Question

Calcium lactate is a salt of a weak acid represented as $Ca ( Lac )_{2}$. Its saturated solution contain $0.13$ mole in $0.50\,L$ solution and $pH$ is $8.4$. Assume complete dissociation of the salt, $p K_{a}$ of the lactic acid is

• A. 6.16
• B. 10.92
• C. 3.085
• D. 5.80

Answer 1

Answer: (C)

Lactic acid is a weak monobasic acid

$\underset{ M }{ Ca ( Lac )_{2}} \rightleftharpoons \underset{2M }{2 Lac ^{-}}+ Ca ^{2+}$

$Ca ( Lac )_{2}=\frac{0.13 \,mol }{0.50 \,L }=0.26 \,mol \,L ^{-1}$

$\therefore [ Lac ]=0.26 \times 2=0.52\, M$

Aqueous solution of lactate is basic due to hydrolysis of $Lac ^{-}$
$Lac^{-}+ H _{2} O \rightleftharpoons LacH + OH^{-}$

$pH =7+\frac{p K_{a}}{2}+\frac{\log C}{2}$

$8.4=7+\frac{p K_{a}}{2}+\frac{\log 0.52}{2}$

$8.4=7+\frac{p K_{a}}{2}+(-0.14)$

$pk _{ a }=3.08$