Conjugate Acid-Base Pairs

Base Strength and Conjugate Acid Strength

Key Idea: The strength of a base is inversely related to the strength of its conjugate acid. A strong base has a weak conjugate acid, and a weak base has a strong conjugate acid.

• Base Strength: Determined by how readily a base accepts a proton ( $ H^+ $ ). Strong bases completely dissociate in water, while weak bases only partially dissociate.

• Examples of Strong Bases: Group 1 hydroxides ( $ NaOH $ , $ KOH $ ), Group 2 hydroxides ( $ Ca(OH)_2 $ , $ Ba(OH)_2 $ ) These completely dissociate in water. $ NaOH \rightarrow Na^+ + OH^- $

• Examples of Weak Bases: Ammonia ( $ NH_3 $ ), amines (organic compounds with $ NH_2 $ group). These partially dissociate in water. $ NH_3 + H_2O \rightleftharpoons NH_4^+ + OH^- $

• ** $ K_b $ (Base Dissociation Constant):** A measure of base strength. A larger $ K_b $ value indicates a stronger base. For the reaction $ B + H_2O \rightleftharpoons BH^+ + OH^- $ , $ K_b = \frac{[BH^+]][OH^-]]}{[B]]} $

• ** $ pK_b $ : ** $ pK_b = -\log{K_b} $ . A smaller $ pK_b $ value indicates a stronger base.

• Conjugate Acid Strength: The strength of the conjugate acid is directly related to the stability of the conjugate acid. Factors affecting stability include:

  • Resonance stabilization
  • Inductive effects
  • Size and electronegativity of the atom holding the positive charge

• Relationship between $ K_a $ and $ K_b $ : For a conjugate acid-base pair in water at 25°C: $ K_a \times K_b = K_w = 1.0 \times 10^{-14} $

• Acid Strength and Conjugate Base Strength: This is the reciprocal relationship.

• **Factors Affecting Acid/Base Strength**: Electrostatic Effects, Resonance Effects]], Inductive Effects]], Hybridization Effects]], Solvent Effects]]

• Practice Problems:

  1. Compare the relative base strengths of $ NH_3 $ and $ CH_3NH_2 $ . Explain your reasoning using $ pK_b $ values or other relevant concepts.
  2. Predict the conjugate acid of $ HPO_4^{2-} $ and determine whether it is a strong or weak acid. Explain.
  3. Given that the $ K_a $ of $ HF $ is $ 7.2 \times 10^{-4} $ , calculate the $ K_b $ of its conjugate base, $ F^- $ .