E3.7 Compare strong and weak acids and bases using equilibrium

Ontario Grade 12 Chemistry

Chemical Systems and Equilibrium

Comparing how far ion formation proceeds at equilibrium

Two clear acid solutions can have the same concentration but different pH values. The difference is not simply how much acid was added. It also depends on how much of the acid forms ions in water. In this lesson, equilibrium provides a way to compare that behaviour. An equilibrium is a state in which forward and reverse changes continue, but the amounts of substances remain steady overall.

What you will learn

Describe strong and weak acids and bases using particle-level models.
Use equilibrium equations and the values of $K_a$ and $K_b$ to compare acid and base strength.
Explain why strength is different from concentration.
Compare a strong acid solution with a weak acid solution using equilibrium calculations.

1. From familiar properties to particles

In earlier chemistry, you learned that acids produce hydrogen ions in water and bases produce hydroxide ions in water. These ions help explain familiar properties: acidic solutions have a pH below 7, while basic solutions have a pH above 7. The pH scale describes how acidic or basic a solution is; for this lesson, the key point is that a larger hydrogen-ion concentration generally means a lower pH.

At the particle level, an acid molecule can transfer a hydrogen ion to a water molecule. A base may produce hydroxide ions directly, or it may react with water to form them. A strong acid or base forms ions to a very large extent. A weak acid or base forms ions only to a limited extent. “Strong” and “weak” describe this extent of ion formation, not whether a solution is concentrated or dilute.

For example, a dilute solution of a strong acid can contain fewer hydrogen ions per litre than a concentrated solution of a weak acid. Strength and concentration are separate ideas. Concentration tells how much dissolved substance is present per unit volume; strength tells how much of it forms ions in water.

Acid and base strength describe the extent of ion formation in water.
Concentration describes the amount of dissolved substance per volume.
A strong acid or base is not automatically concentrated.

2. Equilibrium models for acids and bases

A reversible reaction can proceed in both directions. At equilibrium, the forward and reverse changes continue at the same rate, so the amounts of each substance remain steady. Equilibrium does not mean that the amounts of reactants and products are equal.

A weak acid, written as

\mathrm{HA}

, reacts reversibly with water. The acid transfers a hydrogen ion to water, producing hydronium ions and the conjugate base,

\mathrm{A^-}

. A conjugate base is the particle left when an acid donates a hydrogen ion. The equilibrium equation shows that both sides are present in a weak-acid solution.

The acid ionization constant,

K_a

, is an equilibrium value that indicates the extent of acid ionization. For acids compared at the same conditions, a larger

K_a

means a greater proportion of ion formation and therefore a stronger acid. A small

K_a

means that most acid particles remain un-ionized.

A weak base, written as

\mathrm{B}

, can react reversibly with water to produce its conjugate acid and hydroxide ions. The base ionization constant,

K_b

, describes this equilibrium. For bases compared at the same conditions, a larger

K_b

indicates greater formation of ions and a stronger base.

Strong acids and bases are represented as forming ions essentially completely in water at this level. Their equations use a one-way arrow. Weak acids and bases are represented by reversible arrows because both reactants and products are present at equilibrium. These models help compare behaviour; they do not claim that a reversible reaction stops.

\mathrm{HA(aq) + H_2O(l) \rightleftharpoons H_3O^+(aq) + A^-(aq)}

At equilibrium, amounts are steady, but reactants and products need not be equal.
A larger $K_a$ indicates a stronger acid; a larger $K_b$ indicates a stronger base.
Strong and weak refer to the extent of ion formation, not to the amount initially dissolved.

3. Reading equations and comparing strength

The weak-acid equation gives the equilibrium expression

K_a=[\mathrm{H_3O^+}][\mathrm{A^-}]/[\mathrm{HA}]

. Square brackets mean equilibrium concentration, usually measured in moles per litre. Liquid water is not included in this expression because it is the solvent. The expression compares the concentrations of the ion products with the remaining acid.

For a weak base, the corresponding expression is

K_b=[\mathrm{BH^+}][\mathrm{OH^-}]/[\mathrm{B}]

. Here,

\mathrm{BH^+}

is the base after it accepts a hydrogen ion. These expressions let you compare equilibria quantitatively when the constants are known.

