2.9 Predicting Acid–Base Reactions from pKa Values

Acid-base reactions are fundamental in organic chemistry. They involve proton transfer between molecules, with acids donating protons and bases accepting them. Understanding pKa values is crucial for predicting reaction outcomes and comparing acid-base strengths.

Calculations involving Ka, pKa, and pH help chemists analyze acid-base equilibria and design buffer solutions. These concepts are essential for understanding reaction mechanisms, solubility, and many biological processes in organic chemistry.

Acid-Base Reactions and pKa Values

Predicting acid-base reactions

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• Acids donate protons (H+) and bases accept protons (ammonia, amines)
  • Brønsted-Lowry definition: Acids are proton donors (HCl, acetic acid) and bases are proton acceptors (NaOH, pyridine)
• pKa measures acid strength indicates how readily an acid donates protons
  • Lower pKa values indicate stronger acids dissociate more completely (sulfuric acid pKa -3, HI pKa -10)
  • Higher pKa values indicate weaker acids dissociate less completely (acetic acid pKa 4.76, phenol pKa 9.95)
• Proton transfer occurs from the stronger acid to the stronger base (HCl + NaOH → H2O + NaCl)
  • The acid with the lower pKa donates a proton to the base with the higher pKa (formic acid pKa 3.75 protonates ammonia pKa 9.25)
• Equilibrium favors the formation of the weaker acid and weaker base (acetic acid + sodium acetate ⇌ sodium acetate + acetic acid)
  • The reaction proceeds in the direction that results in the conjugate acid-base pair with the smaller $\Delta$pKa (pyridine + benzoic acid → pyridinium benzoate)
  • This principle is an application of Le Chatelier's principle to acid-base reactions

Comparison of acid-base strengths

• Relative acid strengths determined by comparing pKa values
  • Acids with lower pKa values are stronger than acids with higher pKa values (HBr pKa -9 > HF pKa 3.2)
• Relative base strengths determined by comparing the pKa values of their conjugate acids
  • Bases with higher conjugate acid pKa values are stronger than bases with lower conjugate acid pKa values (NaOH pKa 15.7 > methylamine pKa 10.6)
• The leveling effect occurs when a strong acid reacts with a strong base in a solvent
  • The strongest acid and strongest base that can exist in that solvent will be formed (HCl + NaOH in water → H3O+ + Cl-)
• Proton transfer reactions proceed to completion when the $\Delta$pKa between the acid and the conjugate acid of the base is greater than 3 (HCl pKa -6.3 + NaOH pKa 15.7 → H2O + NaCl)

Calculation of Ka from pKa

• The acid dissociation constant (Ka) measures acid strength indicates extent of dissociation
  • Higher Ka values indicate stronger acids dissociate more completely (HI Ka 1×10^10)
  • Lower Ka values indicate weaker acids dissociate less completely (acetic acid Ka 1.8×10^-5)
• pKa is the negative logarithm of Ka
  • $pKa = -log_{10}(Ka)$ (acetic acid pKa = -log(1.8×10^-5) = 4.74)
• Ka calculated from pKa using the equation:
  • $Ka = 10^{-pKa}$ (For benzoic acid pKa 4.19, Ka = 10^-4.19 = 6.5×10^-5)
• For an acid-base reaction, the equilibrium constant (Keq) calculated from the $\Delta$pKa
  • $Keq = 10^{\Delta pKa}$, where $\Delta pKa = pKa(acid) - pKa(conjugate acid of base)$
  • (For acetic acid pKa 4.76 and ammonia pKa 9.25, Keq = 10^(4.76-9.25) = 3.1×10^-5)

pH, Buffers, and the Henderson-Hasselbalch Equation

• pH is a measure of the acidity or basicity of a solution
• Buffer solutions resist changes in pH when small amounts of acid or base are added
  • Composed of a weak acid and its conjugate base or a weak base and its conjugate acid
• The Henderson-Hasselbalch equation relates pH, pKa, and the concentrations of acid and conjugate base in a buffer solution
  • pH = pKa + log([A-]/[HA])
  • Used to calculate the pH of buffer solutions or to determine the ratio of acid to conjugate base needed for a specific pH