Equilibrium Constant Formula

Equilibrium constant is the ratio of product concentrations to reactant concentrations at equilibrium, each raised to its stoichiometric coefficient.

The Formula

K_c = \frac{[C]^c[D]^d}{[A]^a[B]^b} \quad \text{for } aA + bB \rightleftharpoons cC + dD

When to use: K is the scoreboard at the end of the game — it tells you which side won. Large K means products dominate; small K means reactants dominate.

Quick Example

For the reaction N₂O₄ ⇌ 2NO₂,

K_c = \frac{[NO_2]^2}{[N_2O_4]}

. If K = 0.2 at 25°C, the colorless N₂O₄ dominates — the mixture stays mostly clear.

Notation

K_c

uses molar concentrations (mol/L) in square brackets.

K_p

uses partial pressures (atm) for gaseous equilibria. The subscript tells you which units the expression uses.

What This Formula Means

The ratio of product concentrations to reactant concentrations at equilibrium, each raised to its stoichiometric coefficient.

K is the scoreboard at the end of the game — it tells you which side won. Large K means products dominate; small K means reactants dominate.

Formal View

For gaseous systems,

K_p = \frac{(P_C)^c(P_D)^d}{(P_A)^a(P_B)^b}

. The two forms are related by

K_p = K_c(RT)^{\Delta n}

where

\Delta n = (c+d)-(a+b)

is the change in moles of gas.

Worked Examples

Example 1

medium

For

N_2O_4 \rightleftharpoons 2NO_2

[N_2O_4] = 0.040

M and

[NO_2] = 0.040

M at equilibrium. Find

K_c

Answer

K_c = 0.040

First step

K_c = [NO_2]^2 / [N_2O_4]

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Example 2

medium

For

A \rightleftharpoons B

K_1 = 4

. If reaction 2 is

B \rightleftharpoons A

, what is

K_2

Example 3

hard

For

H_2 + I_2 \rightleftharpoons 2HI

, a

1.0

L vessel initially holds

0.50

mol

H_2

and

0.50

mol

I_2

. At equilibrium

[HI] = 0.80

M. Find

K_c

Common Mistakes

Including pure solids or pure liquids in the equilibrium expression — only aqueous $(aq)$ and gaseous $(g)$ species appear in $K$ - Fix this by naming the substances or sample, checking "Am I tracking reactants, products, atom conservation, evidence of new substances, and the balanced equation?", and attaching units, formulas, states, or evidence to the final statement. - Fix this by naming the substances or sample, checking "Am I tracking reactants, products, atom conservation, evidence of new substances, and the balanced equation?", and attaching units, formulas, states, or evidence to the final statement.
Forgetting to raise concentrations to the power of their coefficients — for $2A \rightleftharpoons B$ , $K = \frac{[B]}{[A]^2}$ , not $\frac{[B]}{[A]}$ - Fix this by naming the substances or sample, checking "Am I tracking reactants, products, atom conservation, evidence of new substances, and the balanced equation?", and attaching units, formulas, states, or evidence to the final statement. - Fix this by naming the substances or sample, checking "Am I tracking reactants, products, atom conservation, evidence of new substances, and the balanced equation?", and attaching units, formulas, states, or evidence to the final statement.
Thinking changing concentration changes $K$ — adding or removing a substance changes the reaction quotient $Q$ , but $K$ remains constant unless temperature changes - Fix this by naming the substances or sample, checking "Am I tracking reactants, products, atom conservation, evidence of new substances, and the balanced equation?", and attaching units, formulas, states, or evidence to the final statement. - Fix this by naming the substances or sample, checking "Am I tracking reactants, products, atom conservation, evidence of new substances, and the balanced equation?", and attaching units, formulas, states, or evidence to the final statement.
Using equilibrium constant from a keyword alone - Signal words like reaction, reactant, product only point to a possible model; the substances and evidence must match too. - Fix this by naming the substances or sample, checking "Am I tracking reactants, products, atom conservation, evidence of new substances, and the balanced equation?", and attaching units, formulas, states, or evidence to the final statement.

Why This Formula Matters

Equilibrium Constant is central because chemistry studies how substances transform while atoms are conserved. It makes symbolic equations, lab evidence, and particle rearrangements part of one explanation.

Frequently Asked Questions

What is the Equilibrium Constant formula?

The ratio of product concentrations to reactant concentrations at equilibrium, each raised to its stoichiometric coefficient.

How do you use the Equilibrium Constant formula?

K is the scoreboard at the end of the game — it tells you which side won. Large K means products dominate; small K means reactants dominate.

What do the symbols mean in the Equilibrium Constant formula?

$K_c$ uses molar concentrations (mol/L) in square brackets. $K_p$ uses partial pressures (atm) for gaseous equilibria. The subscript tells you which units the expression uses.

Why is the Equilibrium Constant formula important in Chemistry?

What do students get wrong about Equilibrium Constant?

Students often know a formula related to equilibrium constant but skip the recognition step: Am I tracking reactants, products, atom conservation, evidence of new substances, and the balanced equation? That leads to a correct-looking substitution attached to the wrong chemical model.

What should I learn before the Equilibrium Constant formula?

Before studying the Equilibrium Constant formula, you should understand: equilibrium, concentration.

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Related Concepts

Chemical Equilibrium Concentration Le Chatelier's Principle

Related Formulas

Concentration Formula