Strong and Weak Acids and Bases

Same concentration, very different behavior

Take 0.10 M hydrochloric acid and 0.10 M acetic acid and drop an identical strip of magnesium into each. The hydrochloric acid fizzes vigorously; the acetic acid bubbles slowly. In a conductivity tester, the hydrochloric acid lights the bulb brightly, while the acetic acid makes it glow faintly. A pH meter reads 1.00 for the hydrochloric acid and about 2.88 for the acetic acid.

The two acids have the same concentration, but their H⁺ concentrations differ by a factor of more than 70. The reason is how far each acid ionizes.

Strong acids and strong bases

Lesson 2.7.5 sorted electrolytes into strong and weak. Acids and bases sort the same way:

A strong acid强酸 ionizes completely in water. The six to know are HCl, HBr, HI, HNO₃, H₂SO₄, and HClO₄.
A strong base强碱 dissociates completely in water. These are the Group 1 hydroxides (LiOH, NaOH, KOH, …) and Ca(OH)₂, Sr(OH)₂, and Ba(OH)₂.

A strong acid solution contains essentially no acid molecules, only H⁺ and the anion. In 0.10 M HCl, [H⁺] = 0.10 M.

Weak acids, weak bases, and ionization constants

A weak acid弱酸 ionizes only partly in water; examples are CH₃COOH, HF, H₂CO₃, HClO, and HCN. A weak base弱碱 reacts only partly with water; the standard example is NH₃.

The ionization of a weak acid is reversible. Writing a weak monoprotic acid as HA:

\ce{HA <=> H+ + A-}

Molecules ionize and ions recombine until the two rates are equal, the dynamic equilibrium of lesson 2.11.3. Just like the K of lesson 2.11.4, this equilibrium has a constant, the acid ionization constant电离常数, Ka:

K_a = \frac{[\ce{H+}][\ce{A-}]}{[\ce{HA}]}

For a weak base, NH₃ + H₂O ⇌ NH₄⁺ + OH⁻, the base ionization constant is Kb = [NH₄⁺][OH⁻]/[NH₃] = 1.8 × 10⁻⁵ at 25 °C. Water is left out because it is the solvent.

Ionization constants depend only on temperature. At a given temperature, the larger Ka, the more the acid ionizes and the stronger it is. Here are Ka values at 25 °C:

Weak acid	Ka (25 °C)
HF	6.4 × 10⁻⁴
HNO₂	4.6 × 10⁻⁴
HCOOH (formic acid)	1.8 × 10⁻⁴
CH₃COOH (acetic acid)	1.8 × 10⁻⁵
H₂CO₃ (first ionization)	4.3 × 10⁻⁷
HClO (hypochlorous acid)	2.9 × 10⁻⁸
HCN (hydrocyanic acid)	4.9 × 10⁻¹⁰

H₂CO₃ is diprotic and ionizes in two steps. The second step is much weaker than the first, so usually only the first counts.

Percent ionization

How far a weak acid ionizes is given by its percent ionization:

\begin{aligned} &\text{percent ionization} \\ &= \frac{[\ce{HA}]_{\text{ionized}}}{[\ce{HA}]_{\text{initial}}} \times 100\% \end{aligned}

Only about 1.3% of the molecules in 0.10 M acetic acid ionize, so [H⁺] ≈ 1.3 × 10⁻³ M, far less than in HCl of the same concentration. Dilute the acetic acid to 0.010 M and its percent ionization rises to about 4.2%: adding water shifts the equilibrium toward the ions (Le Châtelier’s principle, lesson 2.11.5). But [H⁺] falls to about 4.2 × 10⁻⁴ M, because the solution is more dilute.

