Question

An aqueous solution contains $10$% ammonia by mass and has a density $0.99g$ ${cm}^{-3}$. Calculate hydroxyl and hydrogen ion concentration in this solution.
($K_a$ for ${NH}_4^{+}=5.0\times {10}^{-10}M$)

Answer 1

Mass of $1$ litre solution $=1000\times 0.99g=990g$

${NH}_3$ present in $990g$ solution$=99g$

$1$ litre solution contains$=\frac{99}{17}=5.8mole$

${NH}_3+H_{2}O\rightleftharpoons {NH}_4^{+}+{OH}^{-}$

$K_b=\frac{\left[{NH}_4^{+}\right]\left[{OH}^{-}\right]}{\left[{NH}_3\right]}=\frac{x\times x}{(5.8-x)}=\frac{x^2}{(5.8-x)}=\frac{x^2}{\left(5.8\right)}$

$K_b=\frac{K_w}{K_a}=\frac{{10}^{-14}}{5.0\times {10}^{-10}}=2\times {10}^{-5}$

So, $2\times {10}^{-5}=\frac{x^2}{\left(5.8\right)}$

$x=1.078\times {10}^{-2}mol{L}^{-1}$

$\left[{OH}^{-}\right]=x=1.078\times {10}^{-2}M$

$\left[H^{+}\right]=\frac{{10}^{-14}}{1.078\times {10}^{-2}}=9.27\times {10}^{-13}M$