Question

The ionic strength of $C{H}_{3}CO{O}^{-}$ ion in $0.1M$ $C{H}_{3}COOH$ solution having $K_a=1.8\times {10}^{-5}$ is

• A. $0.1$
• B. $0.05$
• C. $6.7\times {10}^{-4}$
• D. $1.34\times {10}^{-3}$

Answer 1

The correct option is C $6.7\times {10}^{-4}$

$C{H}_{3}COOH\rightleftharpoons C{H}_{3}CO{O}^{-}+H^{+}$

$\left[C{H}_{3}CO{O}^{-}\right]=C\alpha =C\sqrt{\frac{K_a}{C}}=\sqrt{K_{a}C}=\sqrt{1.8\times {10}^{-5}\times 0.1}=1.34\times {10}^{-3}$

Ionic strength of $C{H}_{3}CO{O}^{-}=\frac{1}{2}n\left[C{H}_{3}CO{O}^{-}\right]Z^2=\frac{1}{2}\times 1\times 1.34\times {10}^{-3}\times (-1{)}^2=6.7\times {10}^{-4}$
where, n = no. of ions and Z= charge on the ion.
Option C is correct.