7.2 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 |
| HClO2 | chlorous acid | 1.10 × 10–2 | 1.96 | ClO2– | 9.09 × 10–13 | 12.04 |
| 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 |
| C6H5COOH | benzoic acid | 6.46 × 10–5 | 4.19 | C6H5COO– | 1.55 × –10 | 9.81 |
| 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
Ka and pKa
\[\begin{align*} \mathrm{p}K_{\mathrm{a}} &= -\log K_{\mathrm{a}} \\[1.5ex] K_{\mathrm{a}} &= 10^{-\mathrm{p}K_{\mathrm{a}}} \end{align*}\]
Kb and pKb
\[\begin{align*} \mathrm{p}K_{\mathrm{b}} &= -\log K_{\mathrm{b}} \\[1.5ex] K_{\mathrm{b}} &= 10^{-\mathrm{p}K_{\mathrm{b}}} \end{align*}\]
pKa, pKb, and pKw (Ka, Kb, and Kw)
\[\begin{align*} \mathrm{p}K_{\mathrm{a}} + \mathrm{p}K_{\mathrm{b}} &= \mathrm{p}K_{\mathrm{w}} \\[1.5ex] K_{\mathrm{a}} \times K_{\mathrm{b}} &= K_{\mathrm{w}} \end{align*}\]
pH, pOH, and pKw
\[\begin{align*} \mathrm{pH} + \mathrm{pOH} &= \mathrm{p}K_{\mathrm{w}} \end{align*}\]
Practice
Formic acid has a Ka = 1.9 × 10–4. What is the pKa 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
Hydrosulfuric acid (H2S) has a pKa of 7.0. What is the Ka 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
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 Ka or pKa. Higher Ka values correspond to lower pKa 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 pKa of around –1 or lower. Strong bases generally have a pKb 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 |