IMAT Chemistry · Acids, Bases and pH

Strong Acids and Bases: pH and Dilution

A strong acid or base splits completely into ions, so its H⁺ or OH⁻ concentration comes straight from its concentration, and every tenfold dilution moves the pH one unit towards 7.

All Acids, Bases and pH notes

Why this matters

This is where most of the chapter's arithmetic sits. The ministry papers asked for five solutions in order of pH (2023) and how much water dilutes an acid by two pH units (2024); the older papers asked for a pH from a mass of acid, from a hydroxide concentration and after a dilution, and whether a diprotic acid gives more hydrogen ions.

Concept 1 of 3: The strong acids and strong bases to know

Strong means the acid gives up its proton completely in water: no molecules of the acid are left, only ions. There are only a handful of strong acids and strong bases, so it is quicker to learn this short list and treat everything else as weak.

Definition

A strong acid is fully dissociated in water: $\mathrm{HCl \rightarrow H^+ + Cl^-}$ , a one-way arrow.
A strong base is fully dissociated into the metal ion and $\mathrm{OH^-}$ . The Group 1 hydroxides and the heavier Group 2 hydroxides are strong bases.
Strong is about how completely it ionises; concentrated is about how much is dissolved. A dilute strong acid and a concentrated weak acid are both possible.
Diprotic strong acid: $\mathrm{H_2SO_4}$ loses its first proton completely and most of its second in dilute solution. IMAT calculations count 2 $\mathrm{H^+}$ per molecule unless told otherwise.

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.

Practice this conceptself-check · 3 quick reps

Strong is not the same as concentrated

A strong acid is one that is fully ionised, whatever its concentration. A 0.001 mol/L solution of HCl is a dilute strong acid; a 10 mol/L solution of ethanoic acid is a concentrated weak acid. Options that swap these words are wrong.

Concept 2 of 3: pH of a strong acid or a strong base

Because a strong acid ionises fully, the hydrogen ion concentration is just the acid concentration, times two for a diprotic acid. A strong base gives the hydroxide concentration the same way, but that leads to pOH, so one more step (14 minus) gives the pH.

Definition

Strong acid: $[\mathrm{H^+}] = n \times c$ , where $n$ is the number of $\mathrm{H^+}$ per formula unit. Then $\text{pH} = -\log[\mathrm{H^+}]$ .
Strong base: $[\mathrm{OH^-}] = n \times c$ , then $\text{pOH} = -\log[\mathrm{OH^-}]$ and $\text{pH} = 14 - \text{pOH}$ .
Given a mass: moles = mass / molar mass, then concentration = moles / volume in litres.
To rank solutions of equal concentration by pH: strong diprotic acid < strong monoprotic acid < weak acid < neutral salt < weak base < strong base < strong base with 2 $\mathrm{OH^-}$ .

Strong acid and strong base

\text{pH} = -\log(n\,c_{\text{acid}}) \qquad \text{pH} = 14 + \log(n\,c_{\text{base}})

$c$ concentration of the acid or base, in mol/L
$n$ number of $\mathrm{H^+}$ or $\mathrm{OH^-}$ per formula unit

Worked example

Find the pH at 25 °C of (a) 0.020 mol/L sulfuric acid and (b) 0.0050 mol/L barium hydroxide.

Practice this conceptself-check · 4 quick reps

For a base, minus log of the concentration is the pOH

For 0.01 mol/L NaOH,

-\log 0.01 = 2

is the pOH, not the pH. The pH is

14 - 2 = 12

. The pOH value is almost always one of the options.

Count the ions per formula unit

Sulfuric acid gives two

\mathrm{H^+}

and barium or calcium hydroxide two

\mathrm{OH^-}

per formula unit. Their

[\mathrm{H^+}]

[\mathrm{OH^-}]

is double the concentration of the compound, so the pH moves by

\log 2 \approx 0.30

Concept 3 of 3: Diluting a strong acid or base

Adding water does not change the number of moles of

\mathrm{H^+}

; it only spreads them through a bigger volume. Make the volume ten times larger and the concentration is ten times smaller, which is exactly one pH unit. Dilution moves the pH towards 7, but it can never carry an acid past 7, because the water itself is neutral.

Definition

Moles are conserved on dilution: $c_1 V_1 = c_2 V_2$ .
Diluting by a factor of $10^n$ raises the pH of a strong acid by $n$ and lowers the pH of a strong base by $n$ .
The total final volume sets the factor. The water added is the final volume minus the starting volume.
Very dilute acid: below about $10^{-6}$ mol/L the water's own $\mathrm{H^+}$ matters, and the pH approaches 7 from below. $10^{-8}$ mol/L HCl has a pH of about 6.98, not 8.

Dilution

c_1 V_1 = c_2 V_2

$c_1, V_1$ concentration and volume before dilution
$c_2, V_2$ concentration and TOTAL volume after dilution

Worked example

25 mL of 0.10 mol/L HCl is diluted with water to a total volume of 250 mL. Find the pH before and after.

Practice this conceptself-check · 3 quick reps

Diluting an acid never makes it basic

Each tenfold dilution adds about one to the pH of a strong acid, but only until the acid's

\mathrm{H^+}

becomes comparable with water's own. A very dilute acid has a pH just under 7. An answer of pH 8 or more for a diluted acid is always wrong.

Summary — formulas & gotchas at a glance

A revision cheat-sheet for the formulas and gotchas above. Click any concept name to jump back to its full explanation.

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

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