Stronger acid, weaker conjugate base

From lesson 2.12.1, an acid that donates H⁺ leaves its conjugate base behind. The more readily an acid gives up H⁺, the less its conjugate base tends to take it back:

HCl is strong, and its conjugate base Cl⁻ hardly accepts H⁺ at all, so NaCl solution is neutral.
CH₃COOH is weak, and its conjugate base CH₃COO⁻ takes some H⁺ from water (CH₃COO⁻ + H₂O ⇌ CH₃COOH + OH⁻), so sodium acetate solution is slightly basic. A reaction like this, in which ions from a salt take H⁺ from water (or give H⁺ to it) and make the solution basic (or acidic), is called salt hydrolysis盐类的水解. Chinese textbooks cover it fully in a later elective course; AP Chemistry uses the same idea when it treats ions like CH₃COO⁻ as weak bases. The titration curves in lesson 2.12.5 depend on this.

In the model below, each cell is one solute molecule. Pick an acid or base and a concentration, count how many of the 100 molecules are ionized, and compare [H⁺], pH, and the bulb. Lesson 2.12.3 shows how to calculate pH; for now, remember that lower pH means higher [H⁺].

Try it: how do strong and weak acids at the same concentration differ?

Concentration

Bulb brightness is only a sketch of how many ions there are. The H⁺ and OH⁻ from water itself are ignored.

How Chinese textbooks differ

Chinese textbooks write concentrations as c(H⁺) in mol/L and call Ka 电离常数. Percent ionization is sometimes called 电离度 (degree of ionization).
Chinese textbooks write aqueous ammonia as NH₃·H₂O, with NH₃·H₂O ⇌ NH₄⁺ + OH⁻.
US textbooks expect you to memorize six strong acids; the ones Chinese textbooks use most are HCl, H₂SO₄, and HNO₃.
The ICE table is called 三段式 in Chinese textbooks; it is the same method as in lesson 2.11.4.

Example 1: [H⁺] in 0.10 M acetic acid

At 25 °C, find [H⁺] and the percent ionization in 0.10 M CH₃COOH, and compare with 0.10 M HCl. Ka = 1.8 × 10⁻⁵.

Let [H⁺] = x at equilibrium. Then [CH₃COO⁻] = x and [CH₃COOH] = 0.10 − x:

\begin{aligned} K_a &= \frac{[\ce{H+}][\ce{CH3COO-}]}{[\ce{CH3COOH}]} \\ &= \frac{x^2}{0.10 - x} \\ &= 1.8 \times 10^{-5} \end{aligned}

Step-by-step solution

Approximate. Ka is small, so very little acid ionizes and x is much smaller than 0.10. Drop x from the denominator: 0.10 − x ≈ 0.10. Then
$\begin{aligned} x^2 &= 1.8 \times 10^{-5} \times 0.10 \\ &= 1.8 \times 10^{-6} \end{aligned}$
Solve for x.
$\begin{aligned} x &= \sqrt{1.8 \times 10^{-6}} \\ &= 1.34 \times 10^{-3} \end{aligned}$
so [H⁺] ≈ 1.3 × 10⁻³ M.
Percent ionization.
$\frac{1.34 \times 10^{-3}}{0.10} \times 100\% \approx \boxed{1.3\%}$
Check the approximation: why 5%? Writing 0.10 instead of 0.10 − x makes the denominator too big by x ÷ 0.10, which is the percent ionization. If that is under 5%, the denominator is off by less than 5%, and because x comes from a square root, x is off by only about half as much, under 2.5%. Ka has only two significant figures, so an error that small doesn’t matter. Here it is just 1.3%, so the approximation is fine.
Compare with the exact answer. Solving x² + 1.8 × 10⁻⁵x − 1.8 × 10⁻⁶ = 0 without approximating gives x = 1.33 × 10⁻³, less than 1% different.
When you can’t approximate. In very dilute acid, or with a larger Ka, a bigger fraction ionizes. For 0.0010 M acetic acid the shortcut gives x = 1.34 × 10⁻⁴, which is 13% ionization, over 5%, so you solve the quadratic instead (x = 1.25 × 10⁻⁴).
Compare. In 0.10 M HCl, [H⁺] = 0.10 M, more than 70 times higher. That is why magnesium reacts so much faster in the hydrochloric acid.

