Question

For problems 1 and 2, assume an activity coefficient of 1 for all substances and no effect of ionic strength. Eliminate terms in quadratic solutions for [H+ ] only if the weak acid is dissociated < 5%. Reported pKa values can vary depending on the conditions under which they were measured; therefore, in solving the following problems use the pKa values given with the problems.

1. What is the pH of 45 mM H3PO4? Phosphoric acid (H3PO4) is a triprotic acid; pKa1 = 2.12, pKa2 = 7.21, pKa3 = 12.32 Acetic acid pKa = 4.75

Answer 1

H₃PO₄ is a triprotic acid, but nearly all H⁺ ions produced are given in first ionization only. Second and third ionizations are very weak.

Reaction for ionization: H₃PO₄ H⁺ + H₂PO₄^-

        Initial moles         0.045        0          0

Let x moles are dissociated

       At equilibrium        0.045-x     x          x

Ka1 = [H⁺] [H₂PO₄^-] / [H₃PO₄]     (pKa is converted to Ka by using the relation pKa = -log Ka)

   7.5 x 10^-3 = x . x / (0.045 - x)

We are neglecting x in comparison to 0.045.

0.0075 x 0.045 = x²

0.000337 = x²

x = 0.0183 = concentration of H⁺ ions

Now we will calculate pH

pH = -log[H⁺]

    = -log [0.0183]

    = - (- 1.735)

    = 1.735