Relationship between pKa, pH, and Buffer Solutions
Buffer Solutions: A solution that resists changes in pH when small amounts of acid or base are added.
A buffer solution is most effective when the concentrations of the weak acid and its conjugate base are approximately equal (ideally within a factor of 10).
Henderson-Hasselbalch Equation: Relates the pH of a solution, the pKa of the acid, and the ratio of the concentrations of the acid and its conjugate base.
$$ pH = pK_a + log \frac{[A^-]}{[HA]} $$ where:
$ [A^-] $ is the concentration of the conjugate base
$ [HA] $ is the concentration of the weak acid
Titration and pKa
Titration: A technique used to determine the concentration of an unknown solution by reacting it with a solution of known concentration.
The midpoint of a titration curve (where half of the acid has been neutralized) corresponds to the pKa of the weak acid. At this point, $ [HA] = [A^-] $ , so $ pH = pK_a $ .
Acid-Base Indicators: Substances that change color depending on the pH of the solution. The color change occurs within a specific pH range, which is related to the pKa of the indicator.
Polyprotic Acids and pKa Values
Polyprotic Acids: Acids that can donate more than one proton ( $ H^+ $ ) per molecule.
Each proton has its own dissociation constant ( $ K_{a1}, K_{a2}, K_{a3} $ , etc.) and corresponding pKa value ( $ pK_{a1}, pK_{a2}, pK_{a3} $ , etc.).
$ K_{a1} > K_{a2} > K_{a3} $ and $ pK_{a1} < pK_{a2} < pK_{a3} $ : It is always easier to remove the first proton than subsequent protons.
When solving problems with polyprotic acids, it is often acceptable to ignore the second and subsequent dissociations if the $ K_{a} $ values differ by several orders of magnitude, because the contribution of $ H^+ $ from subsequent dissociations is negligible.