The Equilibrium Law Revision Notes for VCE SSCE Chemistry

The Equilibrium Law

Introduction

When a reversible chemical reaction reaches equilibrium, there is a special relationship between the amounts of reactants and products present. Understanding this relationship allows you to predict how much of each substance will be in an equilibrium mixture.

This note focuses on homogeneous chemical systems, where all reactants and products are in the same physical state (all gases, or all aqueous solutions, for example). This differs from heterogeneous chemical systems, where reactants and products exist in different states (such as solids mixed with gases).

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Throughout this note, we'll work with homogeneous systems where the equilibrium law can be applied directly to concentration values. Heterogeneous systems require special treatment that we'll cover in later notes.

The reaction quotient

What is the reaction quotient?

Consider the equilibrium system for ammonia production:

$\text{N}_2(g) + 3\text{H}_2(g) \rightleftharpoons 2\text{NH}_3(g)$

For this reversible reaction, you can prepare an unlimited number of different equilibrium mixtures containing nitrogen, hydrogen, and ammonia. Each mixture will have different concentrations of the three gases, but they all share a special mathematical relationship.

The reaction quotient, $Q$ , (also called the concentration fraction) is a ratio that compares the concentrations of products to reactants at any point during a reaction. For the ammonia synthesis reaction, the reaction quotient is:

$Q = \frac{[\text{NH}_3]^2}{[\text{N}_2][\text{H}_2]^3}$

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Notice how the coefficients from the balanced equation (1 for N₂, 3 for H₂, and 2 for NH₃) become the powers (indices) in the expression. This is a crucial pattern that applies to all equilibrium systems.

The reaction quotient at equilibrium

The table below shows four different equilibrium mixtures for the ammonia synthesis reaction at a constant temperature of 400°C:

Equilibrium mixture	[N₂] (M)	[H₂] (M)	[NH₃] (M)	$\frac{[\text{NH}_3]^2}{[\text{N}_2][\text{H}_2]^3}$
1	0.25	0.75	0.074	0.052
2	0.55	0.65	0.089	0.052
3	0.0025	0.0055	$4.6 \times 10^{-6}$	0.051
4	0.0011	0.0011	$2.7 \times 10^{-7}$	0.051

The remarkable feature shown in this table is that the reaction quotient has an almost constant value of approximately 0.052 for each equilibrium mixture, despite the very different concentrations of the individual components. Some mixtures have high concentrations of all three gases, while others have very low concentrations, yet the ratio remains constant.

This observation reveals a fundamental principle: while you can calculate the reaction quotient $Q$ for any mixture of reactants and products at any time during a reaction, it only has a constant value when the mixture is at equilibrium. When the system reaches equilibrium, the reaction quotient becomes the equilibrium constant, $K$ .

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At equilibrium: $Q = K$

This relationship is central to understanding chemical equilibrium. The reaction quotient equals the equilibrium constant only when the system has reached equilibrium.

Key properties of the equilibrium constant

The equilibrium constant has several important characteristics:

Different chemical reactions have different values of K
The magnitude of $K$ indicates the relative proportions of reactants and products in the equilibrium mixture
For a particular reaction, $K$ is constant for all equilibrium mixtures at a fixed temperature
The value of $K$ changes only if the temperature changes

The expression for the equilibrium law

Statement of the equilibrium law

Through studying many reversible reaction systems, chemists developed a general principle called the equilibrium law. This law provides a systematic way to write expressions for equilibrium constants.

The equilibrium law states that:

The equilibrium constant, $K$ , equals the concentrations of products divided by the concentrations of reactants at equilibrium
The power (index) of each component concentration equals the coefficient for that substance in the balanced chemical equation

For a general chemical equation:

$a\text{W} + b\text{X} \rightleftharpoons c\text{Y} + d\text{Z}$

the equilibrium expression is:

$K = \frac{[\text{Y}]^c[\text{Z}]^d}{[\text{W}]^a[\text{X}]^b}$

where $K$ is the equilibrium constant at a particular temperature.

How to write equilibrium expressions

A useful way to remember the equilibrium law is to think of $K$ as:

$K = \frac{[\text{products}]^{\text{coefficients}}}{[\text{reactants}]^{\text{coefficients}}}$

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Memory Aid: "Products on Top, Reactants on Bottom"

This simple phrase helps you remember the structure of equilibrium expressions. Products always go in the numerator, and reactants always go in the denominator.

