E3.2 Explain reactant and product concentrations at chemical equilibrium

Ontario Grade 12 Chemistry

Chemical Systems and Equilibrium

Ontario Grade 12 Chemistry · E3.2

A sealed container may show a colour change at first and then appear to have a steady colour. The steady appearance is an observable clue: the amounts of coloured substances are no longer changing overall. It does not mean that the reacting particles have stopped changing. This lesson connects that observation to the particle model and explains what reactant and product concentrations are like at equilibrium.

What you will learn

Describe what happens to reactant and product concentrations at chemical equilibrium.
Explain why equilibrium does not require equal reactant and product concentrations.
Use a balanced equation to relate concentration changes and determine equilibrium concentrations.

1. Prerequisite bridge: concentration and reversible reactions

Concentration describes how much of a substance is present in a given volume. In this lesson, concentration is commonly measured in moles per litre, written as

\mathrm{mol/L}

. For example,

0.50\ \mathrm{mol/L}

means that each litre contains

0.50\ \mathrm{mol}

of the substance. A gas mixture can also be described by concentration.

A balanced chemical equation shows the relative amounts of reactants used and products formed. A reactant is a starting substance in a reaction. A product is a substance formed by the reaction. In a reversible reaction, products can also react to form the original reactants. The symbol

\rightleftharpoons

represents a reaction that can proceed in both directions.

A closed system is one in which substances cannot enter or leave. In a closed system, a reversible reaction can reach dynamic equilibrium. Dynamic means that changes continue. Equilibrium means that there is no overall change in the amounts of each substance. At dynamic equilibrium, the forward and reverse reactions continue at equal rates.

c=\frac{n}{V}

Concentration is amount per volume, commonly expressed in $\mathrm{mol/L}$ .
A reversible reaction can proceed in both directions.
Dynamic equilibrium is possible in a closed system when forward and reverse reaction rates are equal.

2. What equilibrium means at the particle level

Before equilibrium, the forward and reverse reactions may occur at different rates. The faster direction causes the amounts of some substances to change overall. As the reaction proceeds, the rates change until they become equal.

At equilibrium, particles continue to react in both directions. Equal reaction rates mean equal numbers of reaction events per unit time in the forward and reverse directions. A reaction event uses or forms substances in the proportions shown by the balanced equation. For example, one forward event for nitrogen tetroxide forming nitrogen dioxide uses one

\mathrm{N_2O_4}

particle and forms two

\mathrm{NO_2}

particles. A reverse event uses two

\mathrm{NO_2}

particles and forms one

\mathrm{N_2O_4}

particle. Equal reaction-event rates therefore do not mean equal total numbers of individual particles are converted in the two directions.

The important concentration result is that each reactant and product concentration remains constant over time at equilibrium. The rates balance the changes in each substance, so no substance has an overall increase or decrease. Constant does not mean zero. The forward and reverse reactions are still occurring.

The concentrations do not have to be equal to one another. A mixture could contain a higher concentration of reactant than product, a higher concentration of product than reactant, or similar concentrations. Equilibrium describes how concentrations behave over time; it does not state that their numerical values match.

A steady colour in a reversible reaction can be consistent with equilibrium if the coloured substances' concentrations are no longer changing overall. The observation alone does not show that all substances have equal concentrations or that particle activity has stopped.

At equilibrium, forward and reverse reaction rates are equal, and both directions continue.
Equal reaction-event rates do not mean equal counts of all kinds of particles converted.
Each concentration remains constant, but concentrations of different substances need not be equal.

3. Using the balanced equation to relate changes

The coefficients in a balanced equation show the relative amounts of substances consumed and formed in a reaction event. They help relate concentration changes as a reaction proceeds. They do not give the final concentration ratio at equilibrium.

For nitrogen tetroxide forming nitrogen dioxide, the balanced equation is

\mathrm{N_2O_4(g)}\rightleftharpoons 2\,\mathrm{NO_2(g)}

. In the forward direction, a decrease in nitrogen tetroxide concentration is accompanied by an increase in nitrogen dioxide concentration that is twice as large. This relation describes changes, not the concentrations already present.

If a substance is consumed in the direction being considered, its concentration change is negative. If a substance is formed, its concentration change is positive. To find an equilibrium concentration, apply the change to the starting concentration: subtract the amount consumed or add the amount formed. Use the balanced equation to find corresponding changes in other substances.

Keep the units consistent. If starting concentrations and changes are in

\mathrm{mol/L}

, the equilibrium concentrations are also in

\mathrm{mol/L}

. Report a result with appropriate significant digits. Do not report more precision than the given values support.

\Delta[\mathrm{NO_2}]=-2\Delta[\mathrm{N_2O_4}]

Balanced-equation coefficients relate the amounts that change together.
A coefficient ratio does not tell you the final equilibrium concentration ratio.
Use the sign of each change and keep concentration units consistent.

4. Interpreting equilibrium concentrations

When given a set of concentrations, first identify which value belongs to each substance. Then distinguish a concentration from a concentration change. A concentration is the amount present per volume; a change describes how much that amount has increased or decreased.

If a question gives initial concentrations and the changes that occur before equilibrium, use the balanced equation to check the change ratio. Add the increase for a product being formed and subtract the decrease for a reactant being consumed. The resulting values are the equilibrium concentrations if the question states that the changes bring the system to equilibrium.

Finally, check whether the values make sense. Concentrations cannot be negative. A substance consumed in the stated forward change should have a lower final concentration than its initial concentration. A substance formed should have a higher final concentration than its initial concentration. These checks can reveal sign or ratio errors.

