The pH scale
Vinegar at pH 2.4 has about 40,000 times more hydronium ions per litre than pure water at pH 7.
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The amount of hydronium ion in a solution can range from more than one mole per litre in strong acid down to less than 10⁻¹⁴ mol per litre in strong base. Writing numbers like 0.0000001 and 0.00000000001 all day is clumsy, so chemists use a logarithmic scale. The pH of a solution is the negative base-10 logarithm of its hydronium ion concentration: pH = −log[H₃O⁺]. Going the other way, [H₃O⁺] = 10^(−pH).
One step means ten times
Pure water at 25 °C has [H₃O⁺] = 1.0 × 10⁻⁷ M, so its pH is 7.00. A solution with [H₃O⁺] = 1.0 × 10⁻³ M has pH 3. That four-step difference means ten times ten times ten times ten: 10,000 times more hydronium. OpenStax gives the hydronium concentration of vinegar as about 4 × 10⁻³ M, which is pH 2.4, and stomach acid with 1.2 × 10⁻³ M as pH 2.92. Because the scale is logarithmic, small-looking changes are large. NOAA reports that the pH of surface ocean water has fallen by about 0.1 since the industrial revolution, and describes this as roughly a 30 percent increase in acidity.
pOH and the number 14
Hydroxide concentration gets its own p-value, pOH = −log[OH⁻]. Taking the logarithm of Kw = [H₃O⁺][OH⁻] = 1.0 × 10⁻¹⁴ gives a neat result at 25 °C: pH + pOH = 14.00. A solution is acidic when [H₃O⁺] is greater than [OH⁻], which means pH below 7; neutral when they are equal, pH 7; and basic when [OH⁻] is greater, pH above 7. For example, 0.0125 M potassium hydroxide gives [OH⁻] = 0.0125 M, so pOH = 1.90 and pH = 14.00 − 1.90 = 12.10.
The number 7 for neutral is true only at 25 °C. The autoionization of water takes in heat, so it increases at higher temperatures. Kw rises to about 5.6 × 10⁻¹³ at 100 °C, and OpenStax calculates that pure water at 80 °C has pH 6.31. That water is still neutral, because [H₃O⁺] and [OH⁻] are still equal. pH values are quoted at 25 °C unless stated otherwise.
Where everyday things sit
Gastric juice sits near pH 1.5 and lime juice near 2, both strongly acidic. Coffee is around 5. Normal rainwater has a pH between 5 and 6 because carbon dioxide from the air dissolves in it to form carbonic acid; rain below pH 5 is called acid rain. Human blood is kept very close to 7.4 by buffers. On the basic side, a 0.1 M solution of baking soda measures 8.3, milk of magnesia about 10.5 and 0.1 M ammonia 11.1. Pick any of these from the menu in the lab to jump to its place on the scale.
In the laboratory pH is measured with a pH meter. A research-grade meter reads to 0.001 pH units; a cheap portable one to about 0.01, with an accuracy of about ±0.2. For a quick estimate, chemists use indicator dyes, which are the subject of the next unit.
pH = −log[H₃O⁺]. [H₃O⁺] = 10^(−pH). Kw = [H₃O⁺][OH⁻] = 1.0 × 10⁻¹⁴. pH + pOH = 14.
- What is the pH of a solution with [H₃O⁺] = 1.0 × 10⁻³ M?
- How many times more H₃O⁺ does a pH 3 solution have than a pH 5 solution?
- At 25 °C a solution has pH 9.0. What is its pOH?
- Stomach acid with [H₃O⁺] = 1.2 × 10⁻³ M has what pH?
- 0.0125 M KOH: what is the pH?
- A solution has pH 8.3. It is…
- Basic
- Acidic
- Neutral
- Impossible to tell
- Pure water at 80 °C has pH 6.31. It is…
- Neutral
- Acidic
- Basic
- Contaminated
- Rain is called acid rain below which pH?
- Blood has pH 7.4. What is [H₃O⁺], to one significant figure?
- 4 × 10⁻⁸ M
- 7.4 × 10⁻⁷ M
- 1 × 10⁻⁷ M
- 4 × 10⁻⁷ M
- A strong acid at pH 2.0 is diluted 10 times. What is the new pH?
- pH = −log[H₃O⁺]; one pH step is a factor of 10.
- At 25 °C: pH + pOH = 14; below 7 acidic, 7 neutral, above 7 basic.
- Neutral pH depends on temperature: 6.31 at 80 °C.
Sources for this course (10)
- OpenStax Chemistry 2e (openstax.org/books/chemistry-2e): 4.2 neutralization and antacids (stomach roughly 0.03 M HCl, milk of magnesia Mg(OH)2, Al(OH)3)
- 14.1 Brønsted-Lowry acids and bases (Boyle 1680, Davy 1815, Arrhenius 1884, Brønsted and Lowry 1923, autoionization about two in a billion molecules, Kw = 1.0 × 10⁻¹⁴ at 25 °C, about 5.6 × 10⁻¹³ at 100 °C)
- 14.2 pH and pOH (pH = −log[H3O+], stomach acid 1.2 × 10⁻³ M gives 2.92, vinegar about 4 × 10⁻³ M gives 2.4, blood 7.3, KOH 0.0125 M gives 12.10, neutral pH 6.31 at 80 °C, rainwater 5 to 6, acid rain below 5, pH meter resolution 0.001, Figure 14.2: 1 M HCl 0, gastric juice about 1.5, lime juice about 2, wine about 3.5, coffee about 5, milk of magnesia about 10.5)
- 14.3 relative strengths (six strong acids and six strong bases, Ka, percent ionization, 0.100 M acetic acid 1.3%)
- 14.6 buffers (normal blood pH about 7.4)
- 14.7 titrations (25.00 mL of 0.100 M HCl or acetic acid with 0.100 M NaOH, Table 14.2, equivalence pH 7.00 and 8.72, half-equivalence pH = pKa, Ka acetic acid 1.8 × 10⁻⁵, methyl orange Ka 4.0 × 10⁻⁴ red HIn and yellow In⁻, interval about pKa ± 1, phenolphthalein colourless below pH 8.3)
- LibreTexts Acid-Base Indicators (litmus about 5 to 8, methyl orange 3.1 to 4.4, phenolphthalein 8.3 to 10.0; chem.libretexts.org) and bromothymol blue 6.0 to 7.6 yellow to blue (Prairie South indicator table via LibreTexts Chemistry 30)
- PubChem acetic acid pKa 4.76 at 25 °C, sodium bicarbonate 0.1 M pH 8.3, ammonia 0.1 N pH 11.1, sodium hydroxide (pubchem.ncbi.nlm.nih.gov)
- NOAA Ocean acidification (noaa.gov: surface ocean pH has fallen by 0.1 since the industrial revolution, about a 30 percent increase in acidity)
- IUPAC CIAAW abridged standard atomic weights.
Checked: 2026-10-17