Example 2: concentrated weak acid vs. dilute strong acid

At 25 °C, which has the higher [H⁺]: 1.0 M acetic acid or 0.010 M hydrochloric acid?

Step-by-step solution

Hydrochloric acid. HCl is a strong acid and ionizes completely, so [H⁺] = [HCl] = 0.010 M.
Acetic acid. As in Example 1, let [H⁺] = x and approximate the denominator as 1.0:
$\begin{aligned} x^2 &\approx 1.8 \times 10^{-5} \times 1.0 \\ x &\approx 4.2 \times 10^{-3}\ \text{M} \end{aligned}$
Check the approximation. 4.2 × 10⁻³ ÷ 1.0 = 0.42%, well under 5%.
Compare. 0.010 > 4.2 × 10⁻³, so the dilute hydrochloric acid has the higher [H⁺], even though the acetic acid is 100 times more concentrated.
Conclusion. Strong vs. weak is about how far an acid ionizes; concentrated vs. dilute is about how much acid is dissolved. They are different things.

Practice: which kind is it?

HNO₃
HF
KOH
NH₃
HClO₄
HCN
Ba(OH)₂
H₂CO₃

Common mistakes

Mistake 1: “Strong means concentrated and weak means dilute.” Strength is about how far an acid ionizes; concentration is about how much is dissolved. 0.010 M HCl is a dilute strong acid and 1.0 M acetic acid is a concentrated weak acid, and the HCl has the higher [H⁺].

Mistake 2: “Hydrofluoric acid dissolves glass, so it must be a strong acid.” HF attacks glass because it reacts with SiO₂, which has nothing to do with how far it ionizes. HF ionizes only partly, so it is a weak acid.

Mistake 3: “Diluting a weak acid raises its percent ionization, so [H⁺] goes up.” The percent ionization does rise, but the dilution itself matters more, so [H⁺] still falls. Diluting 0.10 M acetic acid tenfold drops [H⁺] from 1.3 × 10⁻³ M to 4.2 × 10⁻⁴ M.

Quick check

At the same concentration, which acid solution has the lowest [H⁺]? (See the Ka table.)

A 0.10 M solution of a weak monoprotic acid has [H⁺] = 1.0 × 10⁻³ M. What is its percent ionization?

Summary

Strong acids (HCl, HBr, HI, HNO₃, H₂SO₄, HClO₄) and strong bases (Group 1 hydroxides plus Ca(OH)₂, Sr(OH)₂, Ba(OH)₂) ionize completely in water.
Weak acids and bases ionize partly and reach an equilibrium. Ka (Kb) depends only on temperature; a larger value means a stronger acid (base).
Percent ionization = ionized ÷ initial × 100%. Dilution raises it but lowers [H⁺]. Strong vs. weak and concentrated vs. dilute are different ideas.

On to AP (for later)

AP expects you to know the common strong acids and bases (topic 8.2). Topic 8.3 uses Ka, Kb, and ICE tables to find [H₃O⁺], pH, and percent ionization for weak acids and bases, and often asks whether the x ≪ c approximation is justified. Topic 8.6 explains acid strength from molecular structure: bond polarity, bond strength, and the stability of the conjugate base.

Data sources: Ka values from OpenStax Chemistry 2e, Appendix H.

Strong and Weak Acids and Bases强酸强碱与弱酸弱碱

Learning goals

Before you start

Same concentration, very different behavior

Strong acids and strong bases

Weak acids, weak bases, and ionization constants

Percent ionization

Stronger acid, weaker conjugate base

How Chinese textbooks differ

Example 1: [H⁺] in 0.10 M acetic acid

Example 2: concentrated weak acid vs. dilute strong acid

Common mistakes

Quick check

Summary

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