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  4. The dissociation constant of acetic acid Ka is 1.74× 10-5 at 298 K . The pH of a solution of 0.1 M acetic acid is:

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Q. The dissociation constant of acetic acid $ {{K}_{a}} $ is $ 1.74\times {{10}^{-5}} $ at $ 298\, K $ . The $ pH $ of a solution of $ 0.1\, M $ acetic acid is:

KEAMKEAM 2004

Solution:

For $ 0.1M $ acetic acid, or $
C=0.1\,J{{K}^{-1}}mo{{l}^{-1}} $
$ {{K}_{a}}=1.74\times {{10}^{-5}} $
$ pH=? $
According to Ostwald dilution formula,
$ [{{H}^{+}}]=\sqrt{{{K}_{a}}\times C} $
$ =\sqrt{1.7\times {{10}^{-5}}\times 0.1} $
$ =\sqrt{0.017\times {{10}^{-4}}} $
$ pH=-{{\log }_{10}}[{{H}^{+}}] $
$ =-{{\log }_{10}}[\sqrt{0.017\times {{10}^{-4}}}] $
$ pH=2.88 $