Difficulty: Intermediate | Prerequisites: Balancing chemical equations, basic thermodynamics concepts (enthalpy, entropy, Gibbs free energy).
Chemical reactions rarely go all the way to completion. Most reach a point where the forward and reverse processes balance out, and concentrations stop changing. This chapter introduces that balance point, called equilibrium, and the mathematics that describe it. You will need a solid grasp of balancing equations and a passing familiarity with Gibbs free energy (ΔG) and entropy. If those feel shaky, revisit your thermodynamics notes first.
Equilibrium sits at the heart of general chemistry and keeps reappearing in acid-base chemistry, solubility, electrochemistry, and biochemistry. The tools you learn here, the equilibrium constant and the reaction quotient, are the same tools you will use to predict whether a reaction will proceed forward, shift backward, or sit still.
At equilibrium, the forward and reverse reactions run at the same rate, so concentrations hold steady. The equilibrium constant K tells you where that balance lies. The reaction quotient Q is the same formula applied at any moment, and comparing Q to K tells you which direction the reaction still needs to shift.
Dynamic equilibrium
The state in which the forward and reverse reactions proceed at equal rates, resulting in no net change in the concentrations of reactants or products.
In simple terms, both reactions are still happening, but they cancel each other out so nothing appears to change.
Static equilibrium
A state in which the forward and reverse reactions have both stopped entirely.
Think of it as a completely frozen system, not just a balanced one. Rare in chemistry; mostly a contrast to dynamic equilibrium.
Entropy
A measure of the distribution of energy throughout a system or between a system and its environment.
In simple terms, entropy tracks how spread out the energy is. Systems at equilibrium tend to have maximum entropy and minimum Gibbs free energy.
Equilibrium constant (K_eq)
The ratio of product concentrations to reactant concentrations, each raised to the power of its stoichiometric coefficient, measured at equilibrium and at a fixed temperature.
Think of it as a single number that tells you where the balance point sits: large K means mostly products, small K means mostly reactants.
K_c
The equilibrium constant expressed in terms of molar concentrations.
K_p
The equilibrium constant expressed in terms of partial pressures. Used when the species involved are gases.
Reaction quotient (Q)
The same mathematical expression as K_eq, but calculated using concentrations (or pressures) at any point during the reaction, not only at equilibrium.
Think of it as a snapshot of where the reaction is right now, which you compare against K to work out which way it still needs to shift.
Gibbs free energy (ΔG)
The thermodynamic quantity that determines whether a process is spontaneous. At equilibrium, ΔG = 0.
In simple terms, ΔG tells you whether a reaction will proceed on its own. Negative ΔG means it will; positive ΔG means it will not; zero means it has reached equilibrium.
Reversible reactions do not proceed to completion. Instead, products begin reacting back into reactants as soon as they form.
At dynamic equilibrium, forward and reverse reactions occur at the same rate.
Concentrations of reactants and products stop changing, but the two sides are not necessarily at equal concentrations.
Both reactions are still running; the system is not static.
Static equilibrium is the contrasting case: both reactions have stopped entirely. This distinction matters on exams.
At a given temperature, a system reaches equilibrium when entropy is maximised and Gibbs free energy is minimised.
For a balanced reaction aA + bB ⇌ cC + dD at constant temperature:
K_eq = [C]^c [D]^d / [A]^a [B]^b
K_c uses molar concentrations; K_p uses partial pressures (for gaseous systems).
The exponents in the equilibrium expression equal the stoichiometric coefficients in the balanced equation.
This is different from rate laws, where exponents are found experimentally and often do not match the coefficients.
K_eq can also be understood as the ratio of forward to reverse rate constants: K_eq = k_forward / k_reverse.
For a multi-step reaction, the overall K_eq is the product of the K values for each individual step.
Pure solids and pure liquids are excluded from the equilibrium expression. Their concentrations are constant and folded into K.
K_eq is temperature-dependent. A value of K is only valid at the temperature at which it was measured.
A large K_eq (much greater than 1) means the equilibrium position favours products.
A small K_eq (much less than 1) means the equilibrium position favours reactants.
Q uses the same formula as K_eq, but is calculated from concentrations at any point during the reaction, not only at equilibrium.
Comparing Q to K_eq tells you the direction the reaction must shift:
Q < K_eq: The reaction has not yet reached equilibrium. There are too many reactants relative to products. The forward reaction speeds up (ΔG < 0) until equilibrium is restored.
Q = K_eq: The system is at equilibrium. Forward and reverse rates are equal. ΔG = 0.
