Question

What is the pH of the solution when $0.2mole$ of hydrochloric acid is added to one litre of a solution containing $1M$ acetic acid and acetate ion? Assume that the total volume is one litre ($K_a$ for ${CH}_{3}COOH=1.8\times {10}^{-5}$)

Answer 1

On adding $HCl$, the free hydrogen ions will combine with ${CH}_{3}CO{O}^{-}$ ions to form ${CH}_{3}COOH$ . Thus the concentration of acetic acid increases while that of ${CH}_{3}CO{O}^{-}$ ions decreases
$\left[{CH}_{3}COOH\right]=(0.2+1)=1.2mol{litre}^{-1}$
$\left[Salt\right]=(1-0.2)=0.8mol{litre}^{-1}$
Applying Henderson's equation
$pH=\log \frac{\left[Salt\right]}{\left[Acid\right]}-\log K_a$
$=\log \frac{0.8}{1.2}-\log 1.8\times {10}^{-5}=4.5687$