Acid Reactions and Titration

Chemical Characteristics of Acids and Acid-Base Titrations Introduction Understanding how acids behave in solution is fundamental to chemistry. Some acids are simple—they donate one proton and we're done. But many important acids, like sulfuric acid and phosphoric acid, can donate multiple protons. This significantly changes how they react, especially during titration. In this section, we'll explore polyprotic acids, how they dissociate, how they react with bases, and most importantly, how we use titration to analyze them. Polyprotic Acids A polyprotic acid is an acid that can donate more than one proton ($H^+$) per molecule. This is in contrast to monoprotic acids like hydrochloric acid (HCl), which have only one dissociable proton. Understanding Diprotic Acids Diprotic acids have two dissociable protons. Each dissociation step has its own equilibrium constant: $$H2A \rightleftharpoons H^+ + HA^-$$ $$K{a1} = \frac{[H^+][HA^-]}{[H2A]}$$ $$HA^- \rightleftharpoons H^+ + A^{2-}$$ $$K{a2} = \frac{[H^+][A^{2-}]}{[HA^-]}$$ A crucial observation: $K{a1} > K{a2}$ always. This makes intuitive sense—it's easier to remove the first proton from a neutral molecule than to remove a second proton from a negatively charged species. The negative charge left behind after losing one proton repels the loss of a second proton. Sulfuric acid ($H2SO4$) is the classic example of a diprotic acid. Its first dissociation is strong (essentially complete), while the second dissociation is moderate, with $K{a2} \approx 0.012$. Understanding Triprotic Acids Triprotic acids can donate three protons. They have three successive dissociation steps with constants that follow the same pattern: $$K{a1} > K{a2} > K{a3}$$ Phosphoric acid ($H3PO4$) is the most common triprotic acid you'll encounter: $$H3PO4 \rightleftharpoons H^+ + H2PO4^- \quad (K{a1})$$ $$H2PO4^- \rightleftharpoons H^+ + HPO4^{2-} \quad (K{a2})$$ $$HPO4^{2-} \rightleftharpoons H^+ + PO4^{3-} \quad (K{a3})$$ Each successive dissociation step becomes progressively weaker because removing a proton from an increasingly negative species becomes harder. In solution, you can have species like $H3PO4$, $H2PO4^-$, $HPO4^{2-}$, and $PO4^{3-}$ all coexisting, depending on the pH. Neutralization Reactions and the Equivalence Point When an acid and a base react, they form a salt and water in what's called a neutralization reaction: $$\text{Acid} + \text{Base} \rightarrow \text{Salt} + \text{Water}$$ For example: $$HCl + NaOH \rightarrow NaCl + H2O$$ The key concept here is the equivalence point: the point during a neutralization when the moles of acid and moles of base are exactly equal (according to the stoichiometry of the reaction). At the equivalence point, all the acid has been neutralized. For polyprotic acids, things become more interesting. A diprotic acid has two equivalence points—one when the first proton is removed, and another when the second proton is removed. This is a critical idea that will appear throughout titration problems. Weak Acid–Weak Base Equilibrium and Buffers There's an important relationship between pH, $pKa$, and the ratio of acid to conjugate base in solution. When $pH = pKa$, the concentrations of the weak acid and its conjugate base are equal. When $pH < pKa$, the solution is more acidic, and the protonated acid form dominates (the molecular acid is the major species) When $pH > pKa$, the solution is more basic, and the conjugate base form dominates (the deprotonated form is the major species) This relationship is captured precisely by the Henderson-Hasselbalch equation, but the key insight is recognizing which form is dominant at a given pH. A buffer solution is a mixture of a weak acid and its conjugate base (often prepared by mixing a weak acid with its salt, like acetic acid and sodium acetate). Buffers resist large changes in pH when small amounts of acid or base are added. The buffer "works" because: If you add acid, the conjugate base in the buffer reacts with it If you add base, the weak acid in the buffer reacts with it The most effective buffers occur when $pH = pKa$, which is when the concentrations of acid and conjugate base are equal, providing maximum buffering capacity. Acid-Base Titration: General Principles In an acid-base titration, we use a solution of known concentration (the titrant) to determine the concentration of an unknown acid (or base). Typically, we add a strong base like sodium hydroxide (NaOH) of precisely known concentration to an acid solution of unknown concentration until we reach the equivalence point. We detect the equivalence point using a pH indicator—a dye that changes color at a specific pH. The power of titration is that it gives us a practical, experimental way to find the concentration of an unknown acid or base by measuring volume and using stoichiometry. Diprotic Acid Titration: Key Features When we titrate a diprotic acid with a strong base, the titration curve has distinctive features that differ from titrating a monoprotic acid. Two Equivalence Points A diprotic acid titration produces two equivalence points in sequence: First equivalence point: Reached when one mole of base has been added per mole of diprotic acid. At this point, all protons from the first dissociation have been removed, leaving $HA^-$ in solution. Second equivalence point: Reached when two moles of base have been added per mole of diprotic acid. At this point, both protons have been removed, leaving $A^{2-}$ in solution. Two Buffer Regions Between these equivalence points, you'll observe two distinct buffer regions: First buffer region: Centered at $pH = pK{a1}$, where the mixture is roughly equal parts $H2A$ and $HA^-$ Second buffer region: Centered at $pH = pK{a2}$, where the mixture is roughly equal parts $HA^-$ and $A^{2-}$ Each buffer region is relatively flat—the pH doesn't change dramatically with added base—because the conjugate acid-base pair resists large pH swings. Midpoint Interpretation The midpoint of each buffer region is particularly useful: The first midpoint occurs when half of the first proton has been neutralized (0.5 equivalents of base added). At this point, $[H2A] = [HA^-]$, so $pH = pK{a1}$ The second midpoint occurs when half of the second proton has been neutralized (1.5 equivalents of base added). At this point, $[HA^-] = [A^{2-}]$, so $pH = pK{a2}$ This means that from a titration curve, you can experimentally determine both $pK{a1}$ and $pK{a2}$ by reading the pH values at the two midpoints. Looking at a typical diprotic acid titration curve (like the one above), notice the characteristic S-shape with two distinct rises in pH. The first rise corresponds to the first equivalence point, and the second rise to the second equivalence point. The relatively flat sections between these rises are the buffer regions where the pH changes slowly.