AP® Chemistry review sheet from Aim for Five (aimforfive.com/chem/units/8/8-2)
Unit 8 · Topic 8.2
8.2 pH and pOH of Strong Acids and Bases
Strong acids and strong bases ionize completely in water, so their pH takes just one step: the H₃O⁺ (or OH⁻) concentration comes straight from the starting concentration. You need to know which acids and bases are strong and how many H₃O⁺ or OH⁻ ions each one gives.
Key terms
- strong acid
- strong base
- complete ionization
- pH = −log[H₃O⁺]
- pOH = −log[OH⁻]
The strong acids to memorize
A strong acid gives up its proton to water completely: every molecule reacts, so essentially no un-ionized acid remains. For HCl: HCl(aq) + H₂O(l) → H₃O⁺(aq) + Cl⁻(aq), with a single arrow because the reaction goes to completion.
The six strong acids to know are HCl, HBr, HI, HNO₃, HClO₄ and H₂SO₄. Any other acid you meet in this course should be treated as weak unless you're told otherwise.
For a strong acid that gives one proton (HCl, HBr, HI, HNO₃, HClO₄), [H₃O⁺] equals the acid's starting concentration. For H₂SO₄, only the first proton comes off completely; the second (from HSO₄⁻) is weak.
The strong bases
The strong bases are the hydroxides of group 1 (LiOH, NaOH, KOH and so on) and group 2 (such as Ca(OH)₂, Sr(OH)₂ and Ba(OH)₂). When they dissolve, they break apart completely into metal ions and OH⁻.
A group 1 hydroxide gives one OH⁻ per formula unit, so [OH⁻] equals its concentration. A group 2 hydroxide gives two OH⁻, so [OH⁻] is twice its concentration. 0.010 M Ba(OH)₂ gives 0.020 M OH⁻.
The calculation path
- Strong acid: [H₃O⁺] = acid concentration, then pH = −log[H₃O⁺].
- Strong base: [OH⁻] = base concentration × number of OH⁻ per formula unit, then pOH = −log[OH⁻] and pH = 14.00 − pOH at 25 °C.
- If the acid or base is diluted or made from a mass, find its concentration first: moles ÷ liters of solution.
- No ICE table or equilibrium constant is needed, because ionization is complete.
Diluting a strong acid or base
Diluting doesn't change the moles of acid or base, only the volume, so M₁V₁ = M₂V₂. For example, 10.0 mL of 0.10 M HCl diluted to 100.0 mL becomes 0.010 M, and its pH goes from 1.00 to 2.00. Each tenfold dilution of a strong acid raises the pH by 1 unit; each tenfold dilution of a strong base lowers it by 1 unit.
This pattern stops near pH 7. No amount of dilution can turn an acid solution basic, because water's own H₃O⁺ and OH⁻ take over at very low concentrations.
Strong is not the same as concentrated
Strong and weak describe how completely an acid ionizes. Concentrated and dilute describe how much acid is dissolved per liter. A 0.0010 M solution of HCl is dilute but still strong: every HCl molecule ionizes. A 6 M solution of acetic acid is concentrated but still weak.
Worked examples
Try each one yourself first, then open the solution.
- Example 1Calculator allowed
pH of a strong acid
What is the pH of 0.025 M HNO₃ at 25 °C?
Show the solutionHide the solution
- Step 1: HNO₃ is a strong acid that gives one proton, so [H₃O⁺] = 0.025 M.
- Step 2: pH = −log(0.025) = 1.60.
Answer: pH = 1.60
- Example 2Calculator allowed
Trap: a group 2 hydroxide
What is the pH of 0.0050 M Ba(OH)₂ at 25 °C?
Show the solutionHide the solution
- Step 1: Ba(OH)₂(s) → Ba²⁺(aq) + 2OH⁻(aq). Each formula unit gives two OH⁻.
- Step 2: [OH⁻] = 2 × 0.0050 M = 0.010 M. Using 0.0050 M here is the trap.
- Step 3: pOH = −log(0.010) = 2.00.
- Step 4: pH = 14.00 − 2.00 = 12.00. (The trap answer would be pH 11.70.)
Answer: pH = 12.00
- Example 3Calculator allowed
Strong acid made from a mass
3.2 g of HCl gas (molar mass 36.46 g/mol) is dissolved in water to make 500. mL of solution. What is the pH?
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- Step 1: Moles of HCl: 3.2 g ÷ 36.46 g/mol = 0.0878 mol.
- Step 2: Concentration: 0.0878 mol ÷ 0.500 L = 0.176 M. HCl is strong, so [H₃O⁺] = 0.176 M.
- Step 3: pH = −log(0.176) = 0.76. The mass has two significant figures, so the pH gets two decimal places.
Answer: pH ≈ 0.76
Common mistakes
- Forgetting that group 2 hydroxides give two OH⁻ ions.
- Calculating pOH for a base and reporting it as the pH.
- Treating HF as a strong acid. Even though it's a hydrogen halide, HF is weak.
- Confusing strong with concentrated.
On the exam
- Know the six strong acids and the group 1 and 2 hydroxides cold; many questions hinge on recognizing whether an acid is strong or weak.
- Expect strong acid or base pH calculations as a warm-up step inside titration or mixing problems.
Connected topics
Videos
Check yourself
4 questions on 8.2 pH and pOH of Strong Acids and Bases. Pick an answer to see if you got it, and why.
What is the pH of a 0.0050 M solution of Ba(OH)₂ at 25 °C?
10.0 mL of 0.10 M HNO₃ is diluted with water to a total volume of 1.00 L. How does the pH change?
A solution at 25 °C contains 0.020 M HCl and 0.030 M HBr. What is its pH?
0.56 g of KOH (molar mass 56.11 g/mol) is dissolved in water to make 500. mL of solution at 25 °C. What is the pH?
0 of 4 answered