Equilibrium: Fundamentals, Acids and Bases, and Solubility

This is Unit Ten of Chemistry, Part One: equilibrium fundamentals. Unit Nine asked how fast a reaction goes; this unit asks how far, and the two turn out to be independent questions with independent answers. The through-line is a single comparison. There is a number describing where a reaction settles, called K, and the same expression evaluated at any moment, called Q — and nearly everything in this part, including Le Châtelier's principle, follows from comparing the two. By the end you will be able to say what is equal at equilibrium and what is not; say what K depends on and what it does not; say what comparing Q to K tells you; say what the small-x approximation requires you to check; and say why Le Châtelier's principle works.

Three entries. What is actually equal when a reaction reaches equilibrium, the reading of that word which is wrong and extremely common, and why equilibrium happens at all — which follows directly from the kinetics of the last unit.

Two rates meet.

Chem 1741 Dynamic Equilibrium: Equal Rates, Not Equal Concentrations

Dynamic equilibrium is the state where a reaction's forward and reverse rates are equal, so concentrations stop changing even though both reactions keep occurring. Assuming equilibrium is reached the instant reactants and products first mix ignores the time it takes for those two rates to converge.

The common misreading.

Chem 1743 Twin: "Equilibrium Means Equal Concentrations"

Reading equilibrium as equal reactant and product concentrations is an error — only the two opposing rates are equal, and the concentrations themselves can settle almost anywhere, heavily toward products or heavily toward reactants. A textbook diagram showing similar-sized reactant and product boxes can wrongly suggest amounts must match.

Why it happens.

Chem 1746 Equilibrium as a Consequence of Kinetics

A reaction approaches equilibrium because its forward rate falls as reactants deplete while its reverse rate rises as products accumulate, until the two meet. Equilibrium is not a reaction stopping — both rates continue at that point, and only their difference reaches zero.

Four entries. How the constant is built from a balanced equation, why it is reported without units, the single thing that changes its value, and the two kinds of species left out of it entirely.

Products over reactants.

Chem 1749 Equilibrium Constant Expression Construction

An equilibrium constant expression is the products' equilibrium concentrations, each raised to its coefficient, divided by the reactants' equilibrium concentrations, each raised to its coefficient. Building the expression from an equation's coefficients before that equation is balanced gives a wrong expression entirely — the balance has to come first.

No units.

Chem 1752 K Is Dimensionless

An equilibrium constant is treated as dimensionless, because each concentration or pressure term is really a ratio to a reference standard state, and those reference units cancel. Attaching units to a reported K value misrepresents the activity-based convention the expression rests on.

Only temperature.

Chem 1755 K Depends Only on Temperature

A given reaction's equilibrium constant has one value at a given temperature, and changes only if the temperature changes — not with starting concentrations, not with pressure. Adding more reactant shifts the concentrations present at equilibrium, but it does not change K itself, which is the distinction the whole of Topic 5 rests on.

What gets left out.

Chem 1758 Homogeneous vs. Heterogeneous Equilibria

A homogeneous equilibrium has every species in one phase; a heterogeneous equilibrium spans phases, and its expression omits pure solids and pure liquids entirely, since their concentrations do not vary. Including a pure solid's or liquid's concentration in the expression is a common construction error.

Three entries introducing the second half of this unit's central comparison. The same expression as K but evaluated whenever you like, what putting the two side by side tells you, and one thing K's size does not tell you.

The same form, any moment.

Chem 1761 Reaction Quotient Q Defined

A reaction quotient Q has exactly the same form as K but is calculated from concentrations at any moment, not necessarily at equilibrium. The two share a formula and answer different questions: Q describes where a reaction is now, K describes where it is heading.

Which way it goes.

Chem 1764 Comparing Q to K Predicts Direction

A reaction proceeds forward if Q is less than K, in reverse if Q is greater than K, and is already at equilibrium if the two are equal. The comparison has to be against K — comparing Q to zero gives no directional information at all, since Q's absolute size means nothing without its destination.

Large or small.

Chem 1766 K's Magnitude Read Qualitatively

A very large K means a reaction favours products heavily at equilibrium, and a very small K means it favours reactants heavily. Neither says anything about how fast the reaction gets there: a large K describes equilibrium position, and speed was Unit Nine's separate question.

Four entries. The bookkeeping table every later calculation in this unit assumes, a shortcut that avoids the quadratic formula along with the check that validates it, and the conversion between the pressure and concentration forms of K.

Initial, change, equilibrium.

