Acids and bases

The Bronsted-Lowry model defines acids and bases by proton (H+) transfer:

• an acid is a proton donor;
• a base is a proton acceptor.

Every acid-base reaction is a proton handed from the acid to the base. For example:

$$\text{HCl} + \text{H}_2\text{O} \rightarrow \text{H}_3\text{O}^+ + \text{Cl}^-$$

Here HCl donates a proton (acid) and water accepts it (base), forming the hydronium ion $\text{H}_3\text{O}^+$. We often write $\text{H}^+(aq)$ as shorthand for $\text{H}_3\text{O}^+$.

With ammonia, water instead donates a proton:

$$\text{NH}_3 + \text{H}_2\text{O} \rightleftharpoons \text{NH}_4^+ + \text{OH}^-$$

This definition is more general than the older idea that an acid simply releases H+ in water, because it focuses on the transfer and does not require water as the solvent. A useful skill is to look at any reaction and identify which species loses a proton (the acid) and which gains it (the base).

When an acid donates a proton it forms its conjugate base; when a base accepts a proton it forms its conjugate acid. The two members of a conjugate pair differ by exactly one H+.

In the reaction

$$\text{CH}_3\text{COOH} + \text{H}_2\text{O} \rightleftharpoons \text{CH}_3\text{COO}^- + \text{H}_3\text{O}^+$$

there are two conjugate pairs:

• $\text{CH}_3\text{COOH}$ (acid) / $\text{CH}_3\text{COO}^-$ (its conjugate base);
• $\text{H}_2\text{O}$ (base) / $\text{H}_3\text{O}^+$ (its conjugate acid).

To find a conjugate base, remove one H+, which lowers the charge by one (e.g. neutral $\text{HA} \rightarrow \text{A}^-$, or $\text{NH}_4^+ \rightarrow \text{NH}_3$); to find a conjugate acid, add one H+, which raises the charge by one. So the conjugate base of $\text{H}_2\text{SO}_4$ is $\text{HSO}_4^-$, and the conjugate acid of $\text{NH}_3$ is $\text{NH}_4^+$.

A helpful idea (HL): the stronger an acid, the weaker its conjugate base, and vice versa. A strong acid such as HCl has a very weak conjugate base ($\text{Cl}^-$) that has essentially no tendency to take the proton back.

An amphiprotic species can both donate and accept a proton, so it can act as a Bronsted-Lowry acid or base depending on what it reacts with.

Water is the classic example:

• with HCl it acts as a base (accepts H+): $\text{H}_2\text{O} + \text{HCl} \rightarrow \text{H}_3\text{O}^+ + \text{Cl}^-$;
• with ammonia it acts as an acid (donates H+): $\text{H}_2\text{O} + \text{NH}_3 \rightleftharpoons \text{OH}^- + \text{NH}_4^+$.

Other common amphiprotic species are the hydrogencarbonate ion $\text{HCO}_3^-$ and the hydrogensulfate ion $\text{HSO}_4^-$. Each still has a proton it can donate, yet also a lone pair / negative charge that can accept one.

• Note the related word amphoteric: it describes a substance that reacts with both acids and bases (e.g. $\text{Al}_2\text{O}_3$). Amphiprotic is the narrower term, specifically about donating *and* accepting protons. Every amphiprotic species is amphoteric, but not every amphoteric substance works by proton transfer.

The pH scale measures acidity through the hydrogen-ion concentration. The data booklet gives

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

and the reverse relationship is $[\text{H}^+] = 10^{-\text{pH}}$.

Key features:

• pH is a logarithmic scale, so a change of 1 pH unit means $[\text{H}^+]$ changes by a factor of 10. A change of 2 units is a factor of 100.
• Lower pH = more acidic (higher $[\text{H}^+]$); higher pH = more alkaline.
• At 298 K a neutral solution has pH 7; acids give pH < 7, alkalis give pH > 7.

For example, if $[\text{H}^+] = 1.0 \times 10^{-3}\ \text{mol dm}^{-3}$ then $\text{pH} = 3.00$. If a solution has pH 4.0 and another has pH 6.0, the first has $10^{2} = 100$ times the hydrogen-ion concentration of the second.

Give pH to two decimal places where data allow; the digits after the decimal point are the significant figures (they reflect the mantissa of the logarithm).

