Introduction to Acids and Bases
Use pH, pOH and the temperature-dependent water equilibrium without treating either ion as absent.
AP Chemistry Topic 8.1 · CED printed p. 146 / PDF p. 153. This teaching, practice and feedback were added for the AP edition; original author material remains separately traceable.
Before you start
- Concentration
- Logarithms
- Dynamic equilibrium
An aqueous acid transfers protons to water, producing hydronium, H3O+. H+(aq) is accepted shorthand for the hydrated aqueous proton, not a free bare proton drifting through water. Report hydronium with and hydroxide with pOH = −log[OH−] in the dilute-solution AP model. Lower pH means greater hydronium concentration. A one-unit drop means a factor of ten increase, not a difference of one mole per liter. To undo the logarithm, [H3O+] = 10−pH M. Rigorous pH uses ion activity; molarity is the working approximation here.
Water itself transfers protons: 2H2O(l) ⇌ H3O+(aq) + OH−(aq). Its equilibrium constant is Kw = [H3O+][OH−], equal to 1.0 × 10−14 at 25 °C. Both ions exist in acidic and basic water. When one concentration rises, the other falls enough to maintain the temperature’s Kw; neither becomes literally zero.
Neutral means [H3O+] = [OH−]. In pure water both equal √Kw. At 25 °C they are 1.0 × 10−7 M, giving pH = pOH = 7.00 and pH + pOH = pKw = 14.00. At another temperature Kw changes, so the neutral pH can differ from 7. Decide acidic versus basic by comparing ion concentrations or comparing pH with that temperature’s neutral value. The familiar 0–14 range is common for introductory dilute solutions, not a universal physical boundary on pH.
Let's work through it
- At 25 °C, a solution has [OH−] = 2.50 × 10−5 M.
- [H3O+] = Kw/[OH−] = 1.00 × 10−14/(2.50 × 10−5) = 4.00 × 10−10 M.
- pOH = 4.602 and pH = 9.398. Their sum is 14.000 at this temperature.
- The solution is basic because [OH−] exceeds [H3O+]. Both are still present.
Try it from memory
Pause & retrieve
Try it before you peek.
Write your answer and the reason from memory. Then compare with the worked answer. Your self-assessment is a study decision, not an automatically graded score.
Question 1
Does H+(aq) mean an unhydrated proton?
See every recall question with its answer
These references preserve each prompt and its answer for direct evidence links. Try the interactive questions above before opening the worked reasoning.
Retrieval 1
Does H+(aq) mean an unhydrated proton?
Worked answer and reason
No. It is shorthand for the aqueous hydrated proton; H3O+ is the preferred AP notation.
Solvent molecules surround and interact with the proton.
Retrieval 2
What is neutral at any temperature?
Worked answer and reason
Equal hydronium and hydroxide concentrations.
Neutrality is an ion balance; its pH depends on Kw.
Catch the tempting mistake
- A basic solution has no hydronium.
- Kw is nonzero, so an aqueous equilibrium has both ions.
Put it to work
Give the chemical reason as well as the calculation. Worked solutions are on a separate page.
- Unit 8 problem 1 · ap application · symbolic
Scientific calculator workspace
Use this workspace for arithmetic, logarithms and elementary functions. Keep intermediate precision and report final values with appropriate units and significant figures. Graphing and general equation solving need a suitable approved tool.
Scientific calculator
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For the teacher
- Check the tenfold logarithmic interpretation before allowing calculator work. Require the temperature whenever using the number 14.
Source objectives and scope
Source edition: ap-chemistry-ced-fall2024-local-b5dfe867. See this topic in the course outline →
- 8.1.A
- Calculate the values of pH and pOH, based on K_w and the concentration of all species present in a neutral solution of water.
- 8.1.A.1
- The concentrations of hydronium ion and hydroxide ion are often reported as pH and pOH, respectively. EQN: pH = −log[H_3O^+] EQN: pOH = −log[OH^−] The terms “hydrogen ion” and “hydronium ion” and the symbols H^+(aq) and H_3O^+(aq) are often used interchangeably for the aqueous ion of hydrogen. Hydronium ion and H_3O^+(aq) are preferred, but H^+(aq) is also accepted on the AP Exam.
- 8.1.A.2
- Water autoionizes with an equilibrium constant K_w. EQN: K_w = [H3O+][OH−] = 1.0 × 10−14 at 25°C
- 8.1.A.3
- In pure water, pH = pOH is called a neutral solution. At 25°C, pK_w = 14.0 and thus pH = pOH = 7.0. EQN: pK_w = 14 = pH + pOH at 25°C
- 8.1.A.4
- The value of K_w is temperature dependent, so the pH of pure, neutral water will deviate from 7.0 at temperatures other than 25°C.
Science references for this teaching
- AP Chemistry Course and Exam Description, effective Fall 2024 — Required topic-numbered learning objectives and essential knowledge, all continuations and AP exclusions; supplied PDF SHA256 b5dfe8677ef3d88c613865d2e2a3e8d6125d652e2b24c71ef1e8ce4e011094f0.
- OpenStax Chemistry 2e §14.3, Relative Strengths of Acids and Bases — Conjugate equilibria, percent ionization, structure trends, and the incomplete second ionization of sulfuric acid.
Glossary and deeper reading · 6 refreshers
These editorial refreshers supplement the reading. Definitions and examples are added guidance; original source wording and recorded answers remain in their original context.
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Aqueous solution
An aqueous solution is a solution in which water is the solvent. The dissolved substance may originate as a solid, liquid, or gas, so aqueous does not mean that a solid has melted. For example, sodium chloride dissolved in water is aqueous even though the pure salt is solid.
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Hydronium
Hydronium is the H₃O⁺ ion used in the introductory model of proton behavior in water. Aqueous H⁺ notation is shorthand for a solvated proton rather than a bare proton moving independently in the liquid. For example, a Brønsted acid can transfer a proton to water and form hydronium.
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Equilibrium constant
An equilibrium constant is the value of the reaction quotient at equilibrium for a specified reaction and temperature. Its magnitude indicates equilibrium composition preference rather than reaction speed. For example, a large constant often indicates a product-favored equilibrium, but the starting composition still determines the immediate net direction.
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Ion
An ion is an atom or group of atoms with a net electric charge. Ordinary ion formation changes electron count without changing the element's proton count. For example, a sodium atom losing one electron becomes a sodium ion with charge +1.
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pH
pH is the negative base-ten logarithm of hydronium activity. In suitable dilute models, activity is approximated by molar concentration relative to the standard concentration. For example, lowering hydronium concentration by a factor of ten raises pH by one unit.
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pOH
pOH is the negative base-ten logarithm of hydroxide activity. At a specified temperature, pH plus pOH equals the corresponding pKw, which is approximately 14 at 25 °C. For example, increasing hydroxide activity tenfold lowers pOH by one unit.