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Chemistry: Atoms First 2e · Acid-Base Equilibria

Relative Strengths of Acids and Bases

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On this page 8 sections
  1. In 30 seconds
  2. Why this matters
  3. The college version
  4. Eli explains
  5. Key takeaway
  6. Check yourself
  7. Study tools
  8. Sources & references

In 30 seconds

Not all acids are created equal. A strong acid such as HCl transfers essentially 100% of its protons to water, while a weak acid such as acetic acid transfers only a small fraction, leaving a mixture of acid and its conjugate base at equilibrium. The degree of proton transfer is quantified by the acid ionization constant, Ka:

Ka = [H3O+][A−][HA]

for a weak acid HA reacting with water: HA(aq) + H2O(l) ⇌ H3O+(aq) + A-(aq). The larger the Ka, the stronger the acid. Weak bases are described the same way with the base ionization constant, Kb. Because a conjugate pair shares the water equilibrium, the strengths of an acid and its conjugate base are locked together by

Ka × Kb = Kw = 1.0 × 10-14

at 25 °C. This one relationship lets you rank acids and bases, predict reaction direction, and convert any Ka into the corresponding Kb — the workhorse skill of this topic.

Why this matters

Relative strength is the practical question behind most acid-base chemistry:

  • Choosing an acid or base for a job: Cleaning products use strong bases (lye), food preservation uses weak acids (citric, acetic), and laboratories pick the weakest acid strong enough for a task so it doesn't attack equipment or materials.
  • Drug absorption: A drug that is a weak acid exists as a mixture of neutral HA and charged A− at body pH. Only the neutral form crosses membranes easily; the ratio of forms is set by the drug's Ka (via the Henderson–Hasselbalch idea developed in the buffers topic).
  • Environmental and biological systems: The carbonate system in blood and the oceans, soil chemistry, and the acidity of rain are all governed by which protonated species dominates — a direct function of relative Ka values.
  • Exams: Nearly every acid-base problem — , salt pH, buffer pH — begins with Ka or Kb and the Ka × Kb = Kw relationship.

The college version

Core Concepts

Ka measures acid strength; Kb measures base strength

For the weak acid HA, the equilibrium constant is

Ka = [H3O+][A−][HA]

and for the weak base B, with B(aq) + H2O(l) ⇌ BH+(aq) + OH-(aq),

Kb = [BH+][OH−][B]

Water's concentration is omitted because it is a pure liquid (its activity is effectively constant). Larger Ka means more proton transfer, hence a stronger acid. Values span many orders of magnitude — from about 10-10 for hydrogen cyanide to 10-2 or higher for moderately strong acids — so chemists often convert to the compressed scale pKa = -logKa, where smaller pKa means a stronger acid.

The conjugate strength ladder: Ka × Kb = Kw

Multiplying the expressions for HA and its conjugate base A− gives a striking simplification:

Ka(HA) × Kb(A−) = [H3O+][A−][HA] × [HA][OH−][A−] = [H3O+][OH−] = Kw

At 25 °C this becomes Ka × Kb = 1.0 × 10-14. The consequence is a strict see-saw: the stronger the acid, the weaker its conjugate base. Hydrogen cyanide is a very weak acid (Ka = 4.9 × 10-10), so its conjugate base cyanide is a fairly strong base (Kb = 2.0 × 10-5). Conversely, Cl−, the conjugate base of the strong acid HCl, is such a feeble base that it does not react with water at all.

Ranking common acids

Common weak acids, with typical Ka values at 25 °C, rank as follows (largest Ka = strongest):

AcidKa (approx.)
H3PO4 (first proton)7.5 × 10-3
HF6.3 × 10-4
acetic acid, CH3COOH1.8 × 10-5
H2CO3 (first proton)4.3 × 10-7
HCN4.9 × 10-10

Strong acids (HCl, HNO3, H2SO4 first proton) sit far above this table with Ka so large that ionization is treated as complete. The corresponding conjugate bases rank in exactly the reverse order: CN− is the strongest base in the list, H2PO4− the weakest.

