IMAT Chemistry · Free notes

Acids, Bases and pH: Definitions, pH Calculations, Salts and Buffers

Acids, Bases and pH has 22 past questions since 2011, and the ministry papers from 2023 on have asked 10 of them. That is two or three in every recent paper, which makes it one of the most reliable sources of marks in the chemistry section. The questions mix recall (which theory a reaction fits, which salt gives a basic solution, which acid is weak) with short pH arithmetic done without a calculator. The difficulty sits in the logarithm: one pH unit is a factor of ten, and a base's concentration gives the pOH before it gives the pH.

The handout has every subtopic, worked example, formula and trap with answers shown. The formula sheet is the chapter’s formulas and traps alone, on one page.

IMAT home All formulas on one page

Subtopic notes

Formula & revision sheet

11 formulas · 7 reference tables · 21 gotchas across all subtopics — the exam-eve cheat-sheet

What Makes an Acid or a Base: Three Definitions

Formulas (1)

Conjugate acid-base pairs in a proton transfer · Two conjugate pairs in every proton transfer $\underbrace{\mathrm{HA}}_{\text{acid}} + \underbrace{\mathrm{B}}_{\text{base}} \rightleftharpoons \underbrace{\mathrm{A^-}}_{\text{conj. base}} + \underbrace{\mathrm{HB^+}}_{\text{conj. acid}}$

Reference tables (2)

Arrhenius, Brønsted-Lowry and Lewis definitions of acids and bases3 rows

Theory	Acid	Base	Example
Arrhenius	Gives $\mathrm{H^+}$ in water	Gives $\mathrm{OH^-}$ in water	$\mathrm{HCl}$ and $\mathrm{KOH}$ in water
Brønsted-Lowry	Proton donor	Proton acceptor	$\mathrm{NH_3 + H_2O \rightleftharpoons NH_4^+ + OH^-}$ : water donates, ammonia accepts
Lewis	Electron-pair acceptor	Electron-pair donor	$\mathrm{AlCl_3 + Cl^- \rightarrow AlCl_4^-}$ : $\mathrm{AlCl_3}$ accepts the pair A Lewis acid often has an incomplete octet (boron, aluminium) or is a positive metal ion.

Each definition includes the one above it, so a reaction can be acid-base in the Lewis sense even when no proton moves.

Amphoteric and amphiprotic substances4 rows

Substance	Acting as an acid	Acting as a base
Water	$\mathrm{H_2O \rightarrow OH^-}$ (gives $\mathrm{H^+}$ to $\mathrm{NH_3}$ )	$\mathrm{H_2O \rightarrow H_3O^+}$ (takes $\mathrm{H^+}$ from $\mathrm{HCl}$ )
Hydrogencarbonate ion	$\mathrm{HCO_3^- \rightarrow CO_3^{2-}}$	$\mathrm{HCO_3^- \rightarrow H_2CO_3}$
Aluminium hydroxide	$\mathrm{Al(OH)_3 + OH^- \rightarrow [Al(OH)_4]^-}$	$\mathrm{Al(OH)_3 + 3H^+ \rightarrow Al^{3+} + 3H_2O}$
Amino acid (glycine)	$\mathrm{-COOH \rightarrow -COO^-}$	$\mathrm{-NH_2 \rightarrow -NH_3^+}$

Watch out for (4)

A Lewis acid does not have to contain hydrogen
→ Arrhenius, Brønsted-Lowry and Lewis definitions of acids and bases
A conjugate pair differs by H⁺, not by OH⁻
→ Conjugate acid-base pairs in a proton transfer
An acid can act as a base
→ Conjugate acid-base pairs in a proton transfer
Amphoteric does not mean neutral
→ Amphoteric and amphiprotic substances

The Water Equilibrium and the pH Scale

Formulas (3)

The ionic product of water, Kw · Ionic product of water at 25 °C $K_w = [\mathrm{H^+}][\mathrm{OH^-}] = 1.0 \times 10^{-14}$
pH as a logarithmic scale of hydrogen ion concentration · pH $\text{pH} = -\log_{10}[\mathrm{H^+}] \qquad [\mathrm{H^+}] = 10^{-\text{pH}}$
pOH and the rule pH + pOH = 14 · pOH and pH at 25 °C $\text{pOH} = -\log_{10}[\mathrm{OH^-}] \qquad \text{pH} + \text{pOH} = 14$

Watch out for (2)

pH below 7 does not always mean acidic
→ The ionic product of water, Kw
pH is a scale of tens, and lower means more acid
→ pH as a logarithmic scale of hydrogen ion concentration

Strong Acids and Bases: pH and Dilution

Formulas (2)

pH of a strong acid or a strong base · Strong acid and strong base $\text{pH} = -\log(n\,c_{\text{acid}}) \qquad \text{pH} = 14 + \log(n\,c_{\text{base}})$
Diluting a strong acid or base · Dilution $c_1 V_1 = c_2 V_2$

Reference tables (1)

