]\left[B\right]}=4$ (1)

$\left(ii\right)2A+D\rightleftharpoons C$

$K_{c_2}=\frac{\left[C\right]}{{\left[A\right]}^2\left[D\right]}=6$ (2)

$\left(iii\right)C+D\rightleftharpoons 2B$

$K_{c_3}=\frac{{\left[B\right]}^2}{\left[C\right]\left[D\right]}$ (3)

using equation (1),

$\left[B\right]=\frac{\left[C\right]}{4\left[A\right]}$

put the value of [B] in equation (3)

$K_{c_3}=\frac{{\left[C\right]}^2}{16{\left[A\right]}^2\left[C\right]\left[D\right]}=\frac{\left[C\right]}{16[A{]}^2\left[D\right]}$

From equation (2)

$K_{c_3}=\frac{K_{c_2}}{16}=\frac{6}{16}=\frac{3}{8}$