Chemistry 2e · Acid-Base Equilibria

Relative Strengths of Acids and Bases

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In 30 seconds
Why this matters
The college version
Eli explains
Worked example
Key takeaway
Check yourself
Study tools
Sources & references

In 30 seconds

Not every acid or base is equally aggressive. A such as hydrochloric acid transfers essentially all of its protons to water, while a such as acetic acid transfers only a tiny fraction. This difference is not about how much acid you pour into a beaker — it is an intrinsic property of each molecule, measured with equilibrium constants. This topic builds the quantitative "strength ladder": the acid ionization constant K_a, the base ionization constant K_b, and their logarithmic relatives pK_a and pK_b. Once you can rank acids and bases, you can predict reaction direction, salt-solution pH, and buffer behavior.

Why this matters

Acid strength decides the outcome of countless real processes. In your body, the conjugate pair HCO₃^-/H₂CO₃ keeps blood pH near 7.4; the relative strengths of its members determine how much base the blood can absorb. In food preservation, weak acids like citric and acetic acid are gentle enough to eat yet still stop bacterial growth. In the lab, strong acids give fast, complete reactions, while weak acids are chosen when a controlled, partial reaction is safer. Exams lean heavily on strength comparisons, so ranking acids and predicting reaction direction from K_a or pK_a are routine.

The college version

Core Concepts

The acid ionization constant measures strength

When a weak acid HA dissolves in water, it establishes an equilibrium with water acting as the base:

$HA (aq) + H 2 O (l) ⇌ H 3 O + (aq) + A - (aq)$

The equilibrium constant for this proton transfer is the acid ionization constant:

$K a = [H 3 O +][A -] [HA]$

A larger K_a means the equilibrium lies further toward products — more of the acid has donated its proton — so the acid is stronger. Strong acids such as HCl have K_a values so large that we treat their ionization as complete. Weak acids have small K_a values; acetic acid, for example, has K_a = 1.8 × 10^-5. The base analog is K_b, the equilibrium constant for a base abstracting a proton from water; ammonia has K_b = 1.8 × 10^-5.

Conjugate pairs are locked together

Every acid has a conjugate base (what remains after proton loss), and the two are linked by water's autoionization constant:

$K a (HA) \times K b (A -) = K w = 1.0 \times 10 -14 at 25 ° C$

This relationship explains a famous pattern: the stronger the acid, the weaker its conjugate base. Because HCl is strong, Cl^- is a non-basic spectator; because acetic acid is weak, its conjugate base CH₃COO^- is noticeably basic (see Hydrolysis of Salts). The same rule applies to bases: a strong base like OH^- has a feeble conjugate acid, water.

The pK_a scale: a log ladder for quick ranking

Because K_a values span many orders of magnitude, chemists compress the ladder with a logarithm:

$pK a = - log K a$

Smaller pK_a means stronger acid: HCl has pK_a ≈ -7, acetic acid pK_a = 4.74, and water pK_a = 14. The log form also simplifies the conjugate relationship at 25 °C:

$pK a + pK b = 14$

so NH₄⁺ (pK_a = 9.25) pairs with ammonia (pK_b = 4.75).

Structural trends in acid strength

Two trends let you rank acids without a table. Down a group (HF, HCl, HBr, HI), the H–X bond lengthens and weakens, so acidity increases: HF < HCl < HBr < HI. HF is the only weak one of the four despite fluorine's electronegativity, because the H–F bond is unusually strong. Across a period (CH₄, NH₃, H₂O, HF), the atom holding the proton becomes more electronegative, so acidity increases. Oxyacids follow a third pattern: more oxygen atoms spread negative charge better and strengthen the acid, so HClO₄ > HClO₃ > HClO₂ > HClO.

How It Works / Step-by-Step Process

Write the proton-transfer reaction and identify the two conjugate pairs involved.
Find the K_a (or pK_a) of each acid in the reaction from a table.
Identify which acid is stronger — the larger K_a, or the smaller pK_a.
The reaction proceeds so that the stronger acid and stronger base are consumed, producing the weaker acid and weaker base.
For weak-acid pH, set up an ICE table, apply K_a, and check the 5% rule before using x ≈ K_a C.

Common Confusions

Do Not Confuse	With	Difference
"Strong acid"	"Concentrated acid"	Strength is K_a, an intrinsic property; concentration is molarity. 0.0001 M HCl is strong but dilute.
Strong acid's conjugate base	A strong base	The conjugate base of a strong acid (e.g., Cl^-) is essentially non-basic — a spectator ion.
Larger pK_a	Stronger acid	It is the opposite: smaller pK_a = stronger acid.
K_a × K_b = K_w for any acid/base	Only for a conjugate pair	You cannot multiply the K_a of acetic acid by the K_b of ammonia.
HF as a strong acid because F is electronegative	HF is weak	The H–F bond is unusually strong; down-group hydrides (HCl, HBr, HI) are the strong ones.

Eli explains

The same idea, in plain words

Explain it like I’m 10

Some acids give away their proton almost instantly; others only pass it along once in a while. We rank them by counting how often they give it away — that is their "strength." If an acid is great at giving protons, its leftover partner is bad at taking them back. It has nothing to do with how much acid you have.

