5.2 Acid-Base Relationships

Below is a table of some acids and their conjugate bases.

Acid	Name	Ka	pKa	C. Base	Kb	pKb
HCl	hydrochloric acid	2 × 106	-6.3	Cl–	5 × 10–21	20.3
H2SO4	sulfuric acid	1 × 103	-3	HSO4–	1 × 10–17	17
HNO3	nitric acid	2 × 101	-1.3	NO3–	5 × 10–16	15.3
H3O+	hydronium ion	1	0	H2O	1 × 10–14	14
HF	hydrofluoric acid	6.76 × 10–4	3.17	F–	1.48 × 10–11	10.83
HNO2	nitrous acid	5.13 × 10–4	3.29	NO2–	1.95 × 10–11	10.71
CH3COOH	acetic acid	1.75 × 10–5	4.76	CH3COO–	5.71 × 10–10	9.24
H2CO3	carbonic acid	4.26 × 10–7	6.37	HCO3–	2.35 × 10–8	7.63
NH4+	ammonium ion	5.62 × 10–10	9.25	NH3	1.78 × 10–5	4.75
H2O	water	1 × 10–14	14	OH–	1	0
NH3	ammonia	1 × 10–37	37	NH2–	1 × 1023	-23

Equations

K_a and pK_a

\[\begin{align*} \mathrm{p}K_{\mathrm{a}} &= -\log K_{\mathrm{a}} \\[1.5ex] K_{\mathrm{a}} &= 10^{-\mathrm{p}K_{\mathrm{a}}} \end{align*}\]

K_b and pK_b

\[\begin{align*} \mathrm{p}K_{\mathrm{b}} &= -\log K_{\mathrm{b}} \\[1.5ex] K_{\mathrm{b}} &= 10^{-\mathrm{p}K_{\mathrm{b}}} \end{align*}\]

pK_a, pK_b, and pK_w (K_a, K_b, and K_w)

\[\begin{align*} \mathrm{p}K_{\mathrm{a}} + \mathrm{p}K_{\mathrm{b}} &= \mathrm{p}K_{\mathrm{w}} \\[1.5ex] K_{\mathrm{a}} \times K_{\mathrm{b}} &= K_{\mathrm{w}} \end{align*}\]

pH, pOH, and pK_w

\[\begin{align*} \mathrm{pH} + \mathrm{pOH} &= \mathrm{p}K_{\mathrm{w}} \end{align*}\]

Practice

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Formic acid has a K_a = 1.9 × 10^–4. What is the pK_a of the acid?

Solution

\[\begin{align*} \mathrm{p}K_{\mathrm{a}} &= -\log K_{\mathrm{a}} \\[1.5ex] &= -\log (1.9\times 10^{-4}) \\[1.5ex] &= 3.72 \end{align*}\]

Practice

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Hydrosulfuric acid (H₂S) has a pK_a of 7.0. What is the K_a of the acid?

Solution

\[\begin{align*} K_{\mathrm{a}} &= 10^{-\mathrm{p}K_{\mathrm{a}}} \\[1.5ex] &= 10^{-7} \\[1.5ex] &= 1\times 10^{-7} \end{align*}\]

Practice

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Rank the acids from strongest to weakest.

Acid	Ka	pKa
ammonium ion	5.65 × 10-10
formic acid		3.72
acetic acid	1.76 × 10-5
benzoic acid		4.19

Solution

Convert everything to K_a or pK_a. Higher K_a values correspond to lower pK_a values and correspond to stronger acids.

Acid	Ka	pKa
formic acid	1.9 × 10-4	3.72
benzoic acid	6.46 × 10-5	4.19
acetic acid	1.76 × 10-5	4.75
ammonium ion	5.65 × 10-10	9.25

A list of strong acids and bases are given below. Strong acids generally have a pK_a of around –1 or lower. Strong bases generally have a pK_b of –1 or lower.

Strong Acid	Formula	Strong Base	Formula
Hydrochloric acid	HCl	Lithium hydroxide	LiOH
Hydrobromic acid	HBr	Sodium hydroxide	NaOH
Hydroiodic acid	HI	Potassium hydroxide	KOH
Perchloric acid	HClO4	Rubidium hydroxide	RbOH
Chloric	HClO3	Cesium hydroxide	CsOH
Sulfuric	H2SO4	Magnesium hydroxide	Mg(OH)2
Nitric	HNO3	Calcium hydroxide	Ca(OH)2
		Strontium hydroxide	Sr(OH)2
		Barium hydroxide	Ba(OH)2

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