Question

What is the pH of the solution when 0.2 mole of hydrochloric acid is added to one litre of a solution containing 1 M acetic acid and acetate ion? Assume that the total volume is one litre. $K_a$ for ${\text{CH}}_3\text{COOH}=1.8\times {10}^{-5}$

• A. 4.58
• B. 9.16
• C. 7
• D. 2.37

Answer 1

The correct option is A 4.58

On adding HCl, the free hydrogen ions
combine with ${\text{CH}}_3{\text{COO}}^{-}$ ions to form
${\text{CH}}_3\text{COOH}$. Thus, the concentration
of acetic acid increases while that of
${\text{CH}}_3$ ${\text{COO}}^{-}$ ions decreases.

$\left[{\text{CH}}_3\text{COOH}\right]=(0.2+1)=1.2{\text{mol litre}}^{-1}$
$\left[\text{Salt}\right]=(1-0.2)=0.8{\text{mol litre}}^{-1}$

According to Henderson's equation

$\text{pH}={\text{log}}_{10}\frac{\left[\text{Salt}\right]}{\left[\text{Acid}\right]}-\text{log}{k}_a$

$={\text{log}}_{10}\frac{0.8}{1.2}-{\text{log}}_{10}1.8\times {10}^{-5}$

$={\text{log}}_{10}2-{\text{log}}_{10}3-{\text{log}}_{10}1.8\times {10}^{-}5$

= 4.5687