The strong acids and strong bases to know8 rows

Substance	Formula	Type	Ions per formula unit
Hydrochloric acid	$\mathrm{HCl}$	Strong acid	1 $\mathrm{H^+}$
Hydrobromic and hydroiodic acids	$\mathrm{HBr}$ , $\mathrm{HI}$	Strong acids	1 $\mathrm{H^+}$
Hydrofluoric acid	$\mathrm{HF}$	WEAK acid	Only a small fraction ionises The odd one out of the hydrogen halides: the strong H-F bond keeps it a weak acid.
Nitric acid	$\mathrm{HNO_3}$	Strong acid	1 $\mathrm{H^+}$
Perchloric acid	$\mathrm{HClO_4}$	Strong acid	1 $\mathrm{H^+}$
Sulfuric acid	$\mathrm{H_2SO_4}$	Strong acid, diprotic	2 $\mathrm{H^+}$ in IMAT calculations
Sodium and potassium hydroxide	$\mathrm{NaOH}$ , $\mathrm{KOH}$	Strong bases	1 $\mathrm{OH^-}$
Calcium and barium hydroxide	$\mathrm{Ca(OH)_2}$ , $\mathrm{Ba(OH)_2}$	Strong bases	2 $\mathrm{OH^-}$

Ammonia, ethanoic acid, methanoic acid, carbonic acid and phosphoric acid are all weak.

Watch out for (4)

Strong is not the same as concentrated
→ The strong acids and strong bases to know
For a base, minus log of the concentration is the pOH
→ pH of a strong acid or a strong base
Count the ions per formula unit
→ pH of a strong acid or a strong base
Diluting an acid never makes it basic
→ Diluting a strong acid or base

Weak Acids and Bases: Ka, pKa and Kb

Formulas (3)

Ka and pKa: measuring the strength of a weak acid · Acid dissociation constant $K_a = \frac{[\mathrm{H^+}][\mathrm{A^-}]}{[\mathrm{HA}]} \qquad \text{p}K_a = -\log_{10} K_a$
pH of a weak acid solution · Weak acid $[\mathrm{H^+}] \approx \sqrt{K_a\,c} \qquad \text{pH} \approx \tfrac{1}{2}\left(\text{p}K_a - \log_{10} c\right)$
Weak bases, Kb, and Ka × Kb = Kw for a conjugate pair · Conjugate pair at 25 °C $K_a \times K_b = K_w = 1.0 \times 10^{-14} \qquad \text{p}K_a + \text{p}K_b = 14$

Reference tables (1)

Common weak acids and bases, and how many protons they give7 rows

Name	Formula	Strength	Acidic protons
Ethanoic (acetic) acid	$\mathrm{CH_3COOH}$	Weak acid	1 (only the COOH hydrogen)
Methanoic (formic) acid	$\mathrm{HCOOH}$	Weak acid	1
Carbonic acid	$\mathrm{H_2CO_3}$	Weak acid	2
Ethanedioic (oxalic) acid	$\mathrm{HOOC{-}COOH}$	Weak acid	2 (one per COOH group)
Phosphoric acid	$\mathrm{H_3PO_4}$	Weak acid	3
Hydrofluoric acid	$\mathrm{HF}$	Weak acid	1
Ammonia	$\mathrm{NH_3}$	Weak base	Accepts 1 to form $\mathrm{NH_4^+}$

Compare: sulfuric acid is a STRONG diprotic acid. An alcohol OH (ethanol, ethane-1,2-diol) is far too weak to count as an acid in water.

Watch out for (4)

Counting every H atom gives the wrong number of protons
→ Common weak acids and bases, and how many protons they give
A larger pKa is a weaker acid
→ Ka and pKa: measuring the strength of a weak acid
A weak acid's pH is not minus log of its concentration
→ pH of a weak acid solution
A strong acid has a weak conjugate base
→ Weak bases, Kb, and Ka × Kb = Kw for a conjugate pair

Salt Solutions: Neutral, Acidic or Basic

Reference tables (2)

Predicting the pH of a salt solution from its parent acid and base4 rows

Parent acid and base	Ion that reacts with water	Solution	Examples
Strong acid + strong base	Neither ion	Neutral, pH 7	$\mathrm{NaCl}$ , $\mathrm{KNO_3}$ , $\mathrm{KI}$ , $\mathrm{LiBr}$
Strong acid + weak base	The cation gives $\mathrm{H^+}$	Acidic, pH below 7	$\mathrm{NH_4Cl}$ , $\mathrm{NH_4NO_3}$ , $\mathrm{(NH_4)_2SO_4}$
Weak acid + strong base	The anion takes $\mathrm{H^+}$ , leaving $\mathrm{OH^-}$	Basic, pH above 7	$\mathrm{CH_3COONa}$ , $\mathrm{Na_2CO_3}$ , $\mathrm{KF}$ , $\mathrm{Na_3PO_4}$
Weak acid + weak base	Both ions	Depends on Ka against Kb	$\mathrm{CH_3COONH_4}$ is close to pH 7 Ka of the ammonium ion and Kb of the ethanoate ion are almost equal, so their effects cancel.

