GENERAL CHEMISTRY · CHEMICAL EQUILIBRIA STUDY MAP

Compare the quotient.
Predict the response.

Fifteen focused outcomes connect dynamic molecular reactions, equilibrium expressions, acid-base coupling, precipitation thresholds, quantitative solutions, and system stresses across five complete lessons and twenty original questions.

Start the lessons →Build a balanced set ↗Explore all objectives ↓
5official topics
15bounded objectives
5guided lessons
20original questions

Scope boundary

One equilibrium language. Distinct chemical systems.

The ADA names Molecular, Acid/base, Precipitation, Calculations, and Le Chatelier's Principle but does not publish topic-level weights or question quotas. These outcomes organize study; they do not predict the number of questions on a test form.

Chemical Equilibria owns generalized Q/K reasoning, reaction coupling, solubility products, and stress response. The completed Acids and Bases route remains the prerequisite home for pH, strength, Brønsted-Lowry roles, buffers, and titration-region methods.

Equilibrium decision sequence

Four checks before predicting a shift.

  1. 01

    Write the system

    Balance the reversible reaction, label every phase, and identify which amounts or conditions are actually changing.

  2. 02

    Build Q or K

    Place variable products over reactants, apply coefficient exponents, and omit only constant-activity pure phases.

  3. 03

    Compare or solve

    Use Q versus K for direction, a threshold for precipitation, or one stoichiometric reaction extent in an ICE table.

  4. 04

    Verify the boundary

    Check temperature, gas constraints, physical roots, approximations, phase presence, and whether the claim concerns rate or composition.

Official hierarchy → learning sequence

Five branches. Fifteen outcomes.

Open a topic to inspect its outcomes, must-know relationships, model boundaries, prerequisite graph, misconception corrections, representations, and direct free references.

AMolecular3 objectives
Objective 1GC-EQU-MOL-01

Dynamic equilibrium at the molecular scale

Interpret particle models, concentration-time graphs, and rate-time graphs to identify a closed reversible system at equilibrium and distinguish its microscopic activity from its macroscopic constancy.

Must know
At equilibrium, forward and reverse reactions continue at equal, nonzero rates while observable concentrations remain constant over time. Equal reaction rates do not require equal reactant and product concentrations; an equilibrium mixture may contain mostly reactants, mostly products, or appreciable amounts of both.
Model boundary
Equilibrium describes composition and opposing rates in a stated closed model. It does not reveal how quickly equilibrium is reached; detailed rate laws and mechanisms belong to Chemical Kinetics.
Misconception
A reaction stops when it reaches equilibrium. Forward and reverse molecular events continue at equal rates, so the macroscopic composition stays constant even though particles keep reacting.
Earlier objectives in this map
None
Objective 2GC-EQU-MOL-02

Reaction quotients and equilibrium expressions

Derive concentration- or pressure-based reaction quotient and equilibrium-constant expressions from a balanced equation, including the correct treatment of phases and stoichiometric coefficients.

Must know
For a stated forward reaction, product terms appear over reactant terms and each variable term is raised to its balanced stoichiometric coefficient. Pure solids and pure liquids have constant activity and are omitted from introductory Q and K expressions; aqueous solutes and gases remain as concentration or partial-pressure terms.
Model boundary
Use the concentration, partial-pressure, or supplied activity convention named in the problem. Rigorous activity coefficients and standard-state derivations are outside this objective unless supplied.
Misconception
A pure solid is omitted from K because it is not involved in the equilibrium. The solid participates in the reaction, but its activity is constant while that pure phase is present, so it does not appear as a variable term.
Earlier objectives in this map
Dynamic equilibrium at the molecular scale
Objective 3GC-EQU-MOL-03

Composition, direction, and the meaning of K

Use the magnitude of an equilibrium constant and a comparison of Q with K to describe equilibrium composition and predict the net direction needed to reach equilibrium.

Must know
At the stated temperature, Q < K predicts a net forward reaction, Q > K predicts a net reverse reaction, and Q = K identifies equilibrium. A large K indicates product-favored equilibrium composition for the reaction as written, while a small K indicates reactant-favored composition; K magnitude does not measure reaction speed.
Model boundary
Compare Q and K only for the same balanced reaction, expression convention, and temperature. Product-favored does not mean complete conversion, and K alone does not specify the time required to equilibrate.
Misconception
A very large equilibrium constant means the forward reaction is fast. K describes the relative equilibrium composition; rate depends on kinetics and can be slow even when products are strongly favored.
Earlier objectives in this map
Reaction quotients and equilibrium expressions
BAcid/base3 objectives
Objective 1GC-EQU-ACB-01

Acid and base constants in the general K framework

Construct and interpret Ka, Kb, and Kw expressions as specific equilibrium constants for stated aqueous proton-transfer reactions.

