Ionic Equilibrium: Acids, Bases and Salts

Hydrochloric acid in your stomach, acetic acid in vinegar, citric and ascorbic acid in a glass of orange juice, tartaric acid in tamarind paste, washing soda as an everyday base: acids and bases are not laboratory curiosities, they are in your body and your kitchen right now. Yet across the history of chemistry, the words "acid" and "base" have been defined three separate times, each definition wider than the one before it, because each new definition kept running into real substances the old one could not explain. Class 10 worked entirely within the first, narrowest of these three definitions without ever naming it. This chapter introduces all three, and then asks a harder question than Class 10 ever needed to: not just whether something is an acid, but how strongly.

Svante Arrhenius, in the 1880s, defined an acid as a substance that dissociates in water to give H+(aq), and a base as one that gives OH-(aq): HX(aq) -> H+(aq) + X-(aq), and MOH(aq) -> M+(aq) + OH-(aq). This is exactly the definition Class 10 was using all along, just without the name attached. It works well for substances like HCl or NaOH, but it has a real gap: ammonia, NH3, is unmistakably a base, it turns red litmus blue and reacts with acids, yet its molecule contains no OH group at all for it to release. Arrhenius's theory has no way to explain why NH3 counts as a base, which is exactly the crack the next definition was built to fix.

Johannes Bronsted and Thomas Lowry independently proposed a broader definition in 1923: an acid is a species that donates a proton (H+), and a base is a species that accepts one. Watch what happens when ammonia dissolves in water: NH3 + H2O -> NH4+ + OH-. Water hands a proton to ammonia; water is the acid here, ammonia is the base, and the reaction produces a basic solution without ammonia ever needing an OH group of its own. This same reaction reveals something else: every acid-base pair that differs by exactly one proton is called a conjugate acid-base pair. OH- is the conjugate base of the acid H2O, and NH4+ is the conjugate acid of the base NH3. Water is not stuck playing only one role either: react it with HCl instead, and water accepts a proton, acting as a base this time, while HCl donates one, acting as the acid. Whether water behaves as an acid or a base depends entirely on what it is reacting with, and a stronger acid always produces a weaker conjugate base, and vice versa, which is exactly why strong acids like HCl leave behind conjugate bases (Cl-) too weak to have any noticeable effect of their own.

G.N. Lewis, in 1923, went further still and defined acids and bases without any mention of protons at all: a Lewis acid is a species that accepts an electron pair, and a Lewis base is one that donates an electron pair. Every Bronsted base still counts as a Lewis base, since donating a proton pair and accepting nothing requires the base to offer an electron pair to bond with that proton. But the Lewis definition also captures acids that have no proton whatsoever. Boron trifluoride, BF3, has no H+ to give away, yet it reacts eagerly with ammonia: BF3 + :NH3 -> BF3:NH3, because boron in BF3 is short of a full electron octet and greedily accepts the lone pair NH3 offers. By Bronsted-Lowry's proton-based rule, BF3 could never be classed as an acid at all; by Lewis's rule, it clearly is one. This is the widest of the three definitions, and the one modern chemists reach for whenever a reaction's acid-base character has nothing to do with hydrogen at all.

Even perfectly pure water, with no acid or base added, contains a tiny number of ions, because water molecules occasionally react with each other: H2O + H2O <-> H3O+ + OH-. This equilibrium has its own constant, called the ionic product of water, Kw = [H3O+][OH-]. Experimentally, at 298K, pure water's H+ concentration works out to 1.0 x 10^-7 mol/L, and since the reaction produces one OH- for every H3O+, [OH-] is exactly the same, 1.0 x 10^-7 mol/L. Multiply the two together and Kw = (1.0 x 10^-7) x (1.0 x 10^-7) = 1.0 x 10^-14. This single number, Kw = 10^-14 at 298K, is the quiet foundation the entire pH scale is built on: whatever else is dissolved in a water-based solution, the product of its H+ and OH- concentrations always equals Kw, which is exactly why raising one of the two concentrations must lower the other.

Class 10 introduced pH as a scale from 0 to 14, read off a universal indicator's colours, without ever showing where the number comes from. Now it can be defined precisely: pH = -log[H+]. Take pure water's own H+ concentration, 1.0 x 10^-7 M, and pH = -log(10^-7) = 7, exactly the neutral point Class 10 already knew. An acidic solution has more H+ than pure water, so its pH works out below 7; a basic solution has less H+ (and correspondingly more OH-, since the product must still equal Kw), so its pH comes out above 7. Because pH is a logarithmic scale, not a simple straight-line one, a change of just one pH unit means a tenfold change in H+ concentration, which is why a solution of pH 2 is not twice as acidic as pH 4, it has one hundred times more H+ ions.

Class 10 could only say a strong acid ionises fully and a weak acid ionises partly, a qualitative distinction. For a weak acid HA in equilibrium, HA + H2O <-> H3O+ + A-, the equilibrium itself has a constant, the acid ionisation constant, Ka = [H3O+][A-] / [HA]. A larger Ka means the equilibrium sits further towards the ionised side, meaning the acid gives up its proton more readily, so a larger Ka always means a stronger acid. Because these numbers are often awkwardly small, chemists usually quote pKa = -log(Ka) instead, and smaller pKa now means stronger acid. Weak bases get the exact same treatment with their own constant, Kb, and pKb. For a conjugate acid-base pair, the two constants are locked together: Ka x Kb = Kw, which means a strong acid (large Ka) is mathematically guaranteed to have a very weak conjugate base (small Kb), matching exactly what conjugate pairs already showed qualitatively.