Water itself ionizes very slightly - this is autoionization:

$$\text{H}_2\text{O}(l) \rightleftharpoons \text{H}^+(aq) + \text{OH}^-(aq)$$

The equilibrium is described by the ionic product of water, given in the data booklet:

$$K_w = [\text{H}^+][\text{OH}^-]$$

At 298 K, $K_w = 1.00 \times 10^{-14}\ \text{mol}^2\,\text{dm}^{-6}$. In pure water $[\text{H}^+] = [\text{OH}^-] = 1.0 \times 10^{-7}\ \text{mol dm}^{-3}$, giving pH 7.

$K_w$ lets you convert between $[\text{H}^+]$ and $[\text{OH}^-]$ in any aqueous solution: if you know one, divide $K_w$ by it to get the other.

Because autoionization is endothermic, $K_w$ increases with temperature. So at temperatures above 25 degC, $K_w > 10^{-14}$ and the neutral pH falls below 7 - yet the water is still neutral because $[\text{H}^+]$ still equals $[\text{OH}^-]$. "Neutral" means equal H+ and OH-, not exactly pH 7.

Strength is about the degree of ionization in water, and is completely separate from concentration (how much is dissolved).

• A strong acid (e.g. HCl, HNO3, H2SO4) ionizes completely: $\text{HCl} \rightarrow \text{H}^+ + \text{Cl}^-$.
• A weak acid (e.g. ethanoic acid, carbonic acid) ionizes partially and reaches an equilibrium: $\text{CH}_3\text{COOH} \rightleftharpoons \text{CH}_3\text{COO}^- + \text{H}^+$.
• Strong bases (e.g. NaOH, KOH) dissociate fully; a weak base such as ammonia ionizes only partially: $\text{NH}_3 + \text{H}_2\text{O} \rightleftharpoons \text{NH}_4^+ + \text{OH}^-$.

For equal concentrations, a strong acid has a lower pH, higher electrical conductivity, and faster reaction (e.g. with a metal or carbonate) than a weak acid.

Distinguishing experiments (same concentration of two acids): compare pH (strong is lower), conductivity (strong is higher), or rate of reaction with Mg/carbonate (strong is faster). To compare concentration instead, do a titration / measure reacting volume, which depends on the amount of acid, not its strength.

Neutralization is the reaction of an acid with a base to form a salt and water. The species that actually reacts in solution is summarised by the net ionic equation:

$$\text{H}^+(aq) + \text{OH}^-(aq) \rightarrow \text{H}_2\text{O}(l)$$

Common types:

• acid + alkali (soluble base): $\text{HCl} + \text{NaOH} \rightarrow \text{NaCl} + \text{H}_2\text{O}$;
• acid + metal oxide/hydroxide: $\text{H}_2\text{SO}_4 + \text{CuO} \rightarrow \text{CuSO}_4 + \text{H}_2\text{O}$;
• acid + carbonate: also gives carbon dioxide, e.g. $2\text{HCl} + \text{CaCO}_3 \rightarrow \text{CaCl}_2 + \text{H}_2\text{O} + \text{CO}_2$;
• acid + ammonia: $\text{HCl} + \text{NH}_3 \rightarrow \text{NH}_4\text{Cl}$.

Neutralization is exothermic. The enthalpy of neutralization for a strong acid with a strong alkali is almost constant (about $-57\ \text{kJ mol}^{-1}$) because the same reaction $\text{H}^+ + \text{OH}^- \rightarrow \text{H}_2\text{O}$ happens in every case. The salt formed depends on the acid (its anion) and the base (its cation).

A pH (titration) curve plots the pH of the mixture against the volume of titrant added. Its shape reveals the equivalence point and the nature of the acid and base.

Key features of a strong acid + strong base curve:

• it starts at low pH (around 1) and stays fairly flat at first;
• it rises steeply through a near-vertical jump (roughly pH 3 to 11) around the equivalence point;
• the equivalence point sits at the middle of the vertical region, here pH 7.

The equivalence point is where acid and base have been mixed in the stoichiometric ratio. Its pH depends on the combination:

• strong acid + strong base: equivalence pH = 7;
• strong acid + weak base: equivalence pH < 7 (acidic salt formed);
• weak acid + strong base: equivalence pH > 7 (alkaline salt formed);
• weak acid + weak base: the jump is shallow and ill-defined.

When a weak species is involved, the curve also shows a flatter buffer region (HL) before the jump. The position of the steep section guides indicator choice (HL).

For a weak acid the ionization equilibrium $\text{HA} \rightleftharpoons \text{H}^+ + \text{A}^-$ has the acid dissociation constant

$$K_a = \frac{[\text{H}^+][\text{A}^-]}{[\text{HA}]}$$

and for a weak base $\text{B} + \text{H}_2\text{O} \rightleftharpoons \text{BH}^+ + \text{OH}^-$ the base ionization constant is $K_b = \dfrac{[\text{BH}^+][\text{OH}^-]}{[\text{B}]}$. Neither expression is in the data booklet - you build them from the equilibrium.

