Equilibrium: Fundamentals, Acids and Bases, and Solubility

This is Unit Ten of Chemistry, Part Two: acids, bases and titration. Part One built the machinery of equilibrium — K, Q, and the ICE table. This part applies all of it to one family of reactions, and everything here is an equilibrium calculation wearing different clothes. The through-line is that acid strength and acid concentration are unrelated quantities, and most of the errors this part names come from conflating them. It also opens by declining to give a single definition of what an acid is, because there are three, and the book is deliberate that none of them is the right one. By the end you will be able to say how those three definitions relate; say why pH 7 is not always neutral; say what "strong" describes about an acid; say what percent ionisation measures that Ka does not; and tell an equivalence point from an endpoint.

Seven entries. Three definitions of increasing reach, some vocabulary that goes with them, and then an entry whose whole job is to say how they fit together — which is not by one replacing another.

In water.

Chem 1799 The Arrhenius Acid-Base Definition

The Arrhenius definition names an acid as raising hydrogen ion concentration in water, a base as raising hydroxide concentration. It works only in water, leaving familiar bases like ammonia unclassified by its wording alone.

Protons, anywhere.

Chem 1802 The Brønsted-Lowry Acid-Base Definition

The Brønsted-Lowry definition names an acid as a proton donor and a base as a proton acceptor, applying to any reaction rather than only aqueous ones — the same proton transfer, classified in any solvent.

One proton apart.

Chem 1805 Conjugate Acid-Base Pairs

A conjugate acid-base pair differs by exactly one proton — the acid form having it, the base form lacking it. A conjugate base is not automatically weak; its strength is a separate question, taken up later in this part.

Acid meets base.

Chem 1807 Acid-Base Neutralization as a Reaction Type

A neutralisation reaction transfers protons from an acid to a base; between a strong acid and strong base it produces water and a salt. "Neutral" names the reaction type, not the resulting pH, which depends on which acid and base.

Either role.

Chem 1809 Amphiprotic Substances

An amphiprotic substance acts as either a Brønsted-Lowry acid or base depending on its partner; amphoteric is the broader term. Containing hydrogen is not enough — it must both donate and accept protons.

No proton at all.

Chem 1812 The Lewis Acid-Base Definition

The Lewis definition names an acid as an electron-pair acceptor and a base as an electron-pair donor, which covers reactions involving no proton transfer whatever. A reaction with no proton in sight can still be acid-base chemistry under this definition alone.

How they fit.

Chem 1815 Nested Domains of Generality Among the Three Theories

The three theories nest by generality: every Arrhenius pair is also Brønsted-Lowry, every Brønsted-Lowry pair also Lewis, while broader theories reach reactions narrower ones cannot. None is the correct one — each fits the scope it was built to describe.

Three entries. Water reacting with itself, the constant that describes it, and the reason the familiar figure of seven for neutral is less fixed than it looks.

Water on water.

Chem 1818 Autoionization of Water and Kw

Water reacts with itself, one molecule donating a proton to another, giving Kw as the product of hydronium and hydroxide concentrations — at twenty-five degrees, ten to the minus fourteen. Kw holds in any aqueous solution at that temperature, acidic or basic, not only pure water.

Neutral moves.

Chem 1821 Kw's Temperature Dependence

Kw is temperature-dependent, because water's autoionisation is endothermic — so Kw grows as temperature rises above twenty-five degrees, and the neutral pH drops below seven. A pH below seven signals acidic only relative to that temperature's own neutral point, not always relative to seven.

Two scales.

Chem 1824 pH and pOH Scales and Their Relationship

pH is the negative base-ten logarithm of hydrogen ion concentration, pOH the same for hydroxide, and at twenty-five degrees the two sum to fourteen. That shortcut holds only at twenty-five degrees, inherited directly from Kw's own temperature dependence.

Three entries. What the word "strong" actually describes — which is not concentration — the short list of substances it applies to, and a pH calculation that needs no equilibrium work at all.

Essentially complete.

Chem 1827 Strong Acids and Bases: Complete Dissociation

A strong acid or base reacts essentially completely with water, its equilibrium lying so far toward products that the reaction is treated as one-directional. "Strong" describes the extent of that reaction, not the solution's concentration — the twin the course registered back in Unit Three.