Q > K_eq: The reaction has overshot equilibrium. There are too many products. The reverse reaction speeds up (ΔG > 0) until equilibrium is restored.
Once at equilibrium, any further net movement in either direction is non-spontaneous.
Pure solids and pure liquids do not appear in the equilibrium expression.
K_eq is defined at a set temperature. Change the temperature and you change K.
Large K_eq (>> 1): products dominate at equilibrium.
Small K_eq (<< 1): reactants dominate at equilibrium.
These rules are the foundation for predicting how a system responds to disturbances (Le Chatelier's Principle, covered in the companion notes).
Equilibrium constant expression
For aA + bB ⇌ cC + dD:
K_eq = [C]^c · [D]^d / [A]^a · [B]^b
Reaction quotient
Q_c = [C]^c · [D]^d / [A]^a · [B]^b (at any point, not only at equilibrium)
Relationship between K_eq and rate constants
K_eq = k_forward / k_reverse
Q vs K decision rule
Q < K_eq: ΔG < 0, reaction proceeds forward (→)
Q = K_eq: ΔG = 0, system is at equilibrium
Q > K_eq: ΔG > 0, reaction proceeds in reverse (←)
Industrial chemists use equilibrium principles to maximise yield in processes like the Haber process for ammonia synthesis: they manipulate concentration, pressure, and temperature to push the reaction toward products. The same logic applies in biological systems, where the bicarbonate buffer system in your blood uses equilibrium shifts to regulate pH in real time.
Students often think dynamic equilibrium means the concentrations of reactants and products are equal. They are not. "No net change" is not the same as "equal amounts."
Students confuse the exponents in equilibrium expressions with those in rate laws. In K expressions, the exponents always match the balanced equation's stoichiometric coefficients. In rate laws, exponents are determined experimentally.
Students sometimes include pure solids or pure liquids in the equilibrium expression. These are excluded because their concentrations are constant.
Students assume K_eq changes when you add or remove a reactant. It does not. K_eq only changes with temperature. Adding or removing a substance changes Q, not K.
⚠️ Know the difference between dynamic and static equilibrium. Exams love this distinction.
⚠️ Be able to write a K expression from a balanced equation, correctly excluding solids and liquids.
⚠️ Given Q and K, you must be able to predict the direction of shift and state the sign of ΔG.
⚠️ Know that K_eq = k_forward / k_reverse. This links equilibrium to kinetics.
⚠️ For multi-step reactions, the overall K is the product of the individual K values. This comes up in calculation problems.
True or false: At dynamic equilibrium, the concentrations of products and reactants are always equal.
False. They are constant, not equal.
Fill in the blank: The equilibrium constant K_eq only changes when ______ changes.
Temperature.
True or false: Pure solids should be included in the equilibrium expression.
False. Pure solids and pure liquids are excluded.
Fill in the blank: If Q < K_eq, the reaction shifts toward the ______.
Products (forward direction).
True or false: In equilibrium expressions, the exponents are determined experimentally.
False. They equal the stoichiometric coefficients. (Experimental exponents are for rate laws.)
Q: Write the equilibrium expression for the reaction 2 SO₂(g) + O₂(g) ⇌ 2 SO₃(g).
A: K_eq = [SO₃]² / ([SO₂]² · [O₂])
Q: A reaction has K_eq = 4.0 × 10⁻³ at 300 K. Does the equilibrium position favour reactants or products?
A: K_eq is much less than 1, so the equilibrium strongly favours reactants.
Q: At a certain moment, Q = 10 and K_eq = 2 for a reaction. In which direction will the reaction shift?
A: Q > K_eq, so the reaction shifts to the left (reverse direction) to reduce product concentrations and restore equilibrium.
Q: Why are pure solids excluded from the equilibrium expression?
A: The concentration of a pure solid is constant (determined by its density and molar mass), so it is folded into the value of K rather than written separately.
Q: A reaction proceeds in two steps with K₁ = 5 and K₂ = 3. What is the overall K_eq?
A: K_eq = K₁ × K₂ = 5 × 3 = 15.
This connects to Le Chatelier's Principle (covered in the companion document) because understanding K and Q is the prerequisite for predicting how a system responds to disturbances in concentration, pressure, or temperature.
Equilibrium concepts also feed directly into acid-base chemistry (Ka, Kb), solubility (Ksp), and electrochemistry (the Nernst equation relates cell potential to Q). If you are comfortable with K and Q here, those later topics will feel like the same idea with different letters.
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