Do not decide whether a mixture is at equilibrium just because reactant and product concentrations are equal or different. The key feature is that each concentration remains constant over time while the forward and reverse reactions continue at equal rates.

Keep each concentration associated with the correct substance.
Check change signs, coefficient ratios, units, and physical possibility.
Equilibrium is about constant concentrations, not equal concentrations.

Worked example

Finding concentrations at equilibrium

In a closed container, the reaction

\mathrm{N_2O_4(g)}\rightleftharpoons 2\,\mathrm{NO_2(g)}

begins with

0.50\ \mathrm{mol/L}

of

\mathrm{N_2O_4}

and

0.00\ \mathrm{mol/L}

of

\mathrm{NO_2}

. By the time equilibrium is reached, the

\mathrm{N_2O_4}

concentration has decreased by

0.20\ \mathrm{mol/L}

. Find both equilibrium concentrations and explain whether they must be equal.

Relate the changes
The balanced equation shows that one $\mathrm{N_2O_4}$ is used for every two $\mathrm{NO_2}$ formed. Therefore, the $\mathrm{NO_2}$ concentration increase is twice the stated decrease in $\mathrm{N_2O_4}$ .
$\Delta[\mathrm{NO_2}]=2(0.20\ \mathrm{mol/L})=0.40\ \mathrm{mol/L}$
Find the equilibrium concentrations
Subtract the amount of $\mathrm{N_2O_4}$ consumed from its initial concentration. Add the amount of $\mathrm{NO_2}$ formed to its initial concentration. Each calculation uses concentrations in $\mathrm{mol/L}$ .
$[\mathrm{N_2O_4}]_{eq}=0.50-0.20=0.30\ \mathrm{mol/L};\quad[\mathrm{NO_2}]_{eq}=0.00+0.40=0.40\ \mathrm{mol/L}$
Interpret the result
The equilibrium concentrations are $0.30\ \mathrm{mol/L}$ for $\mathrm{N_2O_4}$ and $0.40\ \mathrm{mol/L}$ for $\mathrm{NO_2}$ . They are different, which is allowed. Equilibrium requires constant concentrations over time, not equal concentrations.

Answer:

[\mathrm{N_2O_4}]_{eq}=0.30\ \mathrm{mol/L}

and

[\mathrm{NO_2}]_{eq}=0.40\ \mathrm{mol/L}

. The concentrations are not equal, but each can remain constant at equilibrium.

Check: The reactant decrease is

0.20\ \mathrm{mol/L}

and the product increase is

0.40\ \mathrm{mol/L}

. Their ratio matches the balanced equation's 1:2 change ratio.

Common mistakes and how to avoid them

Assuming equilibrium means reactant and product concentrations are equal.

Correction: Equilibrium means each concentration remains constant over time. Different substances can have different equilibrium concentrations.

Thinking that particles stop reacting at equilibrium.

Correction: Forward and reverse reactions continue at equal rates. Their effects balance, so concentrations do not change overall.

Saying equal reaction rates mean equal numbers of every individual particle are converted per unit time.

Correction: Equal rates refer to equal numbers of reaction events per unit time. Each event uses and forms substances in the proportions in the balanced equation.

Using balanced-equation coefficients as the final concentration ratio.

Correction: Coefficients relate changes in amounts. They do not state the final concentrations present at equilibrium.

Lesson summary

Concentration is amount per volume, commonly measured in $\mathrm{mol/L}$ .
At dynamic equilibrium, forward and reverse reaction rates are equal and both directions continue.
Each reactant and product concentration remains constant at equilibrium; the concentrations do not have to be equal.
Balanced-equation coefficients relate concentration changes, not final concentration values.

Check your understanding

Question 1

At equilibrium, a reactant concentration is

0.25\ \mathrm{mol/L}

and a product concentration is

0.60\ \mathrm{mol/L}

. Which statement is correct?

The system cannot be at equilibrium because the concentrations differ.
The system can be at equilibrium if both concentrations remain constant over time.
The product concentration must decrease until it equals the reactant concentration.
Both substances must stop reacting at equilibrium.

Show answer and explanation

The system can be at equilibrium if both concentrations remain constant over time.

Equilibrium requires concentrations to remain constant because the forward and reverse rates are equal. It does not require equal concentrations, and particles continue to react.

Question 2

For

\mathrm{A}\rightleftharpoons 2\,\mathrm{B}

, the concentration of

\mathrm{A}

decreases by

0.15\ \mathrm{mol/L}

as equilibrium is reached. What is the increase in

\mathrm{B}

concentration?

$0.075\ \mathrm{mol/L}$
$0.15\ \mathrm{mol/L}$
$0.30\ \mathrm{mol/L}$
$0.45\ \mathrm{mol/L}$

Show answer and explanation

0.30\ \mathrm{mol/L}

The equation shows that two units of

\mathrm{B}

form for each unit of

\mathrm{A}

consumed. The increase is

2(0.15\ \mathrm{mol/L})=0.30\ \mathrm{mol/L}

.

Key terms

Concentration: The amount of a substance in a stated volume; commonly measured in moles per litre.
Reactant: A starting substance in a chemical reaction.
Product: A substance formed in a chemical reaction.
Reversible reaction: A reaction that can proceed from reactants to products and from products back to reactants.
Dynamic equilibrium: A condition in a closed system where forward and reverse reactions continue at equal rates, so concentrations remain constant overall.

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E3.2 · Explain reactant and product concentrations at chemical equilibrium