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Acid-Base Equilibria (Pt. 7)
Conjugate Acid/Base Pairs and Relationships Between Ka, Kb, and Kw
By Shawn P. Shields, Ph.D.
This work is licensed by Dr. Shawn P. Shields-Maxwell under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
Recall: Conjugate Acid-Base Pairs
Conjugate acid-base pairs are two related species differing only by a proton (H+).
base
conjugate acid for NH3
acid conjugate base for HF
The equilibrium constant K is “renamed” for acids to Ka
The Equilibrium Constant Ka for Weak Acids
An equilibrium exists between the weak acid (HA) and its products.
𝐊 𝐚=¿¿
C
H
H
H
C O H
O
C
H
H
H
C O
O
Ka and Kb for Conjugate Acid-Base Pairs
Suppose acetic acid (CH3COOH) is dissolved in water…
acetic acid
conjugate base for acetic acid
“loseable” H+
C
H
H
H
C O H
O
C
H
H
H
C O
O
Ka and Kb for Conjugate Acid-Base Pairs
Suppose acetate (CH3COO-) is dissolved in water…
acetate conjugate acid for acetate
acetate gained H+ from water
C
H
H
H
C O H
O
C
H
H
H
C O
O
Ka and Kb for Conjugate Acid-Base Pairs
CH3COOH and CH3COO- are conjugate acid-base pairs
acetic acid
acetate (base)
Ka = 1.76 10-5 Kb = 5.68 10-10
Multiply Ka and Kb for Conjugate Acid-Base Pairs
Use this relationship to interconvert between Ka and Kb.
pKa and pKb
Calculate the pKa for an acid as
pKa = log Ka
Calculate the pKb for a base as
pKb = log Kb
Inverse logs for pKa, pKa, and pKwpKa = log Ka 10pKa = Ka
pKb = log Kb 10pKb = Kb
pKw = log Kw = 14 10pKw = Kw
Recall: Kw (and pKw) will have different values at temperatures other than 25C
A Few More Relationships Between pKa, pKb, and pKw
pKa + pKb = pKw
pKw = log [Kw] = 14 (at 25C)
pKa + pKb = 14 (at 25C)