14.3 Relative Strengths of Acids and Bases

Acid-base strength and equilibrium are crucial concepts in chemistry. They help us understand how substances interact in solution, influencing pH and chemical reactions. Knowing how to compare acid and base strengths allows us to predict and control these interactions.

Molecular structure plays a key role in determining acid-base strength. Factors like inductive effects, resonance, and electronegativity affect how easily substances donate or accept protons. This knowledge is essential for understanding chemical behavior and solving equilibrium problems.

Acid-Base Strength and Equilibrium

Acid vs base strength comparisons

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• Acid ionization constant ($K_a$) quantifies acid strength higher $K_a$ indicates stronger acid (HCl vs CH3COOH)
• Base ionization constant ($K_b$) quantifies base strength higher $K_b$ indicates stronger base (NaOH vs NH3)
• $pK_a$ and $pK_b$ scales are negative logarithms of $K_a$ and $K_b$ lower $pK_a$ indicates stronger acid, lower $pK_b$ indicates stronger base
• Conjugate acid-base pairs related by $K_a \times K_b = K_w$, where $K_w$ is ionization constant of water ($1.0 \times 10^{-14}$ at 25°C)
• Acid dissociation is the process by which an acid releases a proton in solution, influencing its strength

Molecular structure in acid-base strength

• Inductive effects influence strength electron-withdrawing groups (halogens, nitro) stabilize conjugate base making acid stronger, electron-donating groups (alkyl) destabilize conjugate base making acid weaker
• Resonance effects influence strength stabilization of conjugate base makes acid stronger (carboxylic acids, phenols) due to charge delocalization
• Hybridization of atom bonded to acidic hydrogen affects strength $sp^2$ or $sp$ hybridized atoms form stronger acids than $sp^3$ due to greater s-character in bonding orbital
• Electronegativity of atom bonded to acidic hydrogen affects strength more electronegative atoms (oxygen, nitrogen) form stronger acids than less electronegative (carbon)
• Leveling effect occurs when a solvent limits the strength of an acid or base, making very strong acids or bases appear equally strong in that solvent

Weak acid-base equilibrium problems

1. Write acid-base equilibrium expression and corresponding $K_a$ or $K_b$ expression
   • Weak acid HA: $HA + H_2O \rightleftharpoons H_3O^+ + A^-$, $K_a = \frac{[H_3O^+][A^-]}{[HA]}$
   • Weak base B: $B + H_2O \rightleftharpoons BH^+ + OH^-$, $K_b = \frac{[BH^+][OH^-]}{[B]}$
2. Use initial, change, equilibrium (ICE) table to set up equilibrium concentrations
   • Initial concentrations based on given problem
   • Change in concentrations determined by reaction stoichiometry
   • Equilibrium concentrations are sum of initial and change values
3. Substitute equilibrium concentrations into $K_a$ or $K_b$ expression and solve for unknown variable
   • If necessary, use approximation $x << [HA]_0$ or $x << [B]_0$ to simplify calculation, where $x$ is change in concentration and $[HA]_0$ or $[B]_0$ is initial concentration of acid or base
4. Calculate pH of solution using equilibrium concentration of $H_3O^+$ or $OH^-$
   • $pH = -\log{[H_3O^+]}$ and $[pOH](https://www.fiveableKeyTerm:pOH) = -\log{[OH^-]}$
   • $pH + pOH = 14$ at 25°C

Advanced Acid-Base Concepts

• Buffer solutions resist changes in pH when small amounts of acid or base are added
• The Henderson-Hasselbalch equation relates pH to the concentrations of a weak acid and its conjugate base in a buffer solution
• Autoionization of water occurs when water molecules react with each other to produce hydronium and hydroxide ions, maintaining a constant ion product in pure water