Question

In an aqueous solution of volume $500mL$, when the reaction of $2A{g}^{+}+Cu\rightleftharpoons C{u}^{2+}+2Ag$ reached equilibrium the $\left[C{u}^{2+}\right]$ was $xM$. When $500mL$ of water is further added, at the equilibrium $\left[C{u}^{2+}\right]$ will be :

• A. $2xM$
• B. $xM$
• C. between $xM$ and $x/2M$
• D. less than $x/2M$

Answer 1

The correct option is D less than $x/2M$

$2A{g}^{+}+Cu\rightleftharpoons C{u}^{2+}+2Ag$
At equilibrium $ax$
if $V$ is $500mL$
$K_c=\frac{\left(\frac{x\times 1000}{500}\right)}{{\left(\frac{a\times 1000}{500}\right)}^2}=\frac{x}{2a^2}$
If volume is doubled, then $a$ becomes $a/2$; Let $x$ be $x^{\prime }$, then if $V=1000mL$
$K_c=\frac{x^{\prime }}{{\left(a/2\right)}^2}=\frac{4x^{\prime }}{a^2}$
$\therefore \frac{x}{2a^2}=\frac{4x^{\prime }}{a^2}$ or $x^{\prime }=\frac{x}{8}$ or $x^{\prime }<\frac{x}{2}$
$K_c=\frac{\left[C{u}^{2+}\right]}{{\left[A{g}^{+}\right]}^2}=\frac{x}{{\left(a\right)}^2}$
to have $K_c$ constant $\left[C{u}^{2+}\right]$ will be less than $\frac{x}{2}$.