Jupiter2U School
Chapter 13

Acids, Bases & pH

High School
At a glance
Core ideaAcids donate protons (H⁺); bases accept them.
Key termpH — −log₁₀[H⁺]; each unit is a tenfold change in acidity.
You can…Calculate pH and find an unknown concentration by titration.
Watch outStrength (Kₐ) is not the same thing as concentration.
Theory

Proton donors and acceptors

The Brønsted–Lowry definition is the workhorse: an acid donates a proton (H⁺); a base accepts one. When an acid donates a proton it becomes its conjugate base; a base that accepts one becomes its conjugate acid. Acids and bases therefore always act in conjugate pairs.

HA + H₂O ⇌ H₃O⁺ + A⁻   acid / conjugate base pair

Water self-ionises: 2H₂O ⇌ H₃O⁺ + OH⁻, with Kw = [H⁺][OH⁻] = 1.0 × 10⁻¹⁴ at 25 °C. The pH scale compresses the huge range of [H⁺] logarithmically:

pH = −log₁₀[H⁺]   •   pH + pOH = 14 (at 25 °C)

Strong acids/bases dissociate completely (HCl, NaOH); weak ones only partially, described by the acid dissociation constant Ka (larger Ka = stronger acid). Neutral is pH 7; acidic < 7; basic > 7.

0481214 7 = neutral ACIDIC BASIC
Each whole step on the pH scale is a tenfold change in hydrogen-ion concentration — pH 3 is ten times more acidic than pH 4.
7
Neutral pH at 25 °C
×10
Acidity change per pH unit
10⁻¹⁴
Kw = [H⁺][OH⁻] at 25 °C
14
pH + pOH at 25 °C
Explanation

The logarithm behind the scale

The pH scale is logarithmic because hydrogen-ion concentrations span an enormous range — from about 1 M in strong acid to 10⁻¹⁴ M in strong base. Each whole pH unit is a tenfold change in [H⁺]: a solution of pH 3 is ten times more acidic than pH 4 and one hundred times more acidic than pH 5. This is why small pH shifts matter so much — blood held near pH 7.4 would be lethal if it drifted even a few tenths.

Strong versus weak is about the degree of dissociation, not concentration. Concentrated ethanoic acid is still a weak acid because most of its molecules stay intact; dilute hydrochloric acid is strong because essentially every molecule releases its proton. Strength (an intrinsic property, Ka) and concentration (how much you dissolved) are independent ideas that beginners often conflate.

Acids

  • Donate a proton, H⁺ (Brønsted–Lowry)
  • pH < 7; raise [H⁺], lower [OH⁻]
  • Turn blue litmus red
  • Become a conjugate base after donating
  • e.g. HCl (strong), ethanoic acid (weak)

Bases

  • Accept a proton, H⁺
  • pH > 7; raise [OH⁻], lower [H⁺]
  • Turn red litmus blue
  • Become a conjugate acid after accepting
  • e.g. NaOH (strong), ammonia (weak)
Practical

Worked example — acid–base titration

25.0 mL of NaOH of unknown concentration is neutralised by 20.0 mL of 0.100 M HCl. Find the NaOH concentration. Reaction: HCl + NaOH → NaCl + H₂O.

  1. Find moles of the known: n(HCl) = c × V = 0.100 × 0.0200 = 2.00 × 10⁻³ mol.
  2. Use the mole ratio from the equation: HCl : NaOH = 1 : 1, so n(NaOH) = 2.00 × 10⁻³ mol.
  3. Divide by the NaOH volume: c(NaOH) = n / V = (2.00 × 10⁻³) / 0.0250.
  4. Compute: c(NaOH) = 0.0800 M.
  5. Answer: the sodium hydroxide is 0.0800 M. An indicator (e.g. phenolphthalein) marks the endpoint where moles of acid equal moles of base.

pH check: for the 0.100 M HCl, since HCl is strong, [H⁺] = 0.100 M, so pH = −log(0.100) = 1.00.

Q&A
What is the pH of a 0.0010 M solution of a strong acid?

Strong acid dissociates fully, so [H⁺] = 1.0 × 10⁻³ M. pH = −log(1.0 × 10⁻³) = 3.0.

Identify the conjugate base of H₂SO₄ and the conjugate acid of NH₃.

Removing a proton from H₂SO₄ gives its conjugate base HSO₄⁻. Adding a proton to NH₃ gives its conjugate acid NH₄⁺.

A solution has [OH⁻] = 1.0 × 10⁻⁵ M. Find its pH.

pOH = −log(1.0 × 10⁻⁵) = 5.0. Then pH = 14 − pOH = 14 − 5.0 = 9.0 — a weakly basic solution, as expected for excess OH⁻.

Why is a 1 M solution of ethanoic acid less acidic than 1 M HCl?

HCl is a strong acid and dissociates completely, giving [H⁺] ≈ 1 M (pH ≈ 0). Ethanoic acid is weak: only a small fraction ionises (Ka ≈ 1.8 × 10⁻⁵), so [H⁺] is far lower and the pH is around 2.4. Same concentration, very different acidity — strength, not amount, is the difference.

Concept mind map

How the ideas connect

Every key idea in this chapter, branching from the core concept — use it to see the whole picture at a glance.

Protondonor/acceptorpH scale 0-14Strong vs weakNeutralisationIndicatorsTitrationAcids, Bases and pH
Infographic

The key facts, visualised

pH = 7
neutral; below is acidic, above is basic
pH
equals -log of the H+ concentration in mol/L
Acid
a proton (H+) donor (Bronsted-Lowry)
Neutralise
acid + base -> salt + water
Solved examples

Worked problems, step by step

Follow each solution line by line, then try to reproduce it on paper before moving on.

Example 1Find the pH of a solution with [H+] = 1e-3 mol/L.

  1. pH = -log[H+].
  2. pH = -log(1e-3).
  3. The log of 1e-3 is -3, so pH = 3.

Example 225.0 mL of NaOH is neutralised by 20.0 mL of 0.100 M HCl. Find the NaOH concentration.

  1. Moles HCl = 0.100 x 0.0200 = 2.00e-3 mol.
  2. HCl + NaOH react 1:1, so moles NaOH = 2.00e-3 mol.
  3. Concentration = 2.00e-3 / 0.0250 = 0.0800 mol/L.
Practice problem set

Now you try

Work each one out first, then tap to reveal the worked answer.

1What is the pH of a neutral solution?
7, where [H+] equals [OH-].
2Is a solution with pH 2 acidic or basic?
Acidic, because it is below 7 and has a high H+ concentration.
3What are the products of acid plus base?
A salt and water, in a neutralisation reaction.
4What is the difference between a strong and weak acid?
A strong acid fully ionises in water; a weak acid only partly ionises.
5How much does H+ concentration change per pH unit?
By a factor of ten, because the scale is logarithmic.
6What colour is litmus in an acid?
Red; litmus turns blue in a base.