Equilibrium
Chemical equilibrium describes the state a reversible reaction settles into once the forward and reverse reactions proceed at equal rates.
Chemical equilibrium describes the state a reversible reaction settles into once the forward and reverse reactions proceed at equal rates. This subtopic defines equilibrium, introduces the equilibrium constant K and its ICE-table calculation, and shows how comparing the reaction quotient Q to K predicts which direction a reaction will shift — and whether that shift is spontaneous.
Key Takeaways
Chemical equilibrium is the dynamic state where a reversible reaction's forward and reverse rates are equal, keeping concentrations constant over time.
The equilibrium constant expression, K = [C]^c[D]^d/[A]^a[B]^b for aA+bB⇌cC+dD, follows from the Law of Mass Action and uses stoichiometric coefficients as exponents.
Keq is the general term; Kc (concentrations) equals Keq for dilute solutions; Kp (partial pressures) is used for gases.
The ICE table (Initial, Change, Equilibrium) calculates equilibrium concentrations; the 5% rule lets you skip the quadratic formula when the change x is under 5% of the initial concentration.
The reaction quotient Q uses the same expression as K but at any point in time. Comparing Q to Keq predicts direction: Q<Keq shifts forward, Q=Keq is equilibrium, Q>Keq shifts in reverse — and correspondingly, ΔG<0, ΔG=0, or ΔG>0.
Pure solids/liquids are excluded from K, K depends on temperature, a larger Keq favors products, and a reverse reaction's K is 1/Keq of the forward reaction.
Kinetics vs. Equilibrium
Kinetics and equilibrium both describe chemical reactions, but they answer different questions:
Kinetics is the study of reaction rate — how fast a reaction proceeds from reactants to products. Factors like concentration, temperature, and catalysts affect this speed.
Equilibrium is concerned with a reaction's destination — the state where the concentrations of reactants and products stop changing because the forward and reverse reactions are proceeding at the same rate.
Kinetics tells you how fast a reaction runs; equilibrium tells you how far it goes.
Reversible vs. Irreversible Reactions
Reactions fall into two categories based on directionality:
Irreversible reactions proceed in one direction only. Once reactants convert to products, the reaction stops, because the products don't readily convert back. Combustion of gasoline is a typical example — the energy and gases released don't easily reform into gasoline.
Reversible reactions don't proceed to completion. Products can react to regenerate the original reactants, and this back-and-forth can continue indefinitely.
For a reversible reaction, chemical equilibrium is the state where the forward rate (reactants → products) equals the reverse rate (products → reactants). This keeps both reactant and product concentrations constant over time — but the reaction hasn't stopped. It's a dynamic equilibrium: both directions are still occurring, just at matched rates.
The Equilibrium Constant Expression
To quantify a chemical equilibrium, chemists use the equilibrium constant, K. For a generic reversible reaction:
aA + bB ⇌ cC + dD
the equilibrium constant expression is:
K = [C]^c[D]^d / [A]^a[B]^b
Product concentrations, each raised to its stoichiometric coefficient, are multiplied together in the numerator; reactant concentrations, similarly raised to their coefficients, are multiplied together in the denominator.
This expression comes from the Law of Mass Action, which states that at equilibrium, the rate of the forward reaction equals the rate of the reverse reaction. This is why the equilibrium constant expression uses the reaction's stoichiometric coefficients as exponents — unlike a kinetic rate law, where exponents (reaction orders) must be determined experimentally, K's exponents represent the actual proportions of molecules present at the equilibrium balance point itself.
Keq, Kc, and Kp
You'll encounter a few different labels for the equilibrium constant, each with a specific context:
Keq — the general equilibrium constant, usable for any reaction at equilibrium.
Kc — the equilibrium constant expressed in terms of molar concentrations, used for reactions in solution.
Kp — the equilibrium constant expressed in terms of partial pressures, used for gas-phase reactions.
For dilute solutions — the relevant case for most MCAT purposes — Keq = Kc, both calculated in units of concentration.
Calculating Equilibrium Concentrations — The ICE Table
Given initial concentrations and a value for K, you can calculate the equilibrium concentrations of every species using an ICE table — an organized way to track three stages:
Initial (I): the starting concentrations of reactants and products.
Change (C): the change in concentration, represented with a variable x, as the system moves toward equilibrium.
Equilibrium (E): the final concentrations, found as initial ± change (I ± C = E).
Solving directly for x can require the quadratic formula, which is often more work than the exam calls for. In many cases, you can simplify with the 5% rule (also called the small-x approximation): if the change x turns out to be less than 5% of the initial concentration, x is considered negligible compared to that initial value, and a term like (initial − x) can be approximated as just the initial concentration. This is often valid when K is very small or very large, or when the initial concentration is significantly larger than the expected change. Without this assumption, solving requires the quadratic formula — outside the scope of the exam. Conceptually, it's worth knowing when the assumption breaks down: if K is a similar magnitude to the initial concentrations, or there isn't a large excess of reactant, you can't make this simplification and must solve exactly.
Worked Example — ICE Table with the 5% Rule
The transcript for this subtopic references a guided ICE-table example, but its numeric values and reaction identity weren't recoverable from the source (the extracted text mixes fragments of more than one on-screen example with no usable numbers). The example below is an original, independently-checked illustration of the same ICE table and 5% rule method described above — not a transcript-sourced problem.
Consider the gas-phase equilibrium:
A(g) ⇌ B(g) + C(g), with Kc = 1.8 × 10⁻⁵, starting from [A]₀ = 0.100 M and no initial B or C.
