Worked example 1
Find the pH and percent ionization of 0.150 M acetic acid (Ka = 1.8 × 10⁻⁵.
Try it first: Check C/Ka before deciding how to solve.
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Acids, Bases & Aqueous EquilibriaAcids and BasesContent level: Core 24 min
Weak Acids, Ka and Percent Ionization
What you'll be able to do: Calculate the pH and percent ionization of a weak acid solution using Ka and an ICE table.
Introduction
Most acids you meet in biology, food and the lab are weak. Their pH is not the concentration written on the bottle, it is the answer to an equilibrium problem.
These are recommended, not required. You can start this lesson at any time.
Learning objectives
- Write the Ka expression for any weak acid
- Set up and solve an ICE table for a weak acid
- Judge when the small-x approximation is valid
- Calculate percent ionization and explain how it varies with dilution
Lesson
Partial ionization
Acetic acid in water reaches an equilibrium in which most molecules remain intact. The equilibrium constant for that proton transfer is called the acid ionization constant, Ka. Acetic acid has Ka = 1.8 × 10⁻⁵, so at 0.10 M about 1.3% of the acid molecules are ionized at equilibrium (roughly 1 in 75).
Ka = [H₃O⁺][A⁻] / [HA]
pKa as a ranking tool
pKa = -log Ka turns awkward exponents into a readable scale. A smaller pKa means a stronger acid: HF (pKa 3.17) is stronger than acetic acid (4.74), which is far stronger than HCN (9.21).
Compare acids with pKa, not Ka, and remember the ordering reverses.
The ICE table
Let x be the amount of acid that ionizes. Initially [HA] = C and both products are zero; at equilibrium [HA] = C - x and [H₃O⁺] = [A⁻] = x. Substituting gives Ka = x²/(C - x), an exact quadratic.
Ka = x² / (C - x)
The small-x approximation
For the simple monoprotic-acid setup HA + H₂O ⇌ H₃O⁺ + A⁻, C/Ka > 400 is a conservative screen for trying the small-x approximation x = sqrt(Ka × C). The shortcut depends on the equilibrium expression and initial concentrations, so do not apply that ratio as a universal rule to every ICE table. Solve with the approximation, then check whether the change is less than 5% of each nonzero initial concentration it replaces; otherwise solve exactly.
Always check the 5 percent rule. Approximating without checking is the single most common source of wrong weak-acid answers.
Percent ionization
Percent ionization = 100 x x/C. Diluting a weak acid raises the percent ionization while lowering [H₃O⁺], which surprises students. Le Chatelier explains it: dilution favours the side with more dissolved particles, which is the ionized side.
percent ionization = 100 × [H₃O⁺] / C(initial)
Polyprotic acids
H₂CO₃ loses protons in two steps with Ka₁ = 4.3 × 10⁻⁷ and Ka₂ = 4.7 × 10⁻¹¹. Because Ka₂ is roughly ten thousand times smaller, the second step contributes almost nothing to the pH and can normally be ignored.
Test the small-x shortcut before trusting it
The estimate x≈sqrt(KaC) assumes x is small compared with starting concentration C. Check x/C, often against a 5% classroom criterion; if it is too large, solve the quadratic x²/(C-x)=Ka. The estimate may give a roughly plausible pH but an inaccurate percent ionization, especially in dilute weak-acid solutions.
Validate the approximation using the concentration it predicts.
Key ideas
Definition
Ka
The equilibrium constant for proton transfer from an acid to water.
Rule
pKa
pKa = -log Ka; smaller pKa means a stronger acid.
Rule
Small-x test
Valid when C/Ka > 400 and x < 5 percent of C.
Rule
Percent ionization
Rises on dilution even though pH rises too.
Rule
Polyprotic acids
Successive Ka values drop sharply; the first step dominates the pH.
Equation
Acid ionization constant
Ka = [H₃O⁺][A⁻] / [HA]
- [HA] = equilibrium concentration of the un-ionized acid
Equation
Approximate hydronium
[H₃O⁺] = sqrt(Ka x C)
- C = initial acid concentration
Equation
Percent ionization
percent = 100 × [H₃O⁺] / C
- [H₃O⁺] = equilibrium hydronium concentration
Worked examples
Worked example 2
A 0.0100 M solution of a weak acid has pH 3.40. Find Ka.
Try it first: Convert the pH into x, then read the ICE table backwards.
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Worked example 3
Compare the percent ionization of 0.100 M and 0.00100 M HF (Ka = 6.8 × 10⁻⁴.
Try it first: Predict the direction of the change with Le Chatelier before calculating.
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Worked example 4
For HA with C=1.00×10⁻⁴ M and Ka=1.00×10⁻⁵, find the percent ionization.
Try it first: First test sqrt(KaC) against C.
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Common mistakes
Setting [H₃O⁺] equal to the acid concentration.
Why it's wrong: That is true only for strong acids.
Check instead: Use Ka and an ICE table for anything weak.
Using the small-x shortcut without checking.
Why it's wrong: For acids with large Ka or low C, it can be off by tens of percent.
Check instead: Apply the 5 percent rule and solve the quadratic if it fails.
Confusing percent ionization with acid strength.
Why it's wrong: Percent ionization depends on concentration; Ka does not.
Check instead: Compare Ka or pKa when ranking acids.
Assuming a larger pKa means a stronger acid.
Why it's wrong: The log is negative, so the ordering reverses.
Check instead: Smaller pKa is stronger.
Adding the pH of the second ionization step for a polyprotic acid.
Why it's wrong: pH values do not add, and Ka₂ is usually negligible anyway.
Check instead: Solve the first step and check whether the second contributes.
After the lesson · Question bank
Independent practice
Work through new problems on this topic on your own. The lesson's quick checks and worked examples stay above if you need to review a step.
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What you should now know
A weak acid only partially transfers its proton, so HA + H₂O ⇌ H₃O⁺ + A⁻ has Ka = [H₃O⁺][A⁻]/[HA]. A larger Ka, or smaller pKa, means a stronger weak acid. Use an ICE table to find pH. For a simple monoprotic acid HA starting at concentration C with negligible initial products, C/Ka > 400 is a conservative screen for trying x ≈ sqrt(Ka × C); verify the change is under 5% of C, or solve the quadratic. Other equilibrium stoichiometries and starting mixtures need their own check. Percent ionization is 100 × [H₃O⁺]/C(initial), and dilution can increase percent ionization even as pH rises.
- Ka measures how far a weak acid transfers its proton
- Smaller pKa means a stronger acid
- Weak acid pH comes from an ICE table, not from the label concentration
- The small-x shortcut needs the 5 percent check
- Percent ionization rises on dilution while pH also rises
Sources and further reading
This lesson is original Chem Help content. No external sources were adapted.