Conjugate Acid-Base Pairs
Ka and Kb Relationships
Main Idea: The relationship between $ K_a $ (acid dissociation constant) and $ K_b $ (base dissociation constant) for a conjugate acid-base pair is defined by the ion product constant of water, $ K_w $ .
Key Equation:
At 25°C, $ K_w = K_a \times K_b = 1.0 \times 10^{-14} $
This equation holds true for a conjugate acid-base pair. If you know the $ K_a $ of an acid, you can calculate the $ K_b $ of its conjugate base, and vice versa.
Example:
Find the $ K_b $ for the conjugate base of hydrofluoric acid (HF), given that $ K_a $ for HF is $ 7.2 \times 10^{-4} $ .
$ K_b = \frac{K_w}{K_a} = \frac{1.0 \times 10^{-14}}{7.2 \times 10^{-4}} = 1.4 \times 10^{-11} $
Implications:
- Strong acids have weak conjugate bases: A strong acid has a very large $ K_a $ , meaning its conjugate base will have a very small $ K_b $ .
- Weak acids have relatively stronger conjugate bases: A weak acid has a small $ K_a $ , leading to a relatively larger $ K_b $ for its conjugate base (though still less than 1).
- pKa and pKb Relationship: Since $ K_a \times K_b = K_w $ , taking the negative logarithm of both sides gives: $ pK_a + pK_b = 14 $ (at 25°C).
Acid Dissociation Constant, Ka
Base Dissociation Constant, Kb
Ion Product Constant of Water, Kw
pKa and pKb