Chemical Equilibrium: The Equilibrium Constant

Haemoglobin binding oxygen and carrying it from the lungs to the muscles, and haemoglobin binding carbon monoxide instead, are both genuine chemical equilibria, and the entire difference between one sustaining life and the other causing fatal poisoning comes down to exactly where each equilibrium sits. When a liquid evaporates inside a closed container, molecules with enough kinetic energy escape into the vapour phase while vapour molecules simultaneously strike and rejoin the liquid surface, and once the number leaving equals the number returning, the system has reached equilibrium, a state with a constant vapour pressure yet genuinely intense activity still happening at the liquid's own surface the entire time. Equilibrium, whether physical or chemical, never means a process has stopped: it means two opposing processes are proceeding at exactly matched rates, and this chapter builds the single tool, the equilibrium constant, that captures precisely where that balance settles.

Ice and water sealed in a perfectly insulated flask at 273 K show no net change in mass over time, yet real activity continues at the boundary the entire time, water molecules colliding onto ice and adhering while ice molecules simultaneously escape into the liquid, the two transfer rates exactly equal; for any pure substance at atmospheric pressure, the single temperature at which solid and liquid coexist this way is its normal melting or freezing point. Liquid-vapour equilibrium works the same way, and vapour pressure, the constant pressure exerted by vapour once evaporation and condensation rates match, differs from one liquid to the next at the same temperature, a liquid with higher vapour pressure being more volatile and boiling at a lower temperature, which is also exactly why boiling point itself falls at higher altitude, where atmospheric pressure is lower. Solids can equilibrate directly with their own vapour too, without ever passing through a liquid phase: solid iodine placed in a closed vessel fills it with violet vapour of steadily increasing, then constant, intensity, camphor and ammonium chloride behaving the identical way.

A saturated solution, holding the maximum solute a given temperature allows, is itself a dynamic equilibrium between dissolved and undissolved solute, the rate of dissolution exactly matching the rate of crystallisation, a claim confirmed directly by dropping radioactive sugar into an already-saturated ordinary sugar solution: radioactivity soon appears in both the solid and the liquid phase, proof that molecules keep exchanging between phases continuously even while the solution's own overall concentration stays fixed. Gases dissolving in liquids follow Henry's Law instead, the mass of gas dissolved proportional to its own pressure above the liquid, exactly why a sealed soda bottle holds carbon dioxide under pressure and why that same bottle, once opened and left standing, gradually goes flat as dissolved CO2 escapes to reach the new, lower-pressure equilibrium the open atmosphere demands. Every physical equilibrium examined shares five common features: it can only exist in a closed system at a fixed temperature; both opposing processes proceed at the same rate, dynamic yet stable; every measurable property of the system stays constant; that equilibrium state is marked by one specific parameter holding a constant value, melting point, vapour pressure, solubility, or a gas's own dissolved concentration; and the size of that constant value itself reveals how far the physical process has actually proceeded.

Chemical reactions equilibrate the same way physical processes do: as a reversible reaction A plus B forming C plus D proceeds, reactant concentrations fall and product concentrations rise, slowing the forward reaction and speeding the reverse, until eventually the two rates match and every concentration in the mixture stops changing, chemical equilibrium, reachable equally well starting from pure reactants or pure products. Haber's own ammonia synthesis experiments showed this composition constancy directly, but the truly definitive proof came from isotope labelling: running the identical synthesis separately with ordinary hydrogen and with deuterium, reaching equilibrium in each, then mixing the two equilibrium mixtures together and waiting, analysis by mass spectrometer revealed a genuine scramble of hydrogen and deuterium spread across every possible molecular combination, NH3 through ND3, H2 through D2, a result utterly impossible if the reaction had genuinely stopped at equilibrium rather than continuing its forward and reverse steps indefinitely, just now at perfectly matched rates.

Guldberg and Waage, working from many reversible reactions' own experimental data, proposed in 1864 that a reaction's equilibrium mixture concentrations relate through one fixed expression, the law of chemical equilibrium, sometimes called the law of mass action from concentration's older name, active mass. Working through H2 plus I2 forming 2HI at 731 K across six separate experiments, some starting from pure H2 and I2, others from pure HI, reveals the pattern directly: the simple ratio HI over H2 times I2 comes out different every time, genuinely not constant, but HI squared over H2 times I2 comes out to the same fixed value in all six cases regardless of starting point, and the power of 2 on HI is exactly its own stoichiometric coefficient in the balanced equation. For the general reaction aA plus bB forming cC plus dD, this gives Kc equals C to the c times D to the d, all over A to the a times B to the b, using equilibrium concentrations throughout, every exponent matching that species' own coefficient in the balanced equation exactly.

Reversing a reaction's own direction inverts its equilibrium constant exactly, K prime equalling 1 over K, since the numerator and denominator of the original expression simply swap places; and multiplying every coefficient in a balanced equation by some factor n raises the original K to the power n, since each exponent in the expression scales by that same factor. This is a genuinely practical caveat, not a technicality: since H2 plus I2 forming 2HI and one-half H2 plus one-half I2 forming HI describe the exact same chemistry yet carry different K values, 57.0 against its own square root, any quoted equilibrium constant is meaningless without specifying exactly which balanced equation it belongs to.

For reactions involving gases, expressing the equilibrium constant through partial pressure, Kp, is often more convenient than through concentration, Kc, and the two connect directly through the ideal gas law, since pressure and concentration are proportional at fixed temperature, p equals concentration times RT. Substituting this relationship through the equilibrium expression gives Kp equals Kc times RT raised to the power Δn, where Δn is the moles of gaseous products minus the moles of gaseous reactants; when Δn is exactly zero, as in H2 plus I2 forming 2HI, Kp and Kc come out numerically identical, but for a reaction like N2 plus 3H2 forming 2NH3, where Δn equals negative 2, the two values genuinely differ. Equilibrium constants carry units based on concentration or pressure unless every exponent happens to cancel, though specifying a standard state, 1 bar for a gas, 1 molar for a solute, lets K be expressed as a clean, dimensionless number instead, the value itself still depending on which standard state was chosen.

A homogeneous equilibrium keeps every reactant and product in one shared phase, ammonia synthesis entirely gaseous, ester hydrolysis entirely in aqueous solution, but a heterogeneous equilibrium spans more than one phase at once, and a genuinely useful simplification applies whenever a pure solid or pure liquid is involved: its own concentration, mass per unit volume of that pure substance, never actually changes no matter how much of it is present, so it can simply be dropped from the equilibrium expression entirely, folded into the constant itself. Calcium carbonate's own thermal decomposition to calcium oxide and carbon dioxide illustrates this directly: since both CaCO3(s) and CaO(s) are pure solids with fixed concentration, the true equilibrium expression collapses to just Kc equals the concentration of CO2 gas alone, or equivalently Kp equals the partial pressure of CO2 alone, meaning at any given temperature there is one single, fixed CO2 pressure the two solids can coexist with, exactly 2.0 times ten to the fifth pascals at 1100 K in this specific case. This simplification never means the solid or liquid phase is optional, though, some amount of each pure phase must genuinely still be present for the heterogeneous equilibrium to exist at all, its own concentration simply doesn't need to appear in the mathematical expression.