Question

The degree of dissociation of acetic acid in a $0.1M$ solution is $1.32\times {10}^{-2}$, find out its $p{K}_a$ value.
Take $lo{g}_{10}\left(1.76\right)=0.25$

• A. $8.75$
• B. $4.75$
• C. $6.75$
• D. $2.75$

Answer 1

The correct option is B $4.75$

Given: degree of dissociation of $C{H}_{3}COOH=1.32\times {10}^{-2}=0.0132$

So, according to given reaction:

$C{H}_{3}COOH\leftrightharpoons C{H}_{3}CO{O}^{-}+H^{+}$
$initially0.100$
$atequilibrium0.1(1-0.0132)0.1\left(0.0132\right)0.1\left(0.0132\right)$

$K_a=\frac{\left[C{H}_{3}CO{O}^{-}\right]\left[H^{+}\right]}{\left[C{H}_{3}COOH\right]}=\frac{(0.1\times 0.0132)(0.1\times 0.0132)}{(0.1\times (1-0.0132\left)\right)}=1.76\times {10}^{-5}$

$p{K}_a=-lo{g}_{10}\left(K_a\right)$
putting values,
$p{K}_a=-lo{g}_{10}(1.76\times {10}^{-5})=-(0.25-5)$
$p{K}_a=4.75$