pH, pOH & Strong Acids/Bases

The pH scale isn't arbitrary — it's a logarithm, and once you see the log, the whole scale falls into place.

High schoolIntro Gen ChemUni Year 1
⏱️ About 20 min

Every drop of water is quietly splitting apart and reforming — a tiny fraction of it exists as H⁺ and OH⁻ at any instant. Measure how much H⁺, take a logarithm, and you get a single tidy number between roughly 0 and 14. That number is pH.

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The big idea: pH is just a compressed way of writing the hydrogen-ion concentration: pH = −log[H⁺]. Because water self-ionises with Kw = [H⁺][OH⁻] = 1.0×10⁻¹⁴ at 25 °C, pH and pOH always add to 14 — so knowing one gives you the other.
🎯 By the end, you'll be able to
  • Calculate pH from [H⁺] and [H⁺] from pH using pH = −log[H⁺]
  • Use Kw = [H⁺][OH⁻] = 1.0×10⁻¹⁴ and pH + pOH = 14 to switch between them
  • Find the pH of a strong acid or strong base from its concentration
  • Explain why pH 7 is neutral only at 25 °C
📎 Helpful to know first

Water talks to itself

Pure water is never only H₂O. A small fraction of molecules swap a proton: one water grabs an H⁺ from another, giving H₃O⁺ and OH⁻. This is self-ionisation, and at equilibrium the product of the two concentrations is a fixed constant:

\[ K_w = [\ce{H+}][\ce{OH-}] = 1.0\times10^{-14}\ \text{(at 25 °C)} \]
The ion-product of water. In pure water [H⁺] = [OH⁻] = 1.0×10⁻⁷ M, which is why neutral pH is 7.

Why take a logarithm at all?

Hydrogen-ion concentrations span an enormous range — from about 1 M in strong stomach acid down to 10⁻¹⁴ M in concentrated lye. Writing 0.00000001 M is clumsy. A logarithm crushes that range into small numbers, and flips the sign so acids come out positive:

\[ \text{pH} = -\log[\ce{H+}] \qquad \text{pOH} = -\log[\ce{OH-}] \]
The 'p' means 'take −log₁₀'. Every step of 1 pH unit is a 10× change in [H⁺].
🔑 pH + pOH = 14
Take −log of both sides of Kw = [H⁺][OH⁻] = 10⁻¹⁴ and the product becomes a sum: pH + pOH = 14 at 25 °C. So a solution with pOH = 2 automatically has pH = 12. Find one, subtract from 14, and you have the other — no extra work.
✨ Reading the scale
pH < 7: acidic (more H⁺ than OH⁻). pH = 7: neutral. pH > 7: basic. Lower pH means more acidic — and because it's a log scale, pH 3 has ten times the H⁺ of pH 4, and a hundred times that of pH 5.
📝 Worked example: A solution has [H⁺] = 2.0×10⁻³ M. What is its pH, and is it acidic or basic?
  1. Apply pH = −log[H⁺] = −log(2.0×10⁻³).
  2. Split the log: −(log 2.0 + log 10⁻³) = −(0.30 − 3) = −(−2.70).
  3. So pH = 2.70. Because it's below 7, the solution is acidic.
✓ pH = 2.70 — acidic.

Strong acids and bases: the concentration is the answer

A strong acid dissociates essentially completely, so every molecule hands over its proton. That makes life easy: for a strong monoprotic acid, [H⁺] simply equals the acid concentration. 0.010 M HCl gives [H⁺] = 0.010 M, so pH = 2.00.

Strong bases work the same way through OH⁻. For 0.010 M NaOH, [OH⁻] = 0.010 M, so pOH = 2.00 and therefore pH = 14 − 2.00 = 12.00.

📝 Worked example: Find the pH of 0.0050 M HNO₃ (a strong acid).
  1. HNO₃ is strong, so it dissociates fully: [H⁺] = 0.0050 M = 5.0×10⁻³ M.
  2. pH = −log(5.0×10⁻³) = −(log 5.0 − 3) = −(0.70 − 3).
  3. pH = 2.30.
✓ pH = 2.30.
✏️ Practice: A solution has [H⁺] = 1.0×10⁻⁴ M. What is its pH?
Solution
  1. pH = −log[H⁺] = −log(1.0×10⁻⁴).
  2. log(1.0×10⁻⁴) = −4, so pH = −(−4).
  3. pH = 4.00 — acidic.
✏️ Practice: What is the pH of 0.010 M NaOH, a strong base? (Hint: find pOH first, then use pH + pOH = 14.)
Solution
  1. NaOH is strong, so [OH⁻] = 0.010 M = 1.0×10⁻² M.
  2. pOH = −log(1.0×10⁻²) = 2.00.
  3. pH = 14 − pOH = 14 − 2.00 = 12.00 — strongly basic.
⚠️ pH 7 is neutral only at 25 °C
Kw grows with temperature — water self-ionises more when it's hot. At 50 °C, Kw ≈ 5.5×10⁻¹⁴, so neutral water (where [H⁺] = [OH⁻]) sits at pH ≈ 6.6, not 7. It's still neutral — the ion counts are equal — the '7' just isn't magic. Neutral means [H⁺] = [OH⁻]; the number attached to it depends on temperature.
🎮 Interactive: pH Explorer LIVE
Predict first: Which has the lower pH — 0.1 M of a strong acid, or 0.1 M of a weak acid?

An interactive pH scale. Choose strong/weak acid or base and set the concentration; the pH, [H+] and [OH-] update live on a 0–14 colour scale.

Set the acid/base TYPE and the CONCENTRATION independently. Compare a strong and a weak species at the SAME concentration — the pH is very different. That is the whole point: strength (how fully it dissociates) is not the same as concentration (how much is dissolved).

Check your understanding

1. A solution's [H⁺] rises from 1×10⁻⁵ M to 1×10⁻³ M. How does the pH change?
pH = −log[H⁺]. Going from 10⁻⁵ to 10⁻³ is a 100× increase in H⁺, which is 2 log units — pH drops from 5 to 3. More H⁺ means lower pH.
2. At 50 °C, pure neutral water has a pH of about 6.6. Is it acidic?
Neutral means [H⁺] = [OH⁻], not 'pH = 7'. Kw is larger at 50 °C, so neutral sits below 7. pH 7 is only the neutral point at 25 °C.
3. A strong acid solution has pH 3.00. What is [H⁺]?
Invert pH = −log[H⁺]: [H⁺] = 10^(−pH) = 10⁻³ = 1×10⁻³ M. (10⁻¹¹ M would be the OH⁻ concentration.)
🔎 Related lessons
Previous: Acid–Base Definitions Next: Strong vs Weak Acids & Bases Buffers & Henderson–Hasselbalch
✅ Key takeaways
  • pH = −log[H⁺] and pOH = −log[OH⁻]; each pH unit is a 10× change in [H⁺].
  • Kw = [H⁺][OH⁻] = 1.0×10⁻¹⁴ at 25 °C, so pH + pOH = 14.
  • Invert with [H⁺] = 10^(−pH).
  • Strong acid: [H⁺] = concentration; strong base: [OH⁻] = concentration.
  • Neutral means [H⁺] = [OH⁻]; that equals pH 7 only at 25 °C.
➡️ Finding the pH of a strong acid was easy because it dissociates completely. But most acids don't — a weak acid only partly lets go of its protons, and that changes everything. Strength is the next stop.
Want to test yourself on this? Try the Chemistry practice test →