When writing equilibrium expressions, keep these points in mind:

Product concentrations always go in the numerator (top)
Reactant concentrations always go in the denominator (bottom)
Square brackets [ ] mean "the concentration of" in mol L⁻¹ or M
If there is more than one product or reactant, multiply the concentration terms together

Units for equilibrium constants

The units of $K$ depend on the specific balanced equation for the reaction and can vary between different reactions. You can determine the units by substituting M (or mol L⁻¹) for each concentration in the equilibrium expression, then simplifying.

For example, for the ammonia synthesis reaction:

$K = \frac{[\text{NH}_3]^2}{[\text{N}_2][\text{H}_2]^3}$

The units are:

$\frac{\text{M}^2}{\text{M} \times \text{M}^3} = \frac{\text{M}^2}{\text{M}^4} = \text{M}^{-2}$

(or mol⁻² L²)

Worked example: determining units for an equilibrium expression

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Worked Example: Finding Units for an Equilibrium Constant

Problem: The decomposition of N₂O₄ is a reversible reaction:

$\text{N}_2\text{O}_4(g) \rightleftharpoons 2\text{NO}_2(g)$

Write the expression for the equilibrium constant, $K$ , and determine its units.

Solution:

Step 1: Write the expression for $K$ using the equilibrium law pattern (products over reactants with coefficients as powers):

$K = \frac{[\text{NO}_2]^2}{[\text{N}_2\text{O}_4]}$

Step 2: Substitute the units of concentration (M) into the expression:

$\frac{\text{M}^2}{\text{M}} = \text{M}$

Therefore, $K$ has units of M or mol L⁻¹ for this reaction.

The reaction quotient and the equilibrium law

Writing expressions for Q and K

You can write an expression for the equilibrium constant, $K$ , for any system at equilibrium. Similarly, you can write an expression for the reaction quotient, $Q$ , for systems that may not be at equilibrium.

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

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

The key difference is that $Q$ can be calculated for any mixture of reactants and products at any time during a reaction. However, Q only equals K when the mixture is at equilibrium.

Predicting the direction of reaction

Comparing the value of $Q$ to $K$ at a given temperature allows you to predict which direction a reaction will proceed to reach equilibrium. There are three possible scenarios:

When Q < K:

The reaction quotient is smaller than the equilibrium constant. This means there are currently too few products (or too many reactants) compared to equilibrium. The system shifts to the right toward the products. More products form and more reactants are consumed until equilibrium is reached.

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Think of $Q < K$ as the system saying "I need more products!" The reaction moves to the right to produce more products until $Q$ equals $K$ .

When Q = K:

The reaction quotient equals the equilibrium constant. The system is at equilibrium. No net change occurs in the concentrations of reactants or products. The forward and reverse reaction rates are equal.

When Q > K:

The reaction quotient is greater than the equilibrium constant. This means there are currently too many products (or too few reactants) compared to equilibrium. The system shifts to the left toward the reactants. More reactants form and more products are consumed until equilibrium is reached.

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Think of $Q > K$ as the system saying "I have too many products!" The reaction moves to the left to produce more reactants until $Q$ equals $K$ .

This visual representation shows how a reaction system adjusts itself to reach equilibrium. When $Q$ and $K$ are not equal, the reaction proceeds in whichever direction brings them closer together, until they match at equilibrium.

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Exam Tip: Predicting Reaction Direction

When comparing $Q$ and $K$ , remember:

Q < K: reaction moves RIGHT (toward products)
Q > K: reaction moves LEFT (toward reactants)
Q = K: reaction is AT EQUILIBRIUM (no net change)

Think of it this way: the reaction always moves in the direction that makes $Q$ become equal to $K$ .

Remember!

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Key Points to Remember:

The reaction quotient ( $Q$ ) is the ratio of product concentrations to reactant concentrations, with each concentration raised to the power of its coefficient in the balanced equation.
At equilibrium, $Q$ equals the equilibrium constant ( $K$ ). The value of $K$ is constant for a given reaction at a fixed temperature, regardless of the starting concentrations.
The equilibrium law states that $K = \frac{[\text{products}]^{\text{coefficients}}}{[\text{reactants}]^{\text{coefficients}}}$ , where the coefficients from the balanced equation become the powers in the expression.
The units of K depend on the balanced equation and are determined by substituting M (or mol L⁻¹) for each concentration term and simplifying.
Comparing $Q$ to $K$ predicts reaction direction: if $Q < K$ , the reaction shifts right toward products; if $Q > K$ , the reaction shifts left toward reactants; if $Q = K$ , the system is at equilibrium.

The Equilibrium Law (VCE SSCE Chemistry): Revision Notes