Question

$500 \,ml$ each of $2 \times 10^{-2} M \,NaHSO _{4}$ and $2 \times 10^{-2} M$ $Na _{2} SO _{4}$ are mixed. Calculate $\left[ H ^{+}\right]$in final solution. [Given: $K _{ a _{2}\left( H _{2} S O _{4}\right)}=10^{-2}, \sqrt{2}=1.414$ ]
[Write your answer by multiplying with $10^{5}$ ]

Answer 1

$\underset{(0.01-x)}{ HSO _{4}^{-} } \rightleftharpoons \underset{(x)}{H ^{+}}+\underset{(0.01 + x)}{ SO _{4}{ }^{2-} }$
$10^{-4}-10^{-2} x=10^{-2} x+x^{2}$
$x=\frac{-2 \times 10^{-2} \pm \sqrt{4 \times 10^{-4}+4 \times 10^{-4}}}{2}$
$=\frac{-2 \times 10^{-2}+2 \times 10^{-2} \times \sqrt{2}}{2}$
$=10^{-2}+\sqrt{2} 10^{-2}=0.414 \times 10^{-2}$