IMAT Chemistry · Equilibrium, Kinetics and Energetics

Dynamic Equilibrium and the Equilibrium Constant Kc

At dynamic equilibrium the forward and reverse reactions run at the same rate, and the ratio of product to reactant concentrations, Kc, takes a fixed value at a given temperature.

All Equilibrium, Kinetics and Energetics notes

Why this matters

The 2019 paper asked for a Kc value from equilibrium amounts, and the 2023 paper asked what a very small Kc says about where the equilibrium lies. The 2025 paper used an equilibrium with solids in it, which do not appear in Kc.

Concept 1 of 3: Dynamic equilibrium in a closed system

Picture people walking up a down escalator at exactly the speed it moves: they stay in the same place although both motions continue. In a reversible reaction at equilibrium, reactants keep turning into products and products keep turning back, at exactly the same rate. Nothing seems to change, but nothing has stopped.

Definition

A reversible reaction ( $\rightleftharpoons$ ) in a closed system reaches dynamic equilibrium when:

the forward and reverse rates are equal, and neither is zero;
the concentrations stay constant, but they are generally not equal to each other;
the measurable properties (colour, pressure, density) no longer change.

The same equilibrium mixture is reached whether you start from the reactants or from the products, under the same conditions. An open system, where a gas can escape, cannot reach equilibrium.

Feature	At dynamic equilibrium
Forward and reverse rates	Equal, and both greater than zero
Concentrations	Constant, but usually not equal
System	Closed: no matter enters or leaves
Starting point	The same equilibrium is reached from either side
Evidence that it is dynamic	A labelled isotope added to one side soon appears on the other side

Practice this conceptself-check · 3 quick reps

Equilibrium does not mean equal amounts

At equilibrium the rates are equal, not the concentrations. The mixture may be almost all products, almost all reactants, or anything between, depending on K.

Concept 2 of 3: Writing the Kc expression

At equilibrium, whatever amounts you started with, one particular ratio of concentrations always comes out the same at a given temperature. That ratio puts the products on top and the reactants underneath, each raised to the power of its coefficient in the equation. Its value is the equilibrium constant.

Definition

For $a\mathrm{A} + b\mathrm{B} \rightleftharpoons c\mathrm{C} + d\mathrm{D}$ :

Products over reactants, each concentration (in mol/dm³, at equilibrium) raised to the power of its coefficient.
Pure solids and pure liquids are left out: their concentration does not change. So is water when it is the solvent.
The units of Kc depend on the powers: they cancel when the total powers on top and bottom are equal.
Kc changes only with temperature.
For the reverse reaction the constant is $1/K_c$ .

Equilibrium constant

K_c = \frac{[\mathrm{C}]^c\,[\mathrm{D}]^d}{[\mathrm{A}]^a\,[\mathrm{B}]^b}

$[\ ]$ equilibrium concentration, in mol/dm³
$a, b, c, d$ coefficients in the balanced equation

Worked example

Write Kc, with units, for

\mathrm{N_2(g) + 3H_2(g) \rightleftharpoons 2NH_3(g)}

, and for

\mathrm{CaCO_3(s) \rightleftharpoons CaO(s) + CO_2(g)}

Practice this conceptself-check · 3 quick reps

Solids and pure liquids are not in Kc

A solid's concentration is fixed by its density, so it is left out of Kc. Adding or removing some of a solid therefore does not shift an equilibrium. To shift it, change the concentration of a gas or a dissolved species, or the temperature.

Concept 3 of 3: Calculating Kc and what its size means

Kc is a single number that tells you where the equilibrium lies. A huge Kc means the top of the fraction, the products, dominates: the reaction goes almost to completion. A tiny Kc means hardly any products form. To calculate it, you need equilibrium concentrations, so moles must be divided by the volume first.

Definition

Convert every equilibrium amount to a concentration: $c = n/V$ . The volume cancels only when the total powers on top and bottom are equal.
If you are given starting amounts, use a table of initial, change, equilibrium amounts, with the changes in the ratio of the coefficients.
$K_c \gg 1$ : the equilibrium lies to the right (mostly products). $K_c \ll 1$ : it lies to the left (mostly reactants).
K tells you how far, never how fast.
The reaction quotient $Q$ uses the same expression with the current concentrations. If $Q < K$ the reaction moves forward; if $Q > K$ it moves backward; if $Q = K$ it is at equilibrium.

Concentration from amount

c = \frac{n}{V}

$c$ concentration, in mol/dm³
$n$ amount at equilibrium, in mol
$V$ volume of the vessel, in dm³

Worked example

\mathrm{PCl_5(g) \rightleftharpoons PCl_3(g) + Cl_2(g)}

is at equilibrium in a 2.0 dm³ vessel with 0.40 mol

\mathrm{PCl_5}

, 0.20 mol

\mathrm{PCl_3}

and 0.20 mol

\mathrm{Cl_2}

. Find Kc.

Practice this conceptself-check · 4 quick reps

A small Kc means few products, not fewer moles on one side

A Kc much smaller than 1 tells you the equilibrium lies to the left, with mostly reactants. It says nothing about which side of the equation has more moles, and nothing about how fast equilibrium is reached.

Summary — formulas & gotchas at a glance

A revision cheat-sheet for the formulas and gotchas above. Click any concept name to jump back to its full explanation.

Formulas (2)

Writing the Kc expression
Equilibrium constant
$K_c = \frac{[\mathrm{C}]^c\,[\mathrm{D}]^d}{[\mathrm{A}]^a\,[\mathrm{B}]^b}$
Calculating Kc and what its size means
Concentration from amount
$c = \frac{n}{V}$

Reference tables (1)

Dynamic equilibrium in a closed system5 rows

Feature	At dynamic equilibrium
Forward and reverse rates	Equal, and both greater than zero
Concentrations	Constant, but usually not equal
System	Closed: no matter enters or leaves
Starting point	The same equilibrium is reached from either side
Evidence that it is dynamic	A labelled isotope added to one side soon appears on the other side

Watch out for (3)

Equilibrium does not mean equal amounts
→ Dynamic equilibrium in a closed system
Solids and pure liquids are not in Kc
→ Writing the Kc expression
A small Kc means few products, not fewer moles on one side
→ Calculating Kc and what its size means

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