Chem 1768 The ICE Table Method

Solving an equilibrium problem with an ICE table means recording each species' Initial concentration, its Change expressed as a multiple of an unknown x using the stoichiometric coefficients, and the resulting Equilibrium concentration, then substituting that equilibrium row into the K expression and solving for x. Forgetting that a coefficient of two multiplies x in the Change row, not only in the Equilibrium row, gives concentrations that do not satisfy the balanced equation.

Avoiding the quadratic.

Chem 1771 The Small-x Approximation

The small-x approximation assumes x is negligible next to a large initial concentration wherever it is added or subtracted, which simplifies the expression enough to solve directly — then requires checking that x is under about five percent of that initial concentration before the answer is accepted. Skipping the check risks accepting an answer where x was never small enough, in which case the full quadratic has to be solved instead.

Pressure, or concentration.

Chem 1774 Kp vs. Kc Relationship

Kp uses partial pressures where Kc uses concentrations, and the two relate through Kp equals Kc times R T raised to delta n, with delta n the change in gas moles. Using total gas moles for delta n, rather than products minus reactants, gives a wrong conversion factor.

Gases only.

Chem 1777 Converting Between Kp and Kc

Converting means computing delta n from the balanced equation's gas-phase coefficients alone, then substituting delta n, the temperature in kelvin, and the gas constant into the relationship and solving for whichever constant is unknown. Any species that is not a gas is left out of the delta n count — the same omission rule heterogeneous equilibria already follow. Celsius produces an unusable result.

Six entries closing the part, and the book does something worth noticing here. Le Châtelier's principle is usually taught as a rule about stress and shift. This unit derives it instead: a stress moves Q away from K, and the system responds by restoring the equality. Three stresses follow, one thing that is not a stress at all, and the capstone.

Why it works.

Chem 1780 Le Châtelier's Principle as a Q-vs-K Consequence

Le Châtelier's principle states that a stress makes Q no longer equal K, and the system then reacts in whichever direction restores that equality. Saying that stress shifts equilibrium is a description rather than an explanation — the shift happens because the stress moved Q away from K, and the reaction runs until they match again.

Adding, or removing.

Chem 1783 Concentration Stress via Q vs. K

Adding a species lowers Q if that species sits in the denominator, or raises Q if it sits in the numerator, and the system shifts to restore Q to K. Removing a species reverses whichever shift adding it would have caused — predicting the same direction for both is a slip.

Squeeze the container.

Chem 1786 Volume/Pressure Stress via Q vs. K

Compressing a gas equilibrium raises every concentration at once, which changes Q unless the gas moles are equal on both sides, so the system shifts toward the side with fewer moles. Equal gas moles on both sides means no shift at all from a volume change, because Q never moves.

The one that moves K.

Chem 1789 Temperature Stress via Q vs. K

Raising temperature changes K itself — rising for an endothermic reaction, falling for an exothermic one — and treating heat as a reactant or product predicts the shift's direction. This is the distinction to hold: temperature changes K's value, while concentration and volume changes only move Q.

Not a stress.

Chem 1792 Catalyst Has No Effect on Equilibrium Position

A catalyst has no effect on equilibrium position. It lowers the forward and reverse activation energies equally, so it changes how quickly equilibrium is reached without moving Q or K — which confirms from the equilibrium side what Unit Nine established from the kinetics side.

Predict, then compute.

Chem 1795 Capstone: Predicting and Quantifying a Le Châtelier Shift

The capstone takes a system at equilibrium, applies a stress, predicts the shift's direction by asking what the stress did to Q relative to K, and then quantifies the new equilibrium position with an ICE table built from the disturbed concentrations. The qualitative prediction and the numerical answer come from the same comparison — the prediction says which way, and the table says how far.

Five things to carry out of this part. What is equal at equilibrium is the forward and reverse rates; what is not necessarily equal is the concentrations, which can settle heavily toward products, heavily toward reactants, or anywhere between. Both reactions keep running — only their difference reaches zero. K depends only on temperature. It does not change when you add reactant, remove product, or alter the pressure: those move where the concentrations settle without touching the constant itself. Comparing Q to K tells you which direction a reaction will run — forward if Q is below K, reverse if above, nowhere if equal — and the comparison must be against K, since Q's size alone says nothing. The small-x approximation requires checking that x came out under about five percent of the initial concentration it was neglected against; skip that check and you may accept an answer the approximation never justified, in which case the full quadratic is needed. And Le Châtelier's principle works because a stress moves Q away from K: the system then runs in whichever direction restores the equality. Concentration and volume changes move Q, temperature changes K itself, and a catalyst moves neither. Part Two takes up acids and bases, beginning with three definitions of what an acid is.