For a strong acid such as hydrochloric acid, the course-level model treats ion formation as essentially complete. One mole of dissolved hydrochloric acid produces approximately one mole of hydronium ions in a sufficiently dilute solution. A weak acid such as ethanoic acid remains partly as molecules, so its hydronium-ion concentration is less than its starting acid concentration.

When comparing two acids or two bases, compare their

K_a

or

K_b

values under the same conditions. Do not compare an acid's

K_a

directly with a base's

K_b

as though they measured the same reaction. Also, do not infer strength from pH alone if the solutions have different starting concentrations.

K_a=\frac{[\mathrm{H_3O^+}][\mathrm{A^-}]}{[\mathrm{HA}]} \qquad K_b=\frac{[\mathrm{BH^+}][\mathrm{OH^-}]}{[\mathrm{B}]}

Equilibrium expressions use concentrations of dissolved species at equilibrium.
For a given starting concentration, a strong acid generally produces more hydronium ions than a weak acid.
Compare $K_a$ values for acids and $K_b$ values for bases.

4. Using equilibrium to compare acid solutions

For a weak acid with a known starting concentration, an equilibrium calculation estimates how much ionization occurs. Track the concentration change using the balanced equation, substitute equilibrium concentrations into the

K_a

expression, and solve for the hydronium-ion concentration. Then use

\mathrm{pH}=-\log[\mathrm{H_3O^+}]

.

The calculation below compares equal starting concentrations. Its result illustrates the particle model: the strong acid is treated as fully ionized, while only a small fraction of the weak acid is ionized. Report concentration in

\mathrm{mol\,L^{-1}}

and pH to a sensible number of decimal places.

\mathrm{pH}=-\log[\mathrm{H_3O^+}]

A weak-acid calculation uses both the starting concentration and the equilibrium constant.
The hydronium-ion concentration, not the starting acid concentration alone, determines pH.

Worked example

Equal concentrations, different acid strengths

Compare the pH of

0.100\ \mathrm{mol\,L^{-1}}

hydrochloric acid, treated as a strong acid, with the pH of

0.100\ \mathrm{mol\,L^{-1}}

ethanoic acid, a weak acid with

K_a=1.8\times10^{-5}

. Assume the solutions are dilute and use the course-level strong-acid model.

Strong-acid solution
Hydrochloric acid ionizes essentially completely in water. Its one-to-one reaction with water means the hydronium-ion concentration is approximately the initial acid concentration. The concentration units are retained inside the logarithm as the standard concentration ratio is understood.
$[\mathrm{H_3O^+}]=0.100\ \mathrm{mol\,L^{-1}},\quad \mathrm{pH}=-\log(0.100)=1.00$
Set up the weak-acid equilibrium
Ethanoic acid transfers a hydrogen ion to water, but the reaction is reversible. Let $x$ be the amount ionized in moles per litre. The equilibrium concentrations are $x$ for hydronium and ethanoate, and $0.100-x$ for the acid that remains.
$\mathrm{CH_3COOH(aq)+H_2O(l)\rightleftharpoons H_3O^+(aq)+CH_3COO^-(aq)}$
Apply the equilibrium constant
Substitute the equilibrium concentrations into the acid expression. Solving the resulting quadratic gives the positive concentration change. The other mathematical root is not physically suitable because it would imply a negative equilibrium concentration.
$1.8\times10^{-5}=\frac{x^2}{0.100-x},\quad x=1.33\times10^{-3}\ \mathrm{mol\,L^{-1}}$
Find and compare pH
The calculated $x$ is the hydronium-ion concentration. Taking its negative base-ten logarithm gives the weak-acid pH. It is higher than the strong-acid pH, so the weak acid produces fewer hydronium ions at the same starting concentration.
$\mathrm{pH}=-\log(1.33\times10^{-3})=2.88$

Answer: The

0.100\ \mathrm{mol\,L^{-1}}

hydrochloric acid has pH

1.00

. The

0.100\ \mathrm{mol\,L^{-1}}

ethanoic acid has pH

2.88

. At equal starting concentration, the strong acid produces more hydronium ions.

Check: The weak acid's ionized amount is about

1.33\times10^{-3}\ \mathrm{mol\,L^{-1}}

, much less than its initial

0.100\ \mathrm{mol\,L^{-1}}

. That is consistent with a small

K_a

.

