Question

A 0.15 M solution of a weak acid is 3.0% dissociated. Calculate K_a.

Short answer

K_a can be calculated using amount dissociated.

${\text{K}}_{\text{a}}=1.39\times {10}^{-4}$

Step-by-step solution

Step 1:Calculating Amount that is Dissociated

Initial amount of acid present = 0.15 M

Dissociation = 3%

$\text{Amountdissociated}=0.15\times \frac{3}{100}=0.0045$

CalculatingKa 

$\begin{array}{l}{\text{HA}}_{\text{(aq)}}\rightleftarrows {{\text{\hspace{0.33em}\hspace{0.33em}\hspace{1em}H}}^{\text{+}}}_{\text{(aq)}}{{\text{+\hspace{1em}A}}^{\text{-}}}_{\text{(aq)}}\\ 0.1500\\ 0.15-0.00450.00450.0045\end{array}$

$\begin{array}{l}{\text{K}}_{\text{a}}=\frac{{\text{x}}^2}{1-\text{x}}=\frac{{\left(0.0045\right)}^2}{(0.15-0.0045)}\\ {\text{K}}_{\text{a}}=1.39\times {10}^{-4}\end{array}$