Acids & bases (intro)
The idea
Lemon juice, vinegar, soap, and drain cleaner sit on a single chemical axis. Acids release hydrogen ions (H⁺) into solution; bases release hydroxide ions (OH⁻) or soak up H⁺. Mixed together they neutralize each other, producing water and a salt. The pH scale compresses the huge range of possible H⁺ concentrations into a convenient 0–14 ruler: pH = −log[H⁺], with 7 neutral at 25 °C, lower numbers acidic, higher numbers basic.
Because the scale is logarithmic, each step of one pH unit means a tenfold change in H⁺ concentration — that is the point most worth internalizing. The common misconception is reading pH like a linear scale, as if pH 2 were merely twice as acidic as pH 4; it is actually 100 times more concentrated in H⁺. Also keep strong versus concentrated separate: a strong acid like HCl dissociates completely into ions, which is a statement about behavior, while concentration is a statement about how much was dissolved — a dilute strong acid and a concentrated weak acid can even have similar pH.
Worked example
A solution of hydrochloric acid has a concentration of 0.010 M. Find its pH, classify the solution, and determine how many times more concentrated its H⁺ is compared with black coffee at pH 5.0.
- Use the strength of HCl: as a strong acid it dissociates completely, so every dissolved HCl donates its H⁺ and [H⁺] = 0.010 M = 1.0 × 10⁻² M. For a weak acid this shortcut would not be allowed.
- Apply the definition: pH = −log(1.0 × 10⁻²) = 2.00, since the logarithm of 10⁻² is exactly −2.
- Classify: pH 2.00 is well below 7, so the solution is strongly acidic — consistent with stomach acid, which is similar in strength.
- Compare with the coffee using the tenfold-per-unit rule: the pH difference is 5.0 − 2.0 = 3.0 units, so the acid has 10³ = 1000 times the H⁺ concentration.
- Verify directly from the concentrations: 1.0 × 10⁻² M versus 1.0 × 10⁻⁵ M is indeed a factor of 1000, confirming the shortcut.
Answer. The solution has pH 2.00, is strongly acidic, and carries 1000 times the H⁺ concentration of pH 5.0 coffee.
Check your understanding
- Why is a logarithmic scale a sensible choice for reporting acidity, given the range of possible H⁺ concentrations?
- What does it mean chemically when an acid and a base neutralize each other, and what ends up in the beaker?
- If you dilute a strong acid by a factor of ten, what happens to its pH, and why does repeating this never push pH past 7?
- How would you explain the difference between a strong acid and a concentrated acid to a friend who uses the words interchangeably?
Build the foundations first
Acids & bases (intro) builds on these concepts. If any feel shaky, start there.