Question

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

Answer 1

mass of one litre solution$=1000\times 0.99g=990g$

$N{H}_3$ present in 990g solution = 99g

1 litre solution contains=99/17 = 5.8 mole

$N{H}_3+H_{2}O\to N{H}_4^{+}+O{H}^{-}$

$K_b=\frac{\left[N{H}_4^{+}\right]\left[O{H}^{-}\right]}{\left[N{H}_3\right]}=\frac{x^2}{5.8}$

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

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

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

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

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