Acids, Bases and pH — IMAT Chemistry Formulas and Traps

What Makes an Acid or a Base: Three Definitions

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}}

$\mathrm{HA / A^-}$ the first pair: the acid and what is left when it loses $\mathrm{H^+}$
$\mathrm{B / HB^+}$ the second pair: the base and what it becomes after gaining $\mathrm{H^+}$

Arrhenius, Brønsted-Lowry and Lewis definitions of acids and bases

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 substances

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)	$\mathrm{-COOH \rightarrow -COO^-}$	$\mathrm{-NH_2 \rightarrow -NH_3^+}$

Common traps

A Lewis acid does not have to contain hydrogen

Students often assume every acid has an H to give. In the Lewis sense,

\mathrm{BF_3}

,

\mathrm{AlCl_3}

and metal ions are acids because they accept an electron pair. The base is the species with the lone pair, such as

\mathrm{NH_3}

,

\mathrm{H_2O}

or a halide ion.

A conjugate pair differs by H⁺, not by OH⁻

The conjugate base is what remains after an acid loses a proton. It is never formed by adding

\mathrm{OH^-}

, and a conjugate acid is never formed by removing

\mathrm{OH^-}

. Options that describe conjugates in terms of hydroxide ions mix up Brønsted-Lowry with Arrhenius.

An acid can act as a base

A substance's role depends on its partner. Nitric or ethanoic acid accepts a proton from a much stronger acid, such as sulfuric or perchloric acid, and in that reaction it is the base.

Amphoteric does not mean neutral

An amphoteric substance reacts with acids AND with bases. That says nothing about the pH of its own solution:

\mathrm{NaHCO_3}

solution is slightly basic,

\mathrm{NaH_2PO_4}

solution slightly acidic. Do not pick pH 7 just because a species is amphoteric.

The Water Equilibrium and the pH Scale

Learn this subtopic in the notes

The ionic product of water, Kw

Ionic product of water at 25 °C

K_w = [\mathrm{H^+}][\mathrm{OH^-}] = 1.0 \times 10^{-14}

$[\mathrm{H^+}]$ hydrogen ion concentration, in mol/L
$[\mathrm{OH^-}]$ hydroxide ion concentration, in mol/L

pH as a logarithmic scale of hydrogen ion concentration

pH

\text{pH} = -\log_{10}[\mathrm{H^+}] \qquad [\mathrm{H^+}] = 10^{-\text{pH}}

$[\mathrm{H^+}]$ hydrogen ion concentration, in mol/L

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

$[\mathrm{OH^-}]$ hydroxide ion concentration, in mol/L

Common traps

pH below 7 does not always mean acidic

The neutral point is pH 7 only at 25 °C. Kw increases with temperature, so hot pure water has a pH below 7 but is still neutral, because

[\mathrm{H^+}] = [\mathrm{OH^-}]

. Neutral is defined by equal concentrations, not by the number 7.

pH is a scale of tens, and lower means more acid

pH 2 is not twice as acidic as pH 4: it has 100 times the hydrogen ion concentration. And because of the minus sign, the solution with the smaller pH number has the larger

[\mathrm{H^+}]

. IMAT options often offer the ratio of the pH values or the reversed direction.

Strong Acids and Bases: pH and Dilution

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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}})

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

Diluting a strong acid or base

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

The strong acids and strong bases to know

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.

Common traps

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.

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^+}]

or

[\mathrm{OH^-}]

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

\log 2 \approx 0.30

.

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.

Weak Acids and Bases: Ka, pKa and Kb

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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

$[\mathrm{HA}]$ concentration of the un-ionised acid at equilibrium
$[\mathrm{A^-}]$ concentration of the conjugate base at equilibrium

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)

$K_a$ acid dissociation constant
$c$ concentration of acid dissolved, in mol/L

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

$K_a$ constant for the acid of the pair
$K_b$ constant for its conjugate base

Common weak acids and bases, and how many protons they give

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.

Common traps

Counting every H atom gives the wrong number of protons

Ethanoic acid,

\mathrm{CH_3COOH}

, has four hydrogen atoms but only one is acidic: the one on the oxygen of the COOH group. A molecule with two COOH groups is diprotic. A compound with OH groups only on carbon chains (an alcohol or a diol) is not an acid in water at all.

A larger pKa is a weaker acid

pKa runs the opposite way to Ka, just as pH runs the opposite way to

[\mathrm{H^+}]

. The acid with the biggest Ka, or the smallest pKa, is the strongest. When options mix Ka and pKa values, convert them all to one form before comparing.

