Unit 7: Equilibrium

Chemical equilibrium

State of a reversible reaction where forward and reverse reaction rates are equal, so macroscopic concentrations/partial pressures remain constant over time.

Dynamic equilibrium

Equilibrium in which reactions continue in both directions; rates are equal so the net change is zero (the reaction has not stopped).

Reversible reaction

Reaction that can proceed in both forward and reverse directions under the given conditions.

Forward reaction rate

Speed at which reactants form products; typically high initially if only reactants are present, then decreases as reactants are consumed.

Reverse reaction rate

Speed at which products form reactants; typically near zero initially if no products are present, then increases as products accumulate.

Closed system (equilibrium requirement)

A system where reactants/products cannot escape; necessary for a stable equilibrium to be reached and maintained.

Equilibrium position

The relative amounts of reactants and products present at equilibrium (may favor either side; not necessarily 50–50).

Macroscopic constancy at equilibrium

At equilibrium, concentrations/partial pressures are constant over time, meaning no net change—not that amounts are equal or the reaction stops.

Concentration vs. time equilibrium indicator

On a concentration-time graph, equilibrium is indicated when curves become horizontal (level off).

Stoichiometric coefficients (rate/slope connection)

Balanced-equation coefficients determine relative rates of concentration change and relative slopes on early concentration-time graphs.

Haber process (equilibrium example)

Nitrogen and hydrogen react reversibly to form ammonia: N2(g) + 3H2(g) ⇌ 2NH3(g).

Law of Mass Action

Rule that the equilibrium expression is built from the balanced equation as written, using products over reactants with exponents equal to coefficients.

Equilibrium constant (K)

A predictable ratio of product to reactant amounts at equilibrium for a given reaction at a specific temperature.

Kc

Equilibrium constant expressed in terms of equilibrium molar concentrations (molarity) of gases and/or aqueous solutes.

Kp

Equilibrium constant expressed in terms of equilibrium partial pressures of gaseous species.

Equilibrium expression exponents

In K expressions, stoichiometric coefficients become exponents (not multipliers).

Omitting pure solids and pure liquids

Pure solids and liquids are excluded from K (and Q) expressions because their effective concentrations are constant and absorbed into K.

Including gases and aqueous solutes

Gases and dissolved (aqueous) species are included in equilibrium expressions because their concentrations/pressures can change.

Example: CaCO3(s) ⇌ CaO(s) + CO2(g)

For this equilibrium, Kc = [CO2]; solids CaCO3 and CaO are omitted.

Δn (delta n)

For Kp–Kc conversions, Δn = (moles of gaseous products) − (moles of gaseous reactants).

Kp–Kc relationship

For gas equilibria: Kp = Kc(RT)^{Δn}, where R is the gas constant and T is temperature in kelvin.

Interpreting K > 1

If K is greater than 1, products are favored at equilibrium (equilibrium lies to the right).

Interpreting K < 1

If K is less than 1, reactants are favored at equilibrium (equilibrium lies to the left).

Interpreting K ≈ 1

If K is near 1, appreciable amounts of both reactants and products are present at equilibrium.

Unitless K (AP convention)

In AP Chemistry, equilibrium constants are typically treated as unitless (activities provide a more rigorous basis).

Reaction quotient (Q)

A ratio with the same form as K but using current (not necessarily equilibrium) concentrations/pressures to predict direction of shift.

Qc

Reaction quotient calculated from current concentrations (molarities) using the same form as Kc.

Qp

Reaction quotient calculated from current partial pressures using the same form as Kp.

Q < K criterion

If Q is less than K (at the same temperature), the reaction proceeds forward (toward products) to reach equilibrium.

Q > K criterion

If Q is greater than K (at the same temperature), the reaction proceeds in reverse (toward reactants) to reach equilibrium.

Q = K condition

If Q equals K, the system is at equilibrium.

Matching forms when comparing Q and K

Compare Qc to Kc and Qp to Kp; do not mix concentration-based and pressure-based forms.

Le Châtelier’s principle

A system at equilibrium shifts in the direction that counteracts an imposed disturbance to re-establish equilibrium.

Two-stage stress reasoning (Q then shift)

A disturbance changes concentrations/pressures (or temperature) immediately, changing Q; then the system shifts until Q returns to K.

Pressure/volume shift rule (gases)

Decreasing volume (increasing pressure) shifts toward fewer moles of gas; increasing volume (decreasing pressure) shifts toward more moles of gas.

No pressure/volume shift when gas moles equal

If both sides have the same total moles of gas, changing pressure/volume does not shift equilibrium (though pressures change).

Inert gas addition at constant volume

Adding an inert gas at constant volume does not change reacting-gas partial pressures, so there is no shift.

Inert gas addition at constant pressure

Adding an inert gas at constant pressure increases volume, lowering reacting-gas partial pressures and potentially shifting toward more moles of gas.

Temperature as the only stress that changes K

Changing temperature changes the numerical value of K; concentration/pressure/catalysts change position but not K.

Endothermic forward reaction (temperature effect)

If heat is a reactant, increasing temperature favors products and increases K.

Exothermic forward reaction (temperature effect)

If heat is a product, increasing temperature favors reactants and decreases K.

Catalyst (equilibrium effect)

Speeds both forward and reverse reactions by lowering activation energy; equilibrium is reached faster but K and equilibrium position do not change.

Concentration-time graph response to disturbance

Often shows an instantaneous jump for species directly added/removed, followed by gradual changes as the system shifts to a new equilibrium.

ICE table

A setup (Initial, Change, Equilibrium) used to relate equilibrium concentrations/pressures to K and solve for unknowns.

Stoichiometric changes in ICE tables

The Change row uses coefficients to relate changes (e.g., −x, +2x) according to the balanced equation.

Small-x approximation

Assumption that x is negligible compared with an initial concentration; typically acceptable if the percent change is less than about 5%.

Quadratic necessity in equilibrium problems

When the small-x approximation is not valid, solving the K equation often requires the quadratic formula.

Manipulating K by reversing a reaction

If a reaction is reversed, the new equilibrium constant is the reciprocal: K_rev = 1/K.

Manipulating K by scaling coefficients

If all coefficients are multiplied by n, the new equilibrium constant becomes K_new = K^n.

Manipulating K by adding reactions

When reactions are added to form an overall reaction, the overall equilibrium constant is the product: K_overall = K1K2.

Ksp (solubility product constant)

Equilibrium constant for dissolution of a slightly soluble ionic solid; larger Ksp generally indicates greater solubility.

Molar solubility

The equilibrium amount of solid that dissolves per liter; related to ion concentrations through dissolution stoichiometry.

Common ion effect

Decrease in solubility of a slightly soluble salt when an ion common to the salt is added, shifting dissolution equilibrium toward the solid.