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Q. $pK _{ a _{1}}, pK _{ a _{2}}$ and $pK _{ a _{3}}$ of $H _{3} PO _{4}$ are respectively $4,8,12$ respectively TK. To a $50 \,ml$ solution of $0.1 \,M\, Na _{3} PO _{4}$, $50\, ml \,0.2\, M \,HCl$ is added. Find the $pH$ of the mixture obtained at TK.

Equilibrium

Solution:

$PO _{4}^{3-}+2 H ^{+} {\longrightarrow} H _{2} PO _{4}^{-}$
$\therefore pH =\frac{ pK _{ a _{1}}+ pK _{ a _{2}}}{2}=6$