Take a solution of acetic acid at equilibrium, mostly unionised molecules with a small population of H+ and CH3COO- ions, and add sodium acetate to it, a salt that fully dissociates to flood the solution with extra CH3COO- ions, an ion the acetic acid equilibrium already produces on its own. Le Chatelier's principle says the equilibrium HA + H2O <-> H3O+ + A- must respond to that extra A- by shifting back towards the unionised HA side, suppressing the acid's own ionisation and lowering [H+] below what it would have been alone. This suppression of a weak acid's (or weak base's) ionisation by deliberately adding an ion it already produces is called the common ion effect, and it is not just a laboratory curiosity: it is the exact mechanism buffer solutions rely on, which is where this chapter goes next.

Class 10 stated, without fully explaining why, that a salt from a strong acid and a weak base turns out acidic, and a salt from a weak acid and a strong base turns out basic. The mechanism is hydrolysis: a salt's ions reacting back with water. Take sodium acetate, the salt of weak acetic acid and strong sodium hydroxide. Its acetate ion reacts with water, CH3COO- + H2O <-> CH3COOH + OH-, regenerating some acetic acid and, crucially, releasing OH- ions, which is exactly why the solution ends up basic. Take ammonium chloride instead, the salt of strong hydrochloric acid and weak ammonia: its ammonium ion reacts with water, NH4+ + H2O <-> NH4OH + H+, releasing H+ instead, which is why that solution ends up acidic. A salt from a strong acid and a strong base has no ion weak enough to react with water at all, so no hydrolysis happens, and the solution stays neutral, matching Class 10's other case exactly. There is even a formula connecting a salt's pH directly to the strength of its parent acid and base: pH = 7 + half of (pKa - pKb), so a bigger pKa relative to pKb pulls the pH below 7, and a smaller pKa relative to pKb pushes it above 7.

Your blood keeps a pH between about 7.35 and 7.4, and even mild deviation from that narrow range causes real harm, yet your body constantly produces acidic waste that should, by rights, disturb it. It survives because of a buffer solution: a mixture, typically of a weak acid and its own salt (its conjugate base), that resists changing pH when small amounts of acid or base are added to it, or when it is diluted. A mixture of acetic acid and sodium acetate is a buffer, and it works through exactly the common ion effect described earlier: add a little extra acid, and the large reserve of acetate ions already present mops up the new H+; add a little extra base, and the large reserve of unionised acetic acid supplies more H+ to replace what was neutralised. The pH such a buffer settles at follows the Henderson-Hasselbalch equation, pH = pKa + log([salt]/[acid]), and when the acid and its salt are mixed in equal concentration, the log term becomes log(1) = 0, so the buffer's pH simply equals the acid's own pKa. An acetic acid and sodium acetate buffer, in equal concentrations, therefore sits at a pH close to acetic acid's pKa of 4.76, and this is exactly how chemists deliberately design a buffer for any target pH: pick a weak acid whose pKa is close to the pH you want, and mix it with its salt.

Some ionic salts, like calcium chloride, dissolve so readily they even pull water vapour out of the air; others, like barium sulphate, are so sparingly soluble that chemists once simply called them insoluble. Even a sparingly soluble salt sets up a genuine equilibrium once it is in contact with its own saturated solution: BaSO4(s) <-> Ba2+(aq) + SO4^2-(aq). Because the solid's own concentration stays constant, this equilibrium reduces to a single constant, the solubility product, Ksp = [Ba2+][SO4^2-]. For barium sulphate, Ksp is experimentally about 1.1 x 10^-10 at 298K; since each formula unit that dissolves releases one Ba2+ and one SO4^2-, if S is the molar solubility, Ksp = S x S = S^2, so S works out to about 1.05 x 10^-5 mol/L, confirming just how sparingly it dissolves. Solubility product follows the exact same common ion effect logic as before: add extra sulphate ions from a different, more soluble salt, and the equilibrium shifts to push more barium sulphate out of solution as solid, lowering its solubility further, which is a real, deliberately used technique for purifying a compound by selective precipitation.

In Class 7, litmus and turmeric could sort a liquid into acidic, basic or neutral, and nothing more, they were witnesses with no explanation to offer. In Class 10, that colour-changing behaviour was finally traced to a single particle, H+ or OH-, and the pH scale gave acidity a number, even though the number itself was only defined, not yet calculated from anything. Here, that number has been derived from first principles through Kw, acid and base strength have become genuine calculable quantities through Ka and Kb, Class 10's unexplained rule about which salts are acidic or basic has been fully accounted for through hydrolysis, and the same underlying chemistry, the common ion effect, turned out to explain both how buffers keep your blood pH stable and how sparingly soluble salts can be selectively purified. Three classes, one steadily deepening idea: a substance is acidic or basic because of how readily it gives up, or takes on, a single hydrogen ion, and everything else in this chapter is simply that one idea, examined ever more closely.