Percent ionization

The fraction of acid molecules that actually transfer a proton is the percent ionization:

% ionization = [H3O+]eq[HA]0 × 100%

For weak acids it is always less than 100% and, importantly, it increases as the acid is diluted. A 0.10 M acetic acid solution is about 1.3% ionized, but a 0.010 M solution is about 4.2% ionized — the equilibrium shifts toward more dissociation as concentration falls (Le Chatelier's principle at work). Dilution makes a weak acid ionize more, but never to completion.

Structure and strength

Two structural patterns explain most trends. For binary acids down a group (e.g., HCl, HBr, HI), acidity increases as the H–X bond weakens, so HI is the strongest. For oxoacids, acidity increases with the number of oxygen atoms attached to the central atom and with the electronegativity of that atom: HClO is a weak acid, while HClO4 (four oxygens) is among the strongest. More electronegative atoms and more oxygen atoms pull electron density away from the O–H bond, making the proton easier to release.

How It Works / Step-by-Step Process

Worked example 1: converting Ka to Kb for a conjugate pair

Problem. Hydrogen cyanide has Ka = 4.9 × 10-10. Find Kb for its conjugate base, cyanide ion, at 25 °C.

Solution.

  1. Write the conjugate relationship: Ka × Kb = Kw = 1.0 × 10-14.
  2. Rearrange and substitute:

Kb = KwKa = 1.0 × 10-144.9 × 10-10 = 2.0 × 10-5

Dimensional analysis: both K values are dimensionless equilibrium constants, so no units appear — but the magnitude comparison is meaningful: cyanide's Kb is 4 × 104 times larger than HCN's Ka, so cyanide is a noticeably stronger base than HCN is an acid. This is why sodium cyanide solutions are strongly basic.

Worked example 2: pH and percent ionization of a weak acid

Problem. Acetic acid has Ka = 1.8 × 10-5. Find the pH and percent ionization of a 0.10 M solution.

Solution.

  1. Set up the equilibrium: CH3COOH(aq) + H2O(l) ⇌ H3O+(aq) + CH3COO-(aq), with x = [H3O+] = [CH3COO−] at equilibrium and [CH3COOH] = 0.10 - x.
  2. Write the Ka expression:

Ka = x · x0.10 - x = 1.8 × 10-5

  1. Try the approximation 0.10 - x ≈ 0.10 (valid if x is < 5% of 0.10):

x2 ≈ (1.8 × 10-5)(0.10) = 1.8 × 10-6   ⇒  x = 1.3 × 10-3 M

  1. Check the 5% rule: 1.3 × 10-3 / 0.10 = 1.3% < 5%, so the approximation holds. Then

pH = -log(1.3 × 10-3) = 2.87

  1. Percent ionization:

% ionization = 1.3 × 10-30.10 × 100% = 1.3%

Only about one molecule in 75 actually transfers its proton.

Worked example 3: dilution increases percent ionization

Problem. The same acetic acid (Ka = 1.8 × 10-5) is diluted to 0.010 M. Find the percent ionization and compare with the 0.10 M case.

Solution.

  1. Same setup, new initial concentration:

Ka = x20.010 - x ≈ x20.010 = 1.8 × 10-5

  1. Solve:

x2 = 1.8 × 10-7   ⇒  x = 4.2 × 10-4 M

  1. Percent ionization:

% ionization = 4.2 × 10-40.010 × 100% = 4.2%

The check: 4.2 × 10-4 / 0.010 = 4.2% < 5%, so the approximation still holds. Diluting the acid tenfold roughly tripled its percent ionization (1.3% → 4.2%) — even though the solution is less acidic overall, a larger fraction of the acid molecules have ionized.