Must know
Ka and Kb expressions follow the balanced aqueous reaction, with hydronium or hydroxide among the product terms and pure liquid water omitted under the introductory model. For one conjugate acid-base pair at the same temperature, KaKb = Kw; changing temperature can change all three constants and the corresponding neutral pH.
Model boundary
This objective places acid-base constants inside the general equilibrium framework. The completed Acids and Bases route remains the home for pH, strength, Brønsted-Lowry roles, buffers, and titration-region calculations.
Misconception
Liquid water must always appear in every acid-ionization equilibrium expression. Pure liquid water has constant activity and is incorporated into the reported Ka or Kb value in the usual aqueous expression.
Earlier objectives in this map
Reaction quotients and equilibrium expressions
Objective 2GC-EQU-ACB-02

Coupled proton-transfer equilibria

Reverse, scale, or add supplied acid-base equilibria to construct an overall equilibrium constant and use it to identify the thermodynamically favored proton-transfer direction.

Must know
Reversing a reaction replaces K with 1/K, multiplying every coefficient by n replaces K with Kⁿ, and adding reactions multiplies their constants after intermediates cancel. A proton-transfer equilibrium favors the side with the weaker acid and weaker base; compatible Ka, Kb, or pKa data quantify that direction rather than merely naming donor and acceptor roles.
Model boundary
Combine constants only when equations, solvent, temperature, and standard-state conventions are compatible. Supplied equilibrium data outrank an unsupported structural shortcut.
Misconception
When two equilibrium equations are added, their K values are added too. The component reaction quotients multiply, so the corresponding equilibrium constants multiply after the equations are combined.
Earlier objectives in this map
Acid and base constants in the general K framework · Composition, direction, and the meaning of K
Objective 3GC-EQU-ACB-03

Common-ion response and acid-base speciation

Use Q versus K and a species inventory to predict how a common ion or a finite strong-acid or strong-base addition changes a weak acid-base equilibrium.

Must know
Adding a conjugate common ion changes Q and shifts a weak-electrolyte equilibrium toward the un-ionized partner, suppressing further ionization without changing K at constant temperature. A finite strong-acid or strong-base addition reacts stoichiometrically with a buffer partner before the conjugate pair re-equilibrates; buffer pH can change and buffer capacity is not unlimited.
Model boundary
Use this objective for the generalized Q/K explanation of coupled acid-base systems. Numerical initial, buffer, half-equivalence, equivalence, and excess-titrant methods remain in the Acids and Bases learning bank.
Misconception
A buffer keeps pH exactly constant no matter how much acid or base is added. A buffer reduces the pH change only while both conjugate partners retain enough capacity; every finite addition changes their ratio.
Earlier objectives in this map
Coupled proton-transfer equilibria
CPrecipitation3 objectives
Objective 1GC-EQU-PRE-01

Solubility-product expressions and molar solubility

Write a Ksp expression for a sparingly soluble ionic solid and translate between Ksp and molar solubility using the dissolution stoichiometry.

Must know
The pure solid is omitted from Ksp, while each dissolved-ion concentration is raised to its balanced dissolution coefficient. If the molar solubility is s, each equilibrium ion concentration changes by its stoichiometric multiple of s; therefore Ksp equals molar solubility only for particular one-to-one cases under simple conditions.
Model boundary
Do not rank molar solubilities from Ksp values alone when dissolution stoichiometries differ. Complex-ion formation, acid-base coupling, and nonideal activities require supplied equilibria or assumptions.
Misconception
Ksp is always numerically equal to a solid's molar solubility. The ion concentrations and their exponents follow dissolution stoichiometry, so the algebraic relation between Ksp and s depends on the formula.
Earlier objectives in this map
Reaction quotients and equilibrium expressions
Objective 2GC-EQU-PRE-02

Precipitation thresholds after mixing

Calculate the post-mixing ion reaction quotient and compare it with Ksp to classify a solution and predict whether precipitation begins.

