Question

For the reaction $A+B\rightleftharpoons C+D$, the initial concentration of $A$ and $B$ are equal. The equilibrium concentration of $C$ is half of the initial concentration of $A$. The equilibrium constant is ______.

Answer 1

$A+D\rightleftharpoons C+B$
$a$ $a$ $0$ $0$
$a-na-n$ $\frac{a}{2}$ $\frac{a}{2}$
$n=\frac{a}{2}$
$=a-\frac{a}{2}\frac{a-a}{2}\frac{a}{2}\frac{a}{2}$
$=\frac{a}{2}\frac{a}{2}\frac{a}{2}$
$=\frac{\left[C\right]\left[D\right]}{\left[A\right]\left[B\right]}$
$=\frac{\left(\frac{a}{2}\right)\left(\frac{a}{2}\right)}{\left(\frac{a}{2}\right)\left(\frac{a}{2}\right)}$
$=1$