Question

At $298K$, the equilibrium constant is $2\times 10^{15}$ for the reaction :
$Cu(s)+2A{g}^{+}(aq)\rightleftharpoons C{u}^{2+}(aq)+2Ag(s)$
The equilibrium constant for the reaction $\frac{1}{2}C{u}^{2+}(aq)+Ag(s)\rightleftharpoons \frac{1}{2}Cu(s)+A{g}^{+}(aq)$ is $x\times 10^{-8}$. The value of $x$ is ________ (Nearest Integer)

Answer 1

Answer: 2

$K_{eq}^{\prime }=\frac{1}{\sqrt{K_{eq}}}=\frac{1}{\sqrt{2\times 10^{15}}}=x\times 10^{-8}$
$\Rightarrow \frac{1}{\sqrt{20}}\times \frac{1}{10^7}=x\times 10^{-8}$
$\Rightarrow \frac{1}{\sqrt{20}}\times 10^{-7}=x\times 10^{-8}$
$\frac{10}{\sqrt{20}}=x$
$\Rightarrow x=\frac{\sqrt{10}}{\sqrt{2}}=\sqrt{5}=2.236$
$\simeq 2.24$