Question

What is the pH at 25◦C of a 0.16 M solution of the acid HClO which has an ionization constant of 3.5 × 10−8 ? Your answer must be within ± 0.3%

Answer 1

The ionization of HClO is   

   HClO    H⁺     +    ClO^-

initial conc                 0.16           0               0

change                        -a             +a            +a

Equb conc              0.16-a           a              a

Ionization constant , K_a = [H⁺][ClO^-] / [HClO]

                                     = a x a / (0.16-a)

Given that K_a = 3.5x10^-8

   So    a² / (0.16-a) = 3.5x10^-8

                            a² = - 3.5x10^-8 a +5.6x10^-9

                           a² + 3.5x10^-8 a - 5.6x10^-9 = 0

On solving the quadratic equation we have a = 7.5x10^-5 M

So the concentration of H⁺ is [H⁺] = a = 7.5x10^-5 M

pH = -log[H⁺]

     = - log (7.5x10^-5 )

    = 5 - log7.5

    = 5 - 0.9

   = 4.1

Therefore the pH of the solution is 4.1