Must know
Use concentrations after dilution, mixing, and any prior essentially complete reaction—not the unmixed stock concentrations—to calculate the ion quotient. Q < Ksp is unsaturated with respect to that solid, Q = Ksp is saturated equilibrium, and Q > Ksp predicts precipitation until the dissolved-ion quotient returns to Ksp if the solid phase can form.
Model boundary
The Q/Ksp test predicts thermodynamic direction, not nucleation time or crystal habit. Use activities rather than raw concentrations only when the problem supplies a nonideal model.
Misconception
Precipitation can be predicted by multiplying the two stock-solution concentrations before they are mixed. Mixing changes the total volume and may trigger other stoichiometric reactions, so the quotient must use the actual concentrations in the mixture.
Earlier objectives in this map
Solubility-product expressions and molar solubility · Composition, direction, and the meaning of K
Objective 3GC-EQU-PRE-03

Common ions and selective precipitation

Use common-ion shifts and precipitation thresholds to compare solubility changes or determine which solid begins to precipitate first under controlled conditions.

Must know
Adding a dissolved common ion generally lowers the molar solubility and can increase the amount of solid, whereas adding more of a pure solid to an already saturated mixture does not change dissolved-ion concentrations while that phase is present. Selective precipitation compares the counter-ion concentration required to reach each solid's Ksp after stoichiometry and dilution; the smallest tabulated Ksp does not automatically precipitate first when ion ratios or formulas differ.
Model boundary
Account for complexation, pH-dependent ions, amphoterism, or competing reactions only when their constants and conditions are supplied. Do not infer complete separation merely because one threshold is reached first.
Misconception
The compound with the smallest Ksp always precipitates first from any mixture. The threshold depends on Ksp, dissolution stoichiometry, and the actual ion concentrations, so Ksp alone is insufficient across uncontrolled systems.
Earlier objectives in this map
Precipitation thresholds after mixing
DCalculations3 objectives
Objective 1GC-EQU-CAL-01

Evaluate K and Q from chemical data

Calculate K or Q from equilibrium or snapshot concentrations and partial pressures, then interpret the result in the context of the reaction as written.

Must know
K uses equilibrium values, whereas Q uses the same expression with values from any stated instant; an initial mixture is not automatically at equilibrium. Convert moles to the concentration in the stated total volume or to the appropriate partial pressures before substitution, and preserve the balanced-equation exponents.
Model boundary
Use Kc, Kp, or another named constant consistently. Introductory problems may use dimensionless simplified expressions; do not attach invented units or interchange concentration and pressure values without a valid relationship.
Misconception
The starting concentrations can always be substituted into K because the reaction will eventually equilibrate. Starting values evaluate Q unless the problem explicitly states that the starting mixture is already at equilibrium.
Earlier objectives in this map
Reaction quotients and equilibrium expressions · Composition, direction, and the meaning of K
Objective 2GC-EQU-CAL-02

Transform reactions and equilibrium constants

Determine the constant for a reversed, scaled, or summed reaction and relate Kp to Kc for a stated ideal-gas equilibrium.

Must know
Reverse the reaction to use 1/K, multiply every coefficient by n to use Kⁿ, and add reactions to multiply their constants after all canceled species are verified. For an ideal-gas reaction, Kp = Kc(RT)^Δn, where Δn counts gaseous product coefficients minus gaseous reactant coefficients and excludes condensed and aqueous species.
Model boundary
The target equation must match the transformed equations exactly. Use an R value compatible with the stated pressure standard and temperature in kelvins; activity-based standard-state nuance is outside the objective unless supplied.
Misconception
Doubling every reaction coefficient doubles K. Doubling the coefficients squares every term in the quotient, so the transformed constant is K².
Earlier objectives in this map
Evaluate K and Q from chemical data
Objective 3GC-EQU-CAL-03

ICE-table solutions and physical verification

Use an ICE table and the equilibrium expression to determine unknown equilibrium concentrations, selecting a physical root and verifying the completed model.

