Question
The concentration of $$\left[ {{H^ + }} \right]$$ and concentration of $$\left[ {O{H^ - }} \right]$$ of a $$0.1\,M$$ aqueous solution of $$2\% $$ ionised weak monobasic acid is
[ ionic product of water $$ = 1 \times {10^{ - 14}}$$ ]
A.
$$0.02 \times {10^{ - 3}}M\,{\text{and}}\,5 \times {10^{ - 11}}M$$
B.
$$1 \times {10^{ - 3}}M\,{\text{and}}\,3 \times {10^{ - 11}}M$$
C.
$$2 \times {10^{ - 3}}M\,{\text{and}}\,5 \times {10^{ - 12}}M$$
D.
$$3 \times {10^{ - 2}}M\,{\text{and}}\,4 \times {10^{ - 13}}M$$
Answer :
$$2 \times {10^{ - 3}}M\,{\text{and}}\,5 \times {10^{ - 12}}M$$
Solution :
$$\eqalign{
& \left[ {{H^ + }} \right]\,{\text{in monobasic acid}} \cr
& = {\text{molarity}}\, \times \,{\text{degree of ionisation}} \cr
& = 0.1 \times \frac{2}{{100}} \cr
& = 2 \times {10^{ - 3}}M \cr
& {\text{ionisation constant of water}} \cr
& {K_w} = \left( {{H^ + }} \right)\left( {O{H^ - }} \right) \cr
& \left[ {O{H^ - }} \right] = \frac{{{K_w}}}{{\left[ {{H^ + }} \right]}} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{1 \times {{10}^{ - 14}}}}{{2 \times {{10}^{ - 3}}}} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 5 \times {10^{ - 12}}M \cr} $$