A short list.

Chem 1829 The Recognized Strong Acids and Bases, Identified Structurally

The list of strong acids and bases is short and fixed by structure rather than by memorised values. Every acid outside that list is weak by default — including hydrofluoric acid, which is familiar and dangerous but chemically weak, since strength here means extent of ionisation.

Straight to pH.

Chem 1832 Calculating pH of a Strong Acid or Base Solution

Calculating the pH of a strong acid or base solution means taking its molarity directly as the hydronium or hydroxide concentration, since dissociation is complete, then applying the pH or pOH definition and converting between scales if needed. Setting up an ICE table here treats an essentially complete reaction as an equilibrium worth solving — which is the one step this shortcut exists to skip.

Six entries, and this is where Part One's ICE table starts earning its keep. Partial ionisation, the constant measuring how partial, the relationship binding an acid to its conjugate base, and two quantities calculated from all of it.

Only partly.

Chem 1835 Weak Acid Equilibrium and Ka

A weak acid ionises only partially in water, and Ka — its acid ionisation constant — measures how far that equilibrium favours ions over intact acid. Water does not belong in the Ka expression's denominator, and because ionisation is incomplete, molarity cannot stand in for the hydronium concentration.

The base version.

Chem 1838 Weak Base Equilibrium and Kb

A weak base reacts only partially with water, and Kb measures how far that equilibrium favours the protonated base and hydroxide over the intact base. Kb describes a base reacting with water — a different equilibrium from the Ka of that base's own conjugate acid, related but not identical.

Their product.

Chem 1841 The Ka–Kb Relationship for a Conjugate Pair

For any conjugate pair, Ka multiplied by Kb equals Kw — so a stronger conjugate acid always pairs with a weaker conjugate base. A weak acid's conjugate base is not automatically strong; the relationship holds only for a true conjugate pair, and it is what lets one constant be derived from the other.

Build the table.

Chem 1844 Solving for pH of a Weak Acid Solution

Solving for a weak acid's pH means building an ICE table from its initial concentration, substituting the equilibrium row into the Ka expression, applying the small-x approximation where valid, solving for hydronium, and taking the negative logarithm. Accepting a small-x answer without running the percent check risks a pH built on a simplification that was never justified.

How much ionised.

Chem 1847 Percent Ionization Defined

Percent ionisation is the fraction of a weak acid's initial concentration that has ionised at equilibrium, and it rises as the acid is diluted even though Ka stays fixed. It is therefore not a strength ranking — Ka is the concentration-independent measure, and percent ionisation is not.

Over the initial.

Chem 1850 Calculating Percent Ionization

Calculating percent ionisation means finding the equilibrium hydronium concentration, from a measured pH or by solving the Ka expression, then dividing by the acid's original initial concentration and multiplying by a hundred. Dividing by the equilibrium acid concentration rather than the initial gives a number that is not percent ionisation at all.

Four entries. Acids carrying more than one proton, why only the first ionisation usually matters, and why dissolving a salt in water need not give a neutral solution.

One at a time.

Chem 1853 Polyprotic Acids: Stepwise Ionization

A polyprotic acid loses its protons through separate equilibria, each with its own Ka, and each successive Ka is dramatically smaller than the one before — because pulling a proton off an already negative ion is much harder. Treating the steps as equally significant ignores how far the earlier ones suppress the later.

The first step alone.

Chem 1856 Solving Polyprotic Acid pH via the Dominant First Ionization

Solving a polyprotic acid's pH means solving the first ionisation alone with an ICE table, since later steps contribute so little additional hydronium — given how much smaller each successive Ka is — that they can be checked and then safely neglected. Adding contributions from every step as if each were comparable overstates hydronium and so understates the pH.

Not always neutral.

Chem 1859 Salt Hydrolysis: Predicting Acidic, Basic, or Neutral Salts

A salt's pH is predicted by asking whether its ions are conjugates of a strong or a weak acid or base: a weak conjugate reacts with water, a strong one does not. A salt from a strong acid and a strong base, like sodium chloride, dissolves neutral, because neither of its ions hydrolyses.

Which ion reacts.