Because the values span many orders of magnitude, we use logarithms:

$$\text{p}K_a = -\log_{10}K_a \qquad \text{p}K_b = -\log_{10}K_b$$

• Larger $K_a$ / smaller $\text{p}K_a$ = stronger acid.
• For a conjugate pair, $K_a \times K_b = K_w$, so $\text{p}K_a + \text{p}K_b = 14$ at 298 K.

A common approximation for a weak acid of concentration $c$: since $[\text{H}^+] \approx [\text{A}^-]$ and $[\text{HA}] \approx c$, we get $[\text{H}^+] \approx \sqrt{K_a \, c}$. This lets you find the pH of a weak acid from $K_a$ and the concentration.

When a salt dissolves, its ions can react with water (hydrolyse) to make the solution acidic or alkaline. The rule depends on which parent acid and base formed the salt.

• Strong acid + strong base (e.g. NaCl): neutral. Neither ion hydrolyses appreciably.
• Strong acid + weak base (e.g. NH4Cl): acidic. The cation is the conjugate acid of a weak base: $\text{NH}_4^+ \rightleftharpoons \text{NH}_3 + \text{H}^+$.
• Weak acid + strong base (e.g. CH3COONa): alkaline. The anion is the conjugate base of a weak acid: $\text{CH}_3\text{COO}^- + \text{H}_2\text{O} \rightleftharpoons \text{CH}_3\text{COOH} + \text{OH}^-$.
• Weak acid + weak base: depends on the relative $K_a$ and $K_b$.

A quick way to decide: identify the conjugate origin of each ion. The ion that comes from a weak parent is the one that reacts with water and controls the pH. Small, highly charged metal cations (e.g. $\text{Al}^{3+}$, $\text{Fe}^{3+}$) also give acidic solutions because they polarise coordinated water molecules and release H+.

An acid-base indicator is a weak acid (call it HIn) whose acid form and conjugate base form have different colours:

$$\text{HIn} \rightleftharpoons \text{H}^+ + \text{In}^-$$

• In acidic solution (high $[\text{H}^+]$) the equilibrium lies left, so the HIn colour dominates.
• In alkaline solution the equilibrium shifts right, so the In- colour dominates.

The indicator changes colour over a range of roughly $\text{p}K_{\text{In}} \pm 1$, i.e. about two pH units. The end point is where $[\text{HIn}] = [\text{In}^-]$, near $\text{pH} = \text{p}K_{\text{In}}$.

Choosing an indicator for a titration: the indicator's colour-change range must lie within the steep, vertical part of the pH curve.

• strong acid + strong base: most indicators work (wide jump) - e.g. phenolphthalein or methyl orange.
• weak acid + strong base (equivalence pH > 7): use phenolphthalein (range ~8-10).
• strong acid + weak base (equivalence pH < 7): use methyl orange (range ~3-4.5).
• weak acid + weak base: no sharp jump, so no indicator is suitable.

A buffer solution resists changes in pH when small amounts of acid or alkali are added. There are two kinds:

• Acidic buffer: a weak acid + its salt (its conjugate base), e.g. $\text{CH}_3\text{COOH}$ + $\text{CH}_3\text{COONa}$.
• Basic buffer: a weak base + its salt (its conjugate acid), e.g. $\text{NH}_3$ + $\text{NH}_4\text{Cl}$.

How it works (acidic buffer): both the weak acid HA and its conjugate base A- are present in reservoir amounts.

• Add acid (H+): it is mopped up by A-: $\text{A}^- + \text{H}^+ \rightarrow \text{HA}$.
• Add alkali (OH-): it is neutralised by HA: $\text{HA} + \text{OH}^- \rightarrow \text{A}^- + \text{H}_2\text{O}$.

So the added ions are removed and the pH barely changes.

The pH is set by the $K_a$ and the ratio of acid to base: from $K_a = \dfrac{[\text{H}^+][\text{A}^-]}{[\text{HA}]}$, $[\text{H}^+] = K_a \dfrac{[\text{HA}]}{[\text{A}^-]}$. A buffer is most effective when this ratio is near 1, i.e. when $\text{pH} \approx \text{p}K_a$. Buffers are vital in living systems (e.g. blood is buffered near pH 7.4 by the carbonic acid / hydrogencarbonate system).