Question

Calculate the percent dissociation for a 0.22 M solution of chlorous acid (HClO₂, K_a = 1.2 × 10^-2).

Short answer

K_avalue for HClO₂ is not very less that means it dissociates considerably.

The percent dissociation of 0.22 M solution of chlorous acid = 20.8%

Step-by-step solution

Calculating theAmount Dissociated

HClO₂solutiondissociates as,

$\begin{array}{l}{{\text{HClO}}_{\text{2}}}_{\text{(aq)}}\rightleftarrows {{\text{\hspace{0.33em}H}}^{\text{+}}}_{\text{(aq)}}{\text{+ClO}}_{\text{2}}{{}^{\text{-}}}_{\text{(aq)}}\\ 0.2200\\ 0.22-\text{x\hspace{0.33em}\hspace{0.33em}\hspace{1em}\hspace{0.33em}\hspace{0.33em}x\hspace{1em}\hspace{1em}x}\end{array}$

${\text{K}}_a=\frac{{\text{x}}^2}{0.22-\text{x}}=1.2\times {10}^{-2}\Rightarrow \text{x}=0.0457\text{\hspace{0.33em}M}$

(K_a is not small, so any approximation cannot be made here.)

Calculating the Percent Dissociation 

For calculating the percent dissociation, amount dissociated is divided by initial amount (total amount).

$\begin{array}{l}\text{Percent\hspace{0.33em}Dissociation\hspace{0.33em}=\hspace{0.33em}}\frac{\text{Amount\hspace{0.33em}Dissociated}}{\text{Total\hspace{0.33em}Amount}}\times 100=\frac{0.0457}{0.22}\times 100=20.8\%\\ \end{array}$