A weak acid's pH is not minus log of its concentration

-\log c

gives the pH only for a strong acid. For a weak acid of the same concentration the pH is higher, because only a small fraction ionises. Treating a weak acid as strong is the most common wrong option in these questions.

A strong acid has a weak conjugate base

Strength runs in opposite directions within a pair. A strong acid such as HCl has a conjugate base (

\mathrm{Cl^-}

) too weak to take protons from water. A very weak acid such as HCN has a fairly strong conjugate base. An option saying a strong acid has a strong conjugate base is wrong.

Salt Solutions: Neutral, Acidic or Basic

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

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 ions

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 $\mathrm{H^+}$

Common traps

Neutralisation does not always give a neutral solution

A salt is neutral only when both its acid and its base were strong. Sodium ethanoate, made from a weak acid and a strong base, gives a basic solution; ammonium chloride gives an acidic one. Do not choose pH 7 just because the substance is called a salt.

A hydrogen salt is not automatically acidic

Having an H in the anion does not decide the pH.

\mathrm{NaHSO_4}

is acidic, but

\mathrm{NaHCO_3}

is slightly basic. Ask whether the anion gives up its proton more easily than it takes another one.

Some chlorides are acidic

A chloride ion is a spectator, but the metal ion may not be. Aluminium and iron(III) salts give acidic solutions, while sodium and potassium chlorides are neutral.

Neutralisation, Titration, Indicators and Buffers

Learn this subtopic in the notes

Neutralisation and titration calculations

At the equivalence point

n_a\, c_a V_a = n_b\, c_b V_b

$c_a, V_a$ concentration and volume of the acid
$c_b, V_b$ concentration and volume of the base
$n_a, n_b$ $\mathrm{H^+}$ per acid formula, $\mathrm{OH^-}$ per base formula

Buffer solutions and the Henderson-Hasselbalch equation

Henderson-Hasselbalch equation

\text{pH} = \text{p}K_a + \log_{10}\frac{[\mathrm{A^-}]}{[\mathrm{HA}]}

$[\mathrm{A^-}]$ concentration (or moles) of the conjugate base
$[\mathrm{HA}]$ concentration (or moles) of the weak acid

Titration curves, equivalence point pH and indicators

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

Common traps

Use the total volume after mixing

When an acid and a base are mixed and one is in excess, the leftover

\mathrm{H^+}

or

\mathrm{OH^-}

is spread through BOTH volumes added together. Dividing by only the acid's volume gives a concentration that is too high and a pH that is off.

The end point is not always at pH 7

The equivalence point sits at pH 7 only for a strong acid with a strong base. With a weak acid it is basic, with a weak base it is acidic, because the salt formed hydrolyses. Pick the indicator by where the jump is, not by where 7 is.

A strong acid with its own salt is not a buffer

HCl with NaCl cannot resist added acid, because

\mathrm{Cl^-}

does not take up protons. A buffer needs a WEAK acid with its conjugate base, or a weak base with its conjugate acid.

A buffer slows pH change; it does not stop it

A buffer absorbs small additions. Add more acid than it has base to react with and its capacity is used up, after which the pH falls sharply. Options claiming the pH can never change are wrong.

Acids, Bases and pH formulas

What Makes an Acid or a Base: Three Definitions

Conjugate acid-base pairs in a proton transfer

Arrhenius, Brønsted-Lowry and Lewis definitions of acids and bases

Amphoteric and amphiprotic substances

Common traps

The Water Equilibrium and the pH Scale

The ionic product of water, Kw

pH as a logarithmic scale of hydrogen ion concentration

pOH and the rule pH + pOH = 14

Common traps

Strong Acids and Bases: pH and Dilution

pH of a strong acid or a strong base

Diluting a strong acid or base

The strong acids and strong bases to know

Common traps

Weak Acids and Bases: Ka, pKa and Kb

Ka and pKa: measuring the strength of a weak acid

pH of a weak acid solution

Weak bases, Kb, and Ka × Kb = Kw for a conjugate pair

Common weak acids and bases, and how many protons they give

Common traps

Salt Solutions: Neutral, Acidic or Basic

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

Acid salts and salts of small, highly charged metal ions

Common traps

Neutralisation, Titration, Indicators and Buffers

Neutralisation and titration calculations

Buffer solutions and the Henderson-Hasselbalch equation

Titration curves, equivalence point pH and indicators

Common traps

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