Chem 1862 Determining pH of a Salt Solution via Hydrolysis

Determining a salt solution's pH means identifying which ion actually hydrolyses, finding that ion's own Ka or Kb from its conjugate's known value through the Kw relationship, then solving that ionisation with an ICE table exactly as for any weak acid or base. Using a conjugate's own constant directly rather than deriving the partner's through Kw gives a badly wrong pH.

Eight entries closing the part. How an indicator produces a colour change, how one is chosen, the concentration a titration measures, the three curve shapes, and then what a finished curve can be read for — which is more than the equivalence point.

A coloured weak acid.

Chem 1865 Acid-Base Indicators: Mechanism

An acid-base indicator is itself a weak acid or base whose protonated and deprotonated forms differ visibly in colour, so the solution's pH determines which colour appears. An indicator changes colour at its own equilibrium, which is not necessarily at a titration's equivalence point.

Choosing one.

Chem 1868 Indicator Color-Change Range and Titration Indicator Choice

An indicator's colour-change range spans roughly two pH units around its own pKa, and one is chosen so that range falls inside the equivalence point's pH jump. The jump's steepness is what makes a reasonable choice adequate.

Find the unknown.

Chem 1871 Calculating Analyte Concentration from Titration Data

Calculating an unknown analyte's concentration means using the titrant's known molarity and the volume delivered at the equivalence point to find moles of titrant, converting to moles of analyte through the balanced equation's ratio, then dividing by the analyte's original volume. Using the analyte's volume where the titrant's belongs, or the reverse, is the commonest error here.

A sharp jump.

Chem 1874 Titration Curve: Strong Acid–Strong Base Shape

A strong acid–strong base curve starts low, rises gradually, then jumps sharply through pH seven at equivalence before levelling off. That steep jump is the titration's most informative feature, not an artefact to smooth over.

Above seven.

Chem 1876 Titration Curve: Weak Acid–Strong Base Shape

A weak acid–strong base curve starts higher, buffers near half-equivalence, and reaches an equivalence point above pH seven, because the salt produced hydrolyses basic. Expecting every equivalence point at seven ignores that the salt's own hydrolysis is what sets it.

Below seven.

Chem 1878 Titration Curve: Weak Base–Strong Acid Shape

A weak base–strong acid curve starts lower than a strong base's, buffers near half-equivalence, and reaches equivalence below pH seven from acidic salt hydrolysis. It is the weak acid curve inverted rather than the strong-acid-strong-base curve mirrored, and expecting a crossing at seven is a standard error.

Calculated, or seen.

Chem 1881 Equivalence Point vs. Endpoint Distinguished

The equivalence point is where moles of acid and base have exactly reacted — a stoichiometric fact. The endpoint is where the indicator visibly changes colour. The two are related but not identical: one is calculated and the other observed, and a well-chosen indicator makes them close rather than equal.

More than one reading.

Chem 1884 Reading Key Features of a Titration Curve

Reading a titration curve means locating the equivalence point at the steepest section's midpoint, reading the half-equivalence volume at exactly half that volume, and — for a weak acid titration — reading pKa directly off the pH plotted at half-equivalence. For a weak base, that same pH gives the conjugate acid's pKa. Reading pKa anywhere but exactly half-equivalence, where acid and conjugate base concentrations are equal, gives an incorrect value.

Five things to carry out of this part. The three acid-base definitions nest by generality: every Arrhenius pair is Brønsted-Lowry, every Brønsted-Lowry pair is Lewis, and each broader theory reaches reactions the narrower cannot. None is the correct definition. pH seven is not always neutral because Kw depends on temperature: water's autoionisation is endothermic, so warming raises Kw and pushes neutral below seven — and pH plus pOH equals fourteen only at twenty-five degrees. "Strong" describes the extent of an acid's reaction with water, essentially complete, and says nothing about concentration; hydrofluoric acid is weak despite being dangerous. Percent ionisation measures how much of one particular solution has ionised and rises on dilution, while Ka does not move — which is why Ka is the concentration-independent measure of strength. And the equivalence point is the calculated point where acid and base have exactly reacted, while the endpoint is an indicator's observed colour change, chosen to fall close to it. Part Three takes up buffers and solubility.