Acid salts and salts of small, highly charged metal ions5 rows

Salt	Ion that reacts	Solution	Why
$\mathrm{NaHSO_4}$	$\mathrm{HSO_4^-}$	Acidic (about pH 1.5 at 0.1 mol/L)	Gives $\mathrm{H^+}$ easily; almost no pull on protons
$\mathrm{NaHCO_3}$	$\mathrm{HCO_3^-}$	Slightly basic	Takes $\mathrm{H^+}$ more readily than it gives one
$\mathrm{NaH_2PO_4}$	$\mathrm{H_2PO_4^-}$	Slightly acidic	Gives $\mathrm{H^+}$ more readily than it takes one
$\mathrm{Na_2CO_3}$	$\mathrm{CO_3^{2-}}$	Clearly basic (about pH 11 to 12)	Anion of a weak acid, no H to give
$\mathrm{AlCl_3}$ , $\mathrm{FeCl_3}$	The hydrated metal ion	Acidic	The small 3+ ion makes its water ligands release $\mathrm{H^+}$

Watch out for (3)

Neutralisation does not always give a neutral solution
→ Predicting the pH of a salt solution from its parent acid and base
A hydrogen salt is not automatically acidic
→ Acid salts and salts of small, highly charged metal ions
Some chlorides are acidic
→ Acid salts and salts of small, highly charged metal ions

Neutralisation, Titration, Indicators and Buffers

Formulas (2)

Neutralisation and titration calculations · At the equivalence point $n_a\, c_a V_a = n_b\, c_b V_b$
Buffer solutions and the Henderson-Hasselbalch equation · Henderson-Hasselbalch equation $\text{pH} = \text{p}K_a + \log_{10}\frac{[\mathrm{A^-}]}{[\mathrm{HA}]}$

Reference tables (1)

Titration curves, equivalence point pH and indicators4 rows

Titration	pH at equivalence	Salt formed	Suitable indicator
Strong acid + strong base	7	Neutral, e.g. $\mathrm{NaCl}$	Phenolphthalein or methyl orange (the jump is very large)
Weak acid + strong base	Above 7, about 8 to 9	Basic, e.g. $\mathrm{CH_3COONa}$	Phenolphthalein
Strong acid + weak base	Below 7, about 5	Acidic, e.g. $\mathrm{NH_4Cl}$	Methyl orange
Weak acid + weak base	Near 7	Depends on Ka and Kb	None works well: there is no sharp jump

Watch out for (4)

Use the total volume after mixing
→ Neutralisation and titration calculations
The end point is not always at pH 7
→ Titration curves, equivalence point pH and indicators
A strong acid with its own salt is not a buffer
→ Buffer solutions and the Henderson-Hasselbalch equation
A buffer slows pH change; it does not stop it
→ Buffer solutions and the Henderson-Hasselbalch equation

PYQ weightage by concept

18 concepts · 0 PYQs — where the marks actually sit, so you know what to drill first

What Makes an Acid or a Base: Three Definitions0 PYQs · 0%

Concept	PYQs	Share
Arrhenius, Brønsted-Lowry and Lewis definitions of acids and basesfoundation	—	—
Conjugate acid-base pairs in a proton transferfoundation	—	—
Amphoteric and amphiprotic substancesfoundation	—	—

The Water Equilibrium and the pH Scale0 PYQs · 0%

Concept	PYQs	Share
The ionic product of water, Kwfoundation	—	—
pH as a logarithmic scale of hydrogen ion concentrationfoundation	—	—
pOH and the rule pH + pOH = 14foundation	—	—

Strong Acids and Bases: pH and Dilution0 PYQs · 0%

Concept	PYQs	Share
The strong acids and strong bases to knowfoundation	—	—
pH of a strong acid or a strong basefoundation	—	—
Diluting a strong acid or basefoundation	—	—

Weak Acids and Bases: Ka, pKa and Kb0 PYQs · 0%

Concept	PYQs	Share
Common weak acids and bases, and how many protons they givefoundation	—	—
Ka and pKa: measuring the strength of a weak acidfoundation	—	—
pH of a weak acid solutionfoundation	—	—
Weak bases, Kb, and Ka × Kb = Kw for a conjugate pairfoundation	—	—

Salt Solutions: Neutral, Acidic or Basic0 PYQs · 0%

Concept	PYQs	Share
Predicting the pH of a salt solution from its parent acid and basefoundation	—	—
Acid salts and salts of small, highly charged metal ionsfoundation	—	—

Neutralisation, Titration, Indicators and Buffers0 PYQs · 0%

Concept	PYQs	Share
Neutralisation and titration calculationsfoundation	—	—
Titration curves, equivalence point pH and indicatorsfoundation	—	—
Buffer solutions and the Henderson-Hasselbalch equationfoundation	—	—