Question

What is the hydronium ion concentration of a 0.02 M solution of ${Cu}^{2+}$ solution of copper(II) perchlorate? The acidity constant of the following reaction is $5\times {10}^{-9}$.

${Cu}^{2+}(aq.)+2H_{2}O\left(I\right)\rightleftharpoons Cu{\left(HO\right)}^{+}(aq.)+H_3{O}^{+}(aq.)$

• A. $1\times {10}^{-5}$
• B. $7\times {10}^{-4}$
• C. $5\times {10}^{-4}$
• D. $1\times {10}^{-4}$

Answer 1

The correct option is A $1\times {10}^{-5}$

$C{u}^{2+}+2H_{2}O\rightleftharpoons Cu(OH{)}^{+}+H_3{O}^{+}$ $K=5\times {10}^{-9}$

$C=0.02M$

$\alpha \sqrt{\frac{K}{C}}$

$=\sqrt{\frac{5\times {10}^{-9}}{0.002}}$

$=\sqrt{\frac{5\times {10}^{-9}\times {10}^2}{2}}$

$\Rightarrow \sqrt{25\times {10}^{-8}}$

$=5\times {10}^{-4}\alpha 0.1$

Now, $C\alpha =\left[H_3{O}^{+}\right]=0.02\times 5\times {10}^{-4}$

$\Rightarrow {10}^{-5}$