Common mistakes and how to avoid them

Calling an acid strong because its solution is concentrated.

Correction: Concentration is the amount dissolved per volume. Strength is the extent of ion formation. State both when comparing solutions.

Assuming equilibrium means equal concentrations of reactants and products.

Correction: At equilibrium, amounts remain steady overall. The concentrations can be very different.

Using the starting concentration of a weak acid as its hydronium-ion concentration.

Correction: A weak acid ionizes only partly. Use its equilibrium expression to find the hydronium-ion concentration.

Treating every acid or base reaction as complete.

Correction: Use a one-way arrow for the strong-acid or strong-base model and a reversible arrow for a weak acid or weak base.

Lesson summary

Strong acids and bases form ions to a very large extent in water; weak acids and bases form ions only partly.
Equilibrium represents continuing forward and reverse changes with steady overall amounts.
A larger $K_a$ means a stronger acid, and a larger $K_b$ means a stronger base.
Strength is not concentration. For equal starting concentrations, a strong acid generally produces more hydronium ions than a weak acid.

Check your understanding

Question 1

Two weak acids are compared under the same conditions. Acid X has

K_a=4.0\times10^{-4}

and acid Y has

K_a=2.0\times10^{-6}

. Which is stronger?

Acid X, because its larger $K_a$ indicates greater ion formation.
Acid Y, because its smaller $K_a$ indicates greater ion formation.
They are equally strong because both are weak.
There is not enough information because their concentrations are not given.

Show answer and explanation

Acid X, because its larger

K_a

indicates greater ion formation.

For acids compared under the same conditions, the larger

K_a

indicates greater ionization and greater acid strength. Starting concentration is not needed to compare the stated

K_a

values.

Question 2

A weak base has

K_b=3.0\times10^{-5}

. What does this tell you?

The base forms ions partly, and its equilibrium favours the un-ionized base more than the products.
The base ionizes completely because $K_b$ is greater than zero.
The base must be dilute.
The equilibrium concentrations of base and products are equal.

Show answer and explanation

The base forms ions partly, and its equilibrium favours the un-ionized base more than the products.

A weak base reacts reversibly with water. A small

K_b

means the product concentrations are small relative to the remaining base; it says nothing by itself about the starting concentration.

Question 3

A

0.050\ \mathrm{mol\,L^{-1}}

strong acid solution is compared with a

0.050\ \mathrm{mol\,L^{-1}}

weak acid solution. Which statement is generally correct in the course-level model?

The strong acid produces a higher hydronium-ion concentration.
The weak acid produces a higher hydronium-ion concentration because it is weak.
Both must produce equal hydronium-ion concentrations because their starting concentrations match.
Neither solution contains hydronium ions at equilibrium.

Show answer and explanation

The strong acid produces a higher hydronium-ion concentration.

At equal starting concentrations, the strong acid is treated as essentially completely ionized, while the weak acid ionizes only partly. Therefore, the strong acid generally produces more hydronium ions.

Key terms

Equilibrium: A state in which forward and reverse changes continue at equal rates, so amounts remain steady overall.
Ionization: Formation of ions when a substance reacts with water.
Acid ionization constant, $K_a$: An equilibrium value that indicates the extent to which an acid forms ions in water.
Base ionization constant, $K_b$: An equilibrium value that indicates the extent to which a base forms ions in water.
Conjugate base: The particle left after an acid donates a hydrogen ion.
Concentration: The amount of dissolved substance per volume of solution.

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About this lesson and its review

Published by DoAssignment. This reviewed lesson follows Ontario Grade 12 Chemistry (SCH4U), expectation E3.7. It is a study resource, not an official curriculum publication.

Before publication, content is checked for structure, mathematical or chemical notation, calculations, course boundaries, and readability. Errors can still occur, so corrections are welcomed.

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E3.7 · Compare strong and weak acids and bases using equilibrium

Ontario Grade 12 Chemistry

Comparing how far ion formation proceeds at equilibrium

What you will learn

1. From familiar properties to particles

2. Equilibrium models for acids and bases

3. Reading equations and comparing strength

4. Using equilibrium to compare acid solutions

Equal concentrations, different acid strengths

Common mistakes and how to avoid them

Lesson summary

Check your understanding

Question 1

Question 2

Question 3

Key terms

Continue through SCH4U

About this lesson and its review