Common Confusions

Do Not ConfuseWithDifference
Strong acidConcentrated acidStrength = completeness of ionization; concentration = amount present. A dilute strong acid is still strong.
Large KaLarge pKaKa up = stronger acid, but pKa up = weaker acid; the log flips the direction.
Strong acid's conjugate baseNeutral spectatorThe conjugate base of a strong acid is so weak it doesn't react with water (e.g., Cl−); it is not "basic" in solution.
KaKbKa describes acid-to-water proton transfer; Kb describes base-to-water proton acceptance; they multiply to Kw.
Percent ionizationKaPercent ionization depends on concentration (rises on dilution); Ka is a constant at fixed temperature.
Approximate x ≈ Ka CExact answerThe square-root shortcut fails when ionization exceeds ~5%; then solve the full quadratic.
Eli, the EliExplains learning guide

Eli explains

The same idea, in plain words

Explain it like I’m 10

Imagine acids are players who hold a hydrogen "ball" they can pass to water. Strong acids are eager passers — nearly every player throws the ball right away. Weak acids are shy — only a few players pass the ball, and the rest hold onto it. The number Ka tells you how eager the players are: a big number means lots of passing, a tiny number means almost none. And if a player is really good at holding onto the ball (weak acid), the empty-handed partner left behind (the conjugate base) is really good at catching it.

Key takeaways

  • Ka and Kb quantify proton-transfer tendency for weak acids and bases; larger value = stronger.
  • Ka × Kb = Kw = 1.0 × 10-14 at 25 °C — the master relationship for conjugate pairs.
  • Stronger acid ⇔ weaker conjugate base; strong acids have conjugate bases too weak to react with water.
  • pKa = -logKa; smaller pKa = stronger acid (watch the sign on exams).
  • Percent ionization = [H3O+]eq[HA]0 × 100%; it rises with dilution for weak acids.
  • For weak-acid pH problems, use the approximation [H3O+] ≈ Ka [HA]0 only when ionization is < 5%; otherwise solve the quadratic.
  • Structural trends: weaker H–X bond (down a group) and more oxygens/electronegative atoms in oxoacids both strengthen the acid.

Check yourself

5 review questions from the chapter. Try each one, then open the answer.

  1. Write the Ka expression for HF(aq) + H2O(l) ⇌ H3O+(aq) + F-(aq).

    Show answer

    Ka = [H3O+][F−][HF].

  2. Acetic acid has Ka = 1.8 × 10-5. What is Kb for acetate ion at 25 °C?

    Show answer

    Kb = Kw/Ka = 1.0 × 10-14 / 1.8 × 10-5 = 5.6 × 10-10.

  3. Which is the stronger acid: one with Ka = 1.0 × 10-4 or one with pKa = 7? Explain.

    Show answer

    The first, because Ka = 1.0 × 10-4 corresponds to pKa = 4, which is smaller than 7 — smaller pKa means stronger acid.

  4. A 0.10 M weak acid is 2.0% ionized. What is [H3O+] and what is Ka?

    Show answer

    [H3O+] = 0.020 × 0.10 = 2.0 × 10-3 M; Ka ≈ (2.0 × 10-3)2 / 0.10 = 4.0 × 10-5.

  5. Why does percent ionization increase when a weak acid is diluted?

    Show answer

    Dilution shifts the equilibrium HA ⇌ H+ + A− toward more products (more particles), so a larger fraction of the acid ionizes even though the absolute concentration of H3O+ falls.

Keep learning

Ready to build on this? Continue to the next lesson.

Study tools & related lessonsKey vocabulary · Related

Key vocabulary

acid ionization constant (Kₐ)
Equilibrium constant for HA + H2O ⇌ H3O+ + A−
base ionization constant (Kb)
Equilibrium constant for B + H2O ⇌ BH+ + OH−
strong acid/base
Donates/accepts protons essentially completely in water
weak acid/base
Transfers only a fraction of protons, reaching equilibrium
percent ionization
Fraction of acid molecules that ionize, times 100
pKₐ
-logKa

Sources & references

  1. openstax.org — Chemistry Atoms First 2e

This lesson was adapted from the open educational references above; their licenses and attributions are preserved. See Copyright & Licensing.

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