Benzoic acid is a weak monoprotic acid. It has a pKa of 4.20. A student transferred 25.00mL of 0.126M benzoic acid into a beaker. The student then added 20.00mL of distilled water into the beaker. Calculate the equilibrium pH for this benzoic acid solution.

pH of the benzoic acid solution = 3.35

Explanation:

Benzoic acid is a weak monoprotic acid

  pKa = 4.2

⇒ Ka = 6.3 x 10⁻⁵

                                  C₆H₅COOH ⇄ C₆H₅COO⁻ + H⁺

Initial concentration      C molar             0                0

At equilibrium               (c - cα)               cα               cα

                      Acid dissociation constant Ka =

                                              ⇒          6.3 x 10⁻⁵ = α²c ................(1)

(for weak electrolyte 1 -α = 1)

Concentration of benzoic acid C = 25 x 0.126 x 10⁻³ = 0.00315 molar

                  From eqn (1)

                          α² =

                    ⇒  α = √( )

                    ⇒  α = 0.14

So concentration of H⁺ ion = 0.14 x 0.00315 = 0.000441

pH = - log 0.000441 = 3.35    

We not considered H⁺ concentration of water because pH  < 7                  

there are two significant figures.