Worked example

Example 1: pH and percent ionization of acetic acid

Calculate the pH and percent ionization of a 0.10 M acetic acid solution (K_a = 1.8 × 10^-5).

Write the equilibrium and the constant first:

$CH 3 COOH (aq) ⇌ H + (aq) + CH 3 COO - (aq), K a = [H +][CH 3 COO -] [CH 3 COOH]$

Let x be the change in [H⁺]; then [H⁺] = [CH₃COO^-] = x and [CH₃COOH] = 0.10 - x. Because K_a is small, try 0.10 - x ≈ 0.10:

$K a = x 2 0.10 - x \approx x 2 0.10$

$x = \sqrt K a \times 0.10 = \sqrt (1.8 \times 10 -5)(0.10) = \sqrt 1.8 \times 10 -6 = 1.3 \times 10 -3 M$

$pH = - log (1.3 \times 10 -3) = 2.87$

Percent ionization:

$% ionization = [H +] [CH 3 COOH] initial \times 100 = 1.3 \times 10 -3 0.10 \times 100 = 1.3 %$

Since 1.3% < 5%, the approximation was valid. Only about 1 in 75 acetic acid molecules donates a proton — that is what "weak" means.

Example 2: finding K_a of a conjugate acid from K_b

Ammonia has K_b = 1.8 × 10^-5. Find K_a of its conjugate acid NH₄⁺. Write the conjugate relationship, then substitute:

$K a (NH 4 +) = K w K b (NH 3) = 1.0 \times 10 -14 1.8 \times 10 -5 = 5.6 \times 10 -10$

So pK_a(NH₄⁺) = -log(5.6 × 10^-10) = 9.25. Ammonium is a much weaker acid than acetic acid (K_a = 1.8 × 10^-5) even though its parent base, ammonia, is respectable. Because both constants are defined against water's standard state, their numerical product equals K_w and they can be compared directly.

Example 3: predicting reaction direction

Will acetic acid react with ammonia to a significant extent? Compare the acids on each side:

$CH 3 COOH + NH 3 ⇌ CH 3 COO - + NH 4 +$

Acids: CH₃COOH (K_a = 1.8 × 10^-5) vs. NH₄⁺ (K_a = 5.6 × 10^-10). Acetic acid is the stronger acid, so it is the proton donor, and the equilibrium lies far to the right — the weaker acid NH₄⁺ and weaker base CH₃COO^- are favored.

Key takeaways

Large K_a = strong acid; small K_a = weak acid; same logic with K_b for bases.
For any conjugate pair: K_a × K_b = K_w = 1.0 × 10^-14 at 25 °C, so pK_a + pK_b = 14.
Smaller pK_a means a stronger acid — the sign inversion is a classic trap.
Common strong acids: HCl, HBr, HI, HNO₃, H₂SO₄ (first proton), HClO₄.
Stronger acid ⇄ weaker conjugate base; proton transfer favors the weaker acid and base.
Strength ≠ concentration: a dilute strong acid can have a higher pH than a concentrated weak acid.
Binary-acid strength increases down a group; oxyacid strength grows with more oxygen atoms.

Check yourself

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

Which is the stronger acid: one with K_a = 1.0 × 10^-2 or one with pK_a = 5?
Show answer
The one with K_a = 1.0 × 10^-2 (pK_a = 2); smaller pK_a = stronger acid.
If a weak acid has K_a = 4.0 × 10^-6, what is K_b of its conjugate base at 25 °C?
Show answer
K_b = K_w/K_a = (1.0 × 10^-14)/(4.0 × 10^-6) = 2.5 × 10^-9.
A solution of a weak acid HA is 0.25 M and has K_a = 1.6 × 10^-5. Estimate its pH using the approximation, and state why the approximation is valid.
Show answer
x = (1.6 × 10^-5)(0.25) = 2.0 × 10^-3 M, so pH ≈ 2.70. Valid because x/C = 0.8% < 5%.
Why is Cl^- a spectator ion in water but CH₃COO^- is not?
Show answer
Cl^- is the conjugate base of a strong acid, so its K_b is essentially zero; acetate's K_b = 5.6 × 10^-10 is large enough to react with water.
Arrange HF, HCl, HBr, HI from weakest to strongest acid and explain the trend.
Show answer
HF < HCl < HBr < HI. The H–X bond lengthens down the group, so the proton leaves more easily.

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Study tools & related lessonsKey vocabulary · Related

Key vocabulary

acid ionization constant, Kₐ: Equilibrium constant for an acid donating a proton to water; bigger = stronger acid.
base ionization constant, Kb: Equilibrium constant for a base accepting a proton from water; bigger = stronger base.
conjugate acid–base pair: Two species differing by one proton (e.g., NH₄⁺/NH₃).
pKₐ: -logK_a; smaller value = stronger acid.
strong acid: Acid that ionizes essentially completely in water.
weak acid: Acid that ionizes only partially, leaving an equilibrium.
percent ionization: Fraction of weak-acid molecules that donate a proton, as a percentage.

Sources & references

openstax.org — Chemistry 2e

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