Determine the ionization constant (K_a) of a weak acid if its 0.520 M solution has a pH of 2.40.

The plan is to determine the [H⁺] from the pH and use it to determine the equilibrium concentrations of HA and A^–.

pH = -log [H⁺], [H⁺] = 10^-pH = 10^-2.40 = 0.003981 M

Assuming a monoprotic acid HA, the concentration of A is also 0.003981 M because the mole ratio of H⁺ and A^– is 1:1.

HA(aq) → H⁺(aq) + A^–(aq)

or

HA(aq) + H₂O(l) → H₃O⁺(aq) + A^–(aq)

We can also set up an ICE table to determine the concentration of all species:

\[{K_{\rm{a}}}\; = {\mkern 1mu} \frac{{[{{\rm{H}}^{\rm{ + }}}][{{\rm{A}}^{\rm{ – }}}]}}{{[{\rm{HA}}]}}\; = \;\frac{{{{0.003981}^{\rm{2}}}}}{{{\rm{0}}.{\rm{520}}\;{\rm{ – }}\;0.003981}}\; = \;3.07 \times {\rm{1}}{{\rm{0}}^{{\rm{ – 5}}}}\]

Check Also

• Definitions of Acids and Bases
• Acid-Base Reactions
• Acid-Base Titrations
• Conjugate Acid and Conjugate Base
• Autoionization of Water and K_w
• The pH and Acidity
• Acid Strength, K_a, and pK_a
• Base Strength, K_b, and pK_b
• Ka, pKa, Kb, and pK_b Relationship
• The pH of a Strong Acid and Base
• pH + pOH = 14
• The pH of a Weak Acid
• The pH of a Weak Base
• The pH of Polyprotic Acids
• The acidity of a Salt Solution
• The pH of a Salt Solution
• The pH of Salts With Acidic Cations and Basic Anions
• pH Practice Problems
• Acids and Bases Practice Problems
  Acids and Bases Quiz