Question

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

Answer 1

$ 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$