Equilibrium

Dynamic equilibrium means forward and reverse processes continue at equal rates. Equilibrium concentrations need not be equal. The equilibrium constant is associated with a particular balanced reaction and temperature.

At dynamic equilibrium, forward and reverse reaction rates are equal, so macroscopic composition remains constant. Reactant and product concentrations need not be equal. A large equilibrium constant indicates product-favored equilibrium for the equation as written, not necessarily a rapid reaction.

For a concentration-based introductory expression, dissolved and gaseous species appear raised to their stoichiometric coefficients. Pure solids and pure liquids are omitted because their activities are treated as constant. Equilibrium constants are fundamentally activity based; simplified concentration expressions are model approximations.

Q has the same form as K but uses current rather than equilibrium values. If Q < K, net forward reaction increases the quotient toward K. If Q > K, net reverse reaction reduces it. This reasoning is more precise than memorizing that equilibrium always moves “away from a disturbance.”

At fixed temperature, adding material or changing volume can change Q but does not change K. Temperature can change K because it changes the relative thermodynamic favorability. A catalyst changes the time to approach equilibrium without changing K.

An initial–change–equilibrium table keeps concentration changes tied to the balanced coefficients. If A forms 2B, losing x of A creates 2x of B in a fixed-volume model. Substitute equilibrium expressions into K and reject roots that give physically impossible concentrations.

A small-x approximation can simplify the algebra, but check it afterward against the relevant initial concentration. A small K alone does not guarantee a valid approximation at every concentration. If an approximation fails, solve the equation without it.

Compressing an ideal gas mixture changes all partial pressures. If the reaction has different numbers of gaseous moles on its two sides, Q changes in a way that often favors the side with fewer gas moles after compression. If gas mole counts are equal, this simple pressure perturbation does not shift equilibrium.

Adding an inert gas at constant volume leaves reacting gases’ partial pressures unchanged in an ideal model. Adding an inert gas at constant total pressure can change volume and therefore reacting partial pressures. The constraint matters; “adding a gas” is not enough information.

Use products over reactants, with concentrations or partial pressures raised to stoichiometric powers in the appropriate expression. Pure solids and pure liquids are omitted because their activities are effectively constant in the model. A larger amount of a solid does not enter the expression as a larger concentration.

The reaction quotient Q uses current amounts in the same form as K. If Q<K, net forward reaction moves the system toward equilibrium; if Q>K, net reverse reaction does. Changes in concentration or pressure affect Q immediately, while K changes only with temperature for the given reaction. This distinction makes predictions more precise than treating equilibrium as a vague tendency to “oppose everything.”

List initial concentrations, changes proportional to the balanced coefficients, and equilibrium concentrations. If A forms two B, consuming x of A forms 2x of B. Substitute the equilibrium expressions into K and solve for a physically valid value. Negative equilibrium concentrations indicate an invalid root or setup.

A small-x approximation can simplify a weak-reaction calculation when the change is small relative to the initial amount. Check the approximation afterward rather than assuming it from a small K alone. The relevance of the initial concentration and stoichiometry matters. Keep extra digits until the final result, especially when subtracting similar quantities.

For a salt such as MX₂ dissolving into M²⁺ and two X^-, molar solubility s gives [M²⁺]=s and [X^-]=2s in pure water under the simple model. Ksp therefore equals s(2s)², not s². Molar solubility and Ksp are different quantities, and comparing Ksp values directly across different stoichiometries can be misleading.

A common ion changes the initial conditions and can reduce solubility. Precipitation is predicted when the relevant ion product exceeds Ksp. Use concentrations after mixing, because dilution changes them. Other reactions, including acid–base reactions or complex formation, can alter free-ion concentrations and therefore the dissolution equilibrium.

At dynamic equilibrium, forward and reverse rates are equal while microscopic reactions continue. Concentrations are constant under unchanged conditions, but reactant and product concentrations need not be equal. The equilibrium constant describes the appropriate ratio for the balanced reaction at a given temperature.

Use coefficients as exponents and omit pure solids and pure liquids from the usual activity-based expression. Their omission does not mean they cannot participate; their activities are treated as constant while those phases are present. Changing the written reaction changes the corresponding constant: reversal takes a reciprocal, and multiplying coefficients raises K to that power.

The reaction quotient Q uses the same expression evaluated for the current mixture. Q<K predicts net forward change; Q>K predicts net reverse change. State what “forward” means in the written equation. A change in initial composition changes Q, not K at fixed temperature.

List initial concentrations, express changes using one extent and the reaction coefficients, then substitute the equilibrium values into K. For A⇌2B at fixed volume, a decrease x in A accompanies an increase 2x in B. Using equal concentration changes would violate stoichiometry.

Small-change approximations are hypotheses to check after solving. If x is not small relative to the quantity from which it was neglected, return to the full equation. A mathematical root that gives a negative concentration or consumes more reactant than available is physically invalid. Your final values should also reproduce K within appropriate rounding.

Large K means the equilibrium ratio favors products in the specified expression, not that equilibrium is reached quickly or that every reactant molecule disappears. Kinetics determines the time scale. Very small or large equilibrium amounts may still matter when the question concerns detection, solubility or a limiting concentration.

Adding a reactant at fixed temperature often changes Q so reaction partially opposes the disturbance. “Partially” matters: the final concentration of the added reactant can remain above its original value even after some is consumed. An instantaneous concentration jump and the later reaction response are separate stages.

For gas mixtures, compression changes partial pressures. Adding inert gas at fixed volume does not change the partial pressures of unchanged reacting gases in the ideal model, whereas adding it at fixed total pressure expands the container and can change them. Temperature can change K; its effect depends on the reaction’s thermal behavior. A catalyst changes rates without changing K.

Solubility calculations must follow the actual dissolution stoichiometry. For MZ₂, concentrations s and 2s give Ksp=4s³ in pure water under the simple model. A common ion changes the initial concentration, so the pure-water expression may no longer apply. Acid–base reactions that consume a dissolved ion can increase dissolution without changing Ksp at the same temperature.

Write K using appropriate activities or the course’s concentration/pressure approximation, raising terms to stoichiometric coefficients. Pure solids and liquids are omitted from the usual expression because their activities are treated as constant. Omitting them does not mean they are chemically irrelevant or absent.

An ICE table tracks changes constrained by stoichiometry. If one reactant decreases by x and a coefficient requires twice that change for another, use 2x. Equilibrium concentrations must remain nonnegative and consistent with the initial amounts. A mathematically obtained root can be physically invalid.

A small-x approximation must be checked after solving. Compare the neglected change with the initial amount; if it is not sufficiently small for the intended accuracy, solve the more complete expression. A small K alone does not guarantee every possible initial condition justifies the approximation.

At fixed temperature, a concentration or pressure change can alter Q and drive net reaction toward restoring equilibrium, while K remains the same. A temperature change can change K. A catalyst changes the approach rate without changing the equilibrium composition for the same conditions.

For gas equilibria, volume changes alter partial pressures, but the resulting direction depends on gas stoichiometry. Adding an inert gas at fixed volume does not change the reacting gases’ ideal partial pressures, while other constraints can lead to different outcomes. State what is held fixed.

For solubility equilibria, compare the ion product with Ksp and account for stoichiometric ion ratios. A common ion can reduce solubility in the simple model, but additional acid–base or complex-ion chemistry can change the result. Use the specified model rather than assuming all salts dissolve in the same ratio.