Question

$ A\,\,0.1 $ aqueous solution of a weak acid is $ 2% $ ionized. If the ionic product of water is $ 1\times {{10}^{-4}}, $ the $ [O{{H}^{-}}] $ is

• A. $ 5\times {{10}^{-12}}M $
• B. $ 2\times {{10}^{-3}}M $
• C. $ 1\times {{10}^{-4}}M $
• D. None of these

Answer 1

Answer: (A)

Since, it is a weak acid, the equation to calculate $ [{{H}^{+}}] $ is $ =C\times \alpha (\alpha =% $ of ionization) $ =0.1\times 0.02=2\times {{10}^{-3}}M $ $ {{K}_{w}}=[{{H}^{+}}][O{{H}^{-}}] $ $ [O{{H}^{-}}]=\frac{{{K}_{w}}}{[{{H}^{+}}]}=\frac{1\times {{10}^{-14}}}{2\times {{10}^{-3}}} $ $ =5\times {{10}^{-12}}M $