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.

Calculating (Converting Between) Ka and Kb using Kw

Use KW to interconvert between Ka and Kb.

Calculating (Converting Between) Ka and Kb using Kw

Use KW 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

Calculating pKa and pKb

Calculate the pKa pKa = log Ka

Calculate the pKb 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)

Next up, The Conjugate See-Saw and Analyzing Ka and Kb for Acid or Base Relative Strength

(Pt. 8)