A | B | C | |
|---|---|---|---|
Initial | 0.100 | 0 | 0 |
Change | −x | +x | +x |
Equilibrium | 0.100 − x | x | x |
Setting up the equilibrium expression:
Kc = [B][C] / [A] = x² / (0.100 − x)
Since Kc is very small relative to the initial concentration, apply the 5% rule and approximate 0.100 − x ≈ 0.100:
1.8×10⁻⁵ ≈ x² / 0.100, so x² = 1.8×10⁻⁶, so x = 1.34×10⁻³ M
Checking the 5% rule: x/[A]₀ = (1.34 × 10⁻³)/0.100 = 1.34%, well under 5% — the approximation holds.
Equilibrium concentrations: [A] ≈ 0.0987 M, [B] = [C] ≈ 1.34 × 10⁻³ M.
The Reaction Quotient (Q) and Predicting Reaction Direction
Reaching equilibrium takes time — anywhere from microseconds to millennia, depending on the forward and reverse reaction rates. To gauge how far along a reaction is at any given moment, chemists use the reaction quotient, Q, calculated with the same expression as K but using the concentrations present at that specific point in time — not just at equilibrium.
Q is a "snapshot" of the reaction at a moment in time; Keq describes the reaction's "end state." Comparing the two predicts which direction the reaction will shift to reach equilibrium:
Q < Keq: more reactants (and fewer products) than at equilibrium. The forward reaction rate increases, and the reaction proceeds forward — converting more reactants to products — to restore equilibrium.
Q = Keq: the reaction is at dynamic equilibrium. Reactants and products are present in equilibrium proportions, and the forward and reverse rates are equal.
Q > Keq: more products (and fewer reactants) than at equilibrium. The reverse reaction rate increases, and the reaction proceeds in reverse — converting products back to reactants — to restore equilibrium.
Q, Keq, and Spontaneity (ΔG)
Comparing Q to Keq also connects directly to Gibbs free energy (ΔG) and whether a reaction proceeds spontaneously:
Q < Keq: there's a higher concentration of reactants relative to products than at equilibrium. ΔG < 0 — the forward reaction is spontaneous, and the reaction proceeds forward until equilibrium is reached.
Q = Keq: the reaction is at equilibrium. ΔG = 0 — a state of dynamic equilibrium, with no net change in reactant or product concentrations.
Q > Keq: there's a higher concentration of products relative to reactants than at equilibrium. ΔG > 0 — the forward reaction is non-spontaneous, and the reaction proceeds in reverse until equilibrium is reached.
Rules Governing the Equilibrium Constant
A few closing rules apply broadly to K:
Pure solids and pure liquids are excluded from the equilibrium constant expression — their activities are defined as 1, so they don't appear in K.
K is temperature-dependent. The equilibrium constant is characteristic of a specific reaction at a given temperature; changing the temperature changes the value of K.
The magnitude of Keq indicates which side is favored. A larger Keq means the equilibrium position lies further toward products (to the right); a smaller Keq means it favors reactants.
The reverse reaction's K is the reciprocal. If the forward reaction has equilibrium constant Keq, the reverse reaction's equilibrium constant is 1/Keq.
Common MCAT Mistakes
Forgetting to raise concentrations to their stoichiometric coefficients. The exponents in K aren't optional — a coefficient of 2 in the balanced equation means that species' concentration is squared in the equilibrium expression.
Including pure solids or liquids in the equilibrium expression. Their activities are defined as 1, so they're left out of K entirely — only aqueous species and gases appear.
Confusing Q and K. K is a fixed value at a given temperature, describing the reaction at equilibrium. Q uses the identical expression but plugs in concentrations at any arbitrary moment — it changes as the reaction proceeds and equals K only once equilibrium is reached.
Applying the 5% rule without checking it. The approximation is only valid if x actually turns out to be under 5% of the initial concentration — skipping the check (or applying it when K is comparable in magnitude to the initial concentrations) can produce a meaningfully wrong answer.
MCAT-Style Concept Check
Question: At a given temperature, a reaction has Keq = 4.0. At a particular moment, the reaction mixture has Q = 1.0. What will happen, and what is true of ΔG at that moment?
A) The reaction proceeds forward; ΔG < 0
B) The reaction proceeds forward; ΔG > 0
C) The reaction proceeds in reverse; ΔG < 0
D) The reaction proceeds in reverse; ΔG > 0
Answer: A
Explanation: Since Q (1.0) is less than Keq (4.0), the mixture has more reactants relative to products than it will at equilibrium. The forward reaction rate increases to restore equilibrium, so the reaction proceeds forward — converting reactants to products — and this forward progress is spontaneous, meaning ΔG < 0.
FAQ
What's the difference between Q and Keq?
Both use the identical equilibrium-constant expression, but Keq is calculated from concentrations at equilibrium (a fixed value at a given temperature), while Q is calculated from concentrations at any arbitrary point in time. Comparing Q to Keq tells you which direction a reaction needs to shift to reach equilibrium.
Why are pure solids and liquids left out of the equilibrium constant expression?
Their activities are defined as 1 regardless of how much is present, so including them wouldn't change the numeric value of K — only aqueous species and gases, whose concentrations or partial pressures actually vary, appear in the expression.
When can you use the 5% rule instead of the quadratic formula?
When the calculated change in concentration, x, turns out to be less than 5% of the initial concentration. This is common when K is very small or very large relative to the initial concentrations. If x turns out to be 5% or more of the initial concentration, the approximation isn't valid and the quadratic formula is required instead.
Does a larger Keq mean the reaction is faster?
No — Keq describes a reaction's equilibrium position (how far it goes, favoring products vs. reactants), not its rate (how fast it gets there). A reaction can have a very large Keq and still take a long time to reach that equilibrium; rate and equilibrium position are governed by separate factors.
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