Must know
Choose the net direction from the initial inventory or Q, then scale every ICE-table change by the balanced coefficients so all equilibrium concentrations follow one reaction extent. Reject roots that create negative concentrations, substitute the selected values back into K, and verify any small-change approximation against the resulting change rather than assuming it in advance.
Model boundary
Use an algebra-simplifying approximation only when its error is checked against a stated or conventional criterion. Problems requiring coupled nonlinear equilibria need all relevant constants and an explicitly bounded method.
Misconception
Every species changes by the same concentration x in an ICE table. One reaction extent controls the changes, but each species changes by its stoichiometric coefficient times that extent.
Earlier objectives in this map
Evaluate K and Q from chemical data
ELe Chatelier’s principle3 objectives
Objective 1GC-EQU-LCP-01

Concentration stresses through Q and K

Predict the net response to adding or removing a reactant or product by tracking the immediate change in Q and the subsequent return to Q = K.

Must know
At constant temperature, a concentration disturbance can change Q immediately but not K; the system then reacts in the direction that returns Q to K. Changing the amount of a pure solid or pure liquid already present does not change Q or shift the equilibrium composition because that phase has no variable term in the expression.
Model boundary
A shift describes the net reaction after the disturbance, not a promise that every concentration ends above or below its original value. Removing an entire phase can invalidate the model that assumed it was present.
Misconception
An equilibrium shift completely cancels any imposed concentration change. The system responds until Q again equals K; it generally offsets only part of the disturbance rather than restoring every original concentration.
Earlier objectives in this map
Composition, direction, and the meaning of K
Objective 2GC-EQU-LCP-02

Gas volume, pressure, and inert-gas boundaries

Use gas stoichiometry and Qp to predict whether a volume or pressure change shifts an ideal-gas equilibrium, including the boundary for an added inert gas.

Must know
Decreasing volume raises all reactive partial pressures and favors the side with fewer moles of gas; increasing volume favors more gas, while equal gaseous coefficient sums produce no volume-driven shift. Adding an inert gas at constant volume changes total pressure but not the reactive partial pressures or Qp, so it causes no shift in the ideal model; a constant-pressure addition can expand the volume and must be analyzed separately.
Model boundary
Count only gaseous species when comparing gas moles. A pressure change caused by adding a reactive species is a concentration stress, not interchangeable with compression, and nonideal high-pressure behavior requires supplied data.
Misconception
Any increase in total pressure shifts equilibrium toward the side with fewer gas molecules. The cause and constraint matter: an inert gas added at constant volume leaves every reactive partial pressure—and therefore Qp—unchanged.
Earlier objectives in this map
Concentration stresses through Q and K · Transform reactions and equilibrium constants
Objective 3GC-EQU-LCP-03

Temperature, catalysts, and equilibrium position

Predict the effect of a temperature change from the reaction enthalpy and distinguish that equilibrium change from the kinetic effect of a catalyst.

Must know
Temperature is the standard stress here that changes K: heating favors the endothermic direction and cooling favors the exothermic direction, with the direction defined by the reaction and ΔH as written. A catalyst lowers activation barriers for both forward and reverse pathways, speeds approach to equilibrium, and changes neither K nor the equilibrium composition; ordinary concentration or volume stresses also leave K unchanged at fixed temperature.
Model boundary
Do not infer a numerical K at a new temperature without a supplied relationship or data. Equilibrium analysis does not determine a reaction's rate, mechanism, or useful industrial timescale.
Misconception
A catalyst shifts an equilibrium toward products by making the forward reaction faster. The catalyst accelerates both directions and reaches the same equilibrium composition sooner without changing K.
Earlier objectives in this map
Concentration stresses through Q and K

Free source ladder

Trace every boundary.

Official 2026 DAT scopeDefines the five published topic labels—not their weights. ↗OpenStax · Chemical EquilibriaDynamic forward and reverse reactions, constant composition, and molecular-scale equilibrium. ↗OpenStax · Equilibrium ConstantsQ and K expressions, heterogeneous systems, reaction direction, K magnitude, and transformed equations. ↗OpenStax · Shifting EquilibriaConcentration, gas volume, temperature, and catalyst boundaries interpreted through equilibrium response. ↗OpenStax · Equilibrium CalculationsICE tables, equilibrium concentrations, physical roots, and checked algebraic approximations. ↗OpenStax · Relative Strengths of Acids and BasesKa, Kb, pKa, conjugate relationships, and proton-transfer direction. ↗OpenStax · BuffersCommon-ion response, conjugate-pair capacity, and pH limits after finite additions. ↗OpenStax · Precipitation and DissolutionKsp, molar solubility, precipitation thresholds, common ions, and selective precipitation. ↗