ChemistryEquilibriumA-Level

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Equilibrium constant

Expression for equilibrium constant Kc.

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

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Core idea

Overview

The equilibrium constant (Kc) defines the ratio of product concentrations to reactant concentrations at a state of dynamic equilibrium for a chemical system at a specific temperature. It is derived from the law of mass action, where each concentration is raised to the power of its stoichiometric coefficient from the balanced chemical equation.

When to use: This equation is used when a reversible chemical reaction has reached dynamic equilibrium in a closed system at constant temperature. It applies to solutes in a solution or gases, provided their concentrations are expressed in molarity (mol/L).

Why it matters: The value of Kc indicates the extent of a reaction; a large Kc favors products, while a small Kc favors reactants. This is essential for industrial chemists to calculate theoretical yields and optimize reaction conditions for maximum efficiency.

Symbols

Variables

ratio = Equilibrium Ratio, K_c = Equilibrium Constant

r a t i o

Equilibrium Ratio

V a r iab l e

K_{c}

Equilibrium Constant

V a r iab l e

Walkthrough

Derivation

Formula: Equilibrium Constant (Kc)

Gives the ratio of product to reactant concentrations at equilibrium, each raised to their stoichiometric coefficients.

System is at dynamic equilibrium in a closed system.
Concentrations are used as an approximation to activities (A-Level treatment).

Write a General Reaction:

Lowercase coefficients a, b, c, d come from the balanced equation.

a A + b B ⇌ c C + d D

State the Kc Expression:

At a fixed temperature, Kc is constant for the reaction.

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

Note: Pure solids and pure liquids are omitted because their concentration is effectively constant.

Result

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

Source: AQA A-Level Chemistry — Equilibria

Free formulas

Rearrangements

Solve for $r a t i o$

Make ratio the subject

r a t i o = \frac{[ C ] ^{c} [ D ] ^{d}}{[ A ] ^{a} [ B ] ^{b}}

The ratio of products to reactants at equilibrium is the equilibrium constant Kc.

Difficulty: 1/5

Solve for $K_{c}$

Make Kc the subject

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

The equilibrium constant Kc is expressed as the ratio of product concentrations to reactant concentrations, each raised to their stoichiometric coefficients.

Difficulty: 1/5

The static page shows the finished rearrangements. The app keeps the full worked algebra walkthrough.

Visual intuition

Graph

Graph unavailable for this formula.

The graph of the equilibrium constant (Kc) against an independent variable representing reactant or product concentration follows a power law relationship. Depending on the stoichiometric coefficients, the curve shows non-linear growth or decay as the concentration changes, reflecting the multiplicative nature of the equilibrium expression.

Graph type: power_law

Why it behaves this way

Intuition

A dynamic balance where molecules continuously interconvert between reactants and products, but the overall macroscopic concentrations remain constant, like a two-way street with equal traffic flow in both directions

K_{c}

The ratio of the product of equilibrium molar concentrations of products to the product of equilibrium molar concentrations of reactants, each raised to the power of its

It quantifies the relative amounts of products and reactants present at equilibrium, indicating the reaction's tendency to proceed towards products (large Kc) or reactants (small Kc).

[A], [B], [C], [D]

The molar concentration (mol/L) of species A, B, C, or D, respectively, at the point of dynamic equilibrium.

Represents the effective 'amount per volume' of each substance available to participate in the forward or reverse reaction once equilibrium is established.

a, b, c, d

The stoichiometric coefficients of species A, B, C, or D, respectively, as determined by the balanced chemical equation.

These exponents reflect the sensitivity of the equilibrium position to changes in the concentration of that particular species, stemming from the molecularity of the reaction steps.

Signs and relationships

Exponents c, d, a, b: The concentrations are raised to the power of their stoichiometric coefficients because, according to the Law of Mass Action, the rate of an elementary reaction step is proportional to the product of reactant
Division (products in numerator, reactants in denominator): This ratio structure defines Kc as a measure of the extent of reaction. A higher concentration of products (numerator) relative to reactants (denominator)

Free study cues

Insight

Canonical usage

Units for Kc are derived by substituting the concentration units (typically mol dm^-3) into the equilibrium expression and simplifying based on the stoichiometric coefficients of the balanced equation.

Common confusion

Assuming Kc always has the same units or is always dimensionless; units change depending on the change in the number of moles (Δn) between products and reactants.

Dimension note

Kc is dimensionless only when the sum of the stoichiometric coefficients of the products equals the sum of the stoichiometric coefficients of the reactants.

Unit systems

$[X]$ mol dm^-3 · Concentration of species X. In A-level chemistry, the unit mol dm^-3 is standard; in some contexts, mol L^-1 is used interchangeably.

$a, b, c, d$ dimensionless · Stoichiometric coefficients from the balanced chemical equation.

One free problem

Practice Problem

In the reversible reaction N₂O₄(g) ⇌ 2NO₂(g), a chemist measures the equilibrium molarities and determines that the expression [NO₂]² / [N₂O₄] yields a value of 0.00463. Calculate the equilibrium constant Kc for this reaction.

Equilibrium Ratio0.00463

Solve for: $K c$

Hint: At equilibrium, the equilibrium constant Kc is numerically equal to the concentration ratio of products to reactants.

The full worked solution stays in the interactive walkthrough.

Where it shows up

Real-World Context

Calculating Kc for the Haber process at equilibrium.

Study smarter

Tips

Pure solids and pure liquids are assigned an activity of 1 and are omitted from the expression.
The value of Kc is constant for a specific reaction at a specific temperature and does not change with concentration or pressure.
Ensure the chemical equation is fully balanced to correctly identify the stoichiometric exponents for each species.

Avoid these traps

Common Mistakes

Including solids or pure liquids.
Forgetting to use equilibrium concentrations.

Common questions

Frequently Asked Questions

Gives the ratio of product to reactant concentrations at equilibrium, each raised to their stoichiometric coefficients.

This equation is used when a reversible chemical reaction has reached dynamic equilibrium in a closed system at constant temperature. It applies to solutes in a solution or gases, provided their concentrations are expressed in molarity (mol/L).

The value of Kc indicates the extent of a reaction; a large Kc favors products, while a small Kc favors reactants. This is essential for industrial chemists to calculate theoretical yields and optimize reaction conditions for maximum efficiency.

Including solids or pure liquids. Forgetting to use equilibrium concentrations.