When a strong acid is added to water, it dissociates completely: HA → H⁺ + A⁻. In contrast, weak acids only partially dissociate.

The degree of dissociation is quantified by the acid dissociation constant, Ka:

Ka = ([H⁺][A⁻]) / [HA]

where the brackets denote molar concentrations.

Ka is essential for determining the percent of a weak acid that has dissociated at a given pH.

Connecting Ka, pKa, and pH

pH is defined as the negative logarithm (base 10) of the proton concentration:

pH = –log₁₀[H⁺]  ⇒ [H⁺] = 10^–pH

Similarly, the relationship between Ka and its logarithmic counterpart, pKa, is:

pKa = –log₁₀Ka  ⇒ Ka = 10^–pKa

With both pKa and pH known, the percent dissociation can be calculated directly.

Sample Dissociation Calculation

Consider a weak acid HA with a pKa of 4.756. In a solution whose pH is 3.85, determine the percentage of HA that is dissociated.

1. Convert pKa to Ka and pH to [H⁺]:
   • Ka = 10^–4.756 = 1.754 × 10^–5 M
   • [H⁺] = 10^–3.85 = 1.413 × 10^–4 M
2. Because the acid is weak, [H⁺] ≈ [A⁻]. Insert these values into the Ka expression:

   Ka = ([H+][A−]) / [HA] = (1.413 × 10–4 M)(1.413 × 10–4 M) / [HA]

   Solving for [HA] gives 0.0011375 M.
3. Percent dissociation = ([H⁺] / [HA]) × 100 % = (1.413 × 10^–4 M / 0.0011375 M) × 100 % = 12.42 %.

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