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Q.
The ratio of dissociation constant of two weak acids $HA$ and $HB$ is $4 .$ At what molar concentration ratio, the two acids will have same $pH$ in separate solutions:
Solution:
$K _{ a }=\frac{\left[ H ^{+}\right]\left[ A ^{-}\right]}{[ HA ]}=\frac{\left[ H ^{+}\right]^{2}}{[ HA ]}\left(\therefore \left[ H ^{+}\right]=\left[ A ^{-}\right]\right)$
and $K _{ b }=\frac{\left[ H ^{+}\right]\left[ B ^{-}\right]}{[ HB ]}=\frac{\left[ H ^{+}\right]^{2}}{[ HB ]}\left(\therefore \left[ H ^{+}\right]=\left[ B ^{-}\right]\right)$
Also $H ^{+}$are same
$\therefore \frac{ K _{ a }}{ K _{ b }}=\frac{[ HB ]}{[ HA ]}=\frac{4}{1}$
$\frac{[ HA ]}{[ HB ]}=\frac{1}{4}$