pH and strong acids

What you'll learn

What pH measures and why it is a logarithmic scale.
What makes an acid “strong” in A-Level chemistry.
How to calculate pH from the concentration of a strong acid.
How to work backwards from pH to hydrogen ion concentration, including dilution questions.

Starting point: acids in water

In Brønsted–Lowry theory, acids are substances that donate protons. A proton is a hydrogen ion, H⁺, because a hydrogen atom has lost its electron.

In water, a bare H⁺ ion does not really float around on its own; it attaches to water molecules. At A-Level, we usually write H⁺(aq) as a convenient shorthand.

Definition

Acid and hydrogen ion concentration

An acid is a proton donor. In aqueous solution, acids increase the concentration of hydrogen ions, written as $[H+][\text{H}^+]$ , where square brackets mean “concentration in mol dm⁻³”.

The higher the value of $[H+][\text{H}^+]$ , the more acidic the solution.

Concentration reminders

For pH calculations, concentration is usually measured in mol dm⁻³. You will often need:

\frac{n}{V}

where:

$c$ is concentration in mol dm⁻³
$n$ is amount of substance in mol
$V$ is volume in dm³

Remember that 1000 cm³ = 1 dm³, so:

dm3250\ \text{cm}^3 = 0.250\ \text{dm}^3

Common Mistake

Forgetting to convert cm³ to dm³

If you use $\frac{n}{V}$ , the volume must be in dm³ when concentration is in mol dm⁻³. Using cm³ directly makes your concentration 1000 times too small.

Strong acids

A strong acid is not just an acid with a low pH. It has a specific meaning: it dissociates completely in water.

Definition

Strong acid

A strong acid is an acid that fully dissociates in aqueous solution. Dissociation means the acid particles split to form ions in solution.

For example:

HCl(aq)→H+(aq)+Cl−(aq)HNO3(aq)→H+(aq)+NO3−(aq)\begin{aligned} \text{HCl(aq)} &\to \text{H}^+\text{(aq)} + \text{Cl}^-\text{(aq)} \\ \text{HNO}_3\text{(aq)} &\to \text{H}^+\text{(aq)} + \text{NO}_3^-\text{(aq)} \end{aligned}

Hydrochloric acid and nitric acid are both monobasic strong acids.

Definition

Monobasic acid

A monobasic acid donates one proton per acid molecule.

So, for a strong monobasic acid:

concentration[\text{H}^+] = \text{acid concentration}

For example, 0.100 mol dm⁻³ HCl(aq) gives $dm−3[\text{H}^+] = 0.100\ \text{mol dm}^{-3}$ .

Key Idea

Strong monobasic acids

For a strong monobasic acid such as HCl or HNO₃, complete dissociation means every acid molecule forms one H⁺ ion, so $[H+]=c[\text{H}^+] = c$ .

Common Mistake

Strong does not mean concentrated

Strong describes the extent of dissociation. Concentrated describes how many moles of acid are dissolved per dm³. A dilute strong acid can still be fully dissociated.

What pH means

pH is a mathematical way of expressing hydrogen ion concentration.

Definition

pH is defined by the equation $pH=−log⁡10[H+]\text{pH} = -\log_{10}[\text{H}^+]$ . In A-Level calculations, use the numerical value of $[H+][\text{H}^+]$ in mol dm⁻³.

The negative sign is there because acidic solutions have small decimal values of $[H+][\text{H}^+]$ , such as 0.01 mol dm⁻³. Taking the negative logarithm turns these into more convenient positive pH values.

The diagram shows why pH changes are not linear: each decrease of one pH unit means the hydrogen ion concentration is 10 times larger.

Diagram showing the logarithmic relationship between hydrogen ion concentration and pH

Tip

Calculator buttons

Use the base-10 log button, usually labelled log, not the natural log button ln.

Calculating pH of a strong acid

The full method is:

Find the acid concentration in mol dm⁻³.
Use the dissociation ratio to find $[H+][\text{H}^+]$ .
Substitute into $pH=−log⁡10[H+]\text{pH} = -\log_{10}[\text{H}^+]$ .

Example

Calculating pH from a prepared HCl solution

0.365 g of hydrogen chloride, HCl, is dissolved in water and made up to 500 cm³ of solution. Calculate the pH of the solution. Use $Mr(HCl)=36.5M_r(\text{HCl}) = 36.5$ .

Calculate the amount of HCl dissolved:
$\frac{m}{M} = \frac{0.365}{36.5} = 0.0100\ \text{mol}$
Convert the volume into dm³ and calculate the concentration:
$dm3500\ \text{cm}^3 = 0.500\ \text{dm}^3$ $\frac{n}{V} = \frac{0.0100}{0.500} = 0.0200\ \text{mol dm}^{-3}$
Use the fact that HCl is a strong monobasic acid:
$dm−3[\text{H}^+] = 0.0200\ \text{mol dm}^{-3}$
Calculate pH:
$pH=−log⁡10(0.0200)=1.70\text{pH} = -\log_{10}(0.0200) = 1.70$

The pH scale is logarithmic

A pH difference of one unit means a tenfold difference in $[H+][\text{H}^+]$ .

So:

pH 1 has 10 times greater $[H+][\text{H}^+]$ than pH 2.
pH 2 has 100 times greater $[H+][\text{H}^+]$ than pH 4.
pH 3 has 1000 times greater $[H+][\text{H}^+]$ than pH 6.

Example

Comparing acidity using pH

Compare the hydrogen ion concentrations of two solutions: solution A has pH 2.00 and solution B has pH 5.00.

Convert each pH into a hydrogen ion concentration:
$[H+]A=10−2.00[\text{H}^+]_\text{A} = 10^{-2.00}$ $[H+]B=10−5.00[\text{H}^+]_\text{B} = 10^{-5.00}$
Find the ratio:
$[H+]A[H+]B=10−210−5=103\frac{[\text{H}^+]_\text{A}}{[\text{H}^+]_\text{B}} = \frac{10^{-2}}{10^{-5}} = 10^3$
Interpret the result:

Solution A has 1000 times greater hydrogen ion concentration than solution B.

Common Mistake

Treating pH as a linear scale

A solution with pH 2 is not “twice as acidic” as pH 4. It has 100 times greater $[H+][\text{H}^+]$ .

Working backwards from pH

You can rearrange the pH equation:

[H+]=10−pH[\text{H}^+] = 10^{-\text{pH}}

This is useful when you are given pH and asked for hydrogen ion concentration, or the concentration of a strong monobasic acid.

Example

Finding acid concentration from pH

A solution of nitric acid has pH 2.30. Calculate the concentration of HNO₃(aq), assuming complete dissociation.

Use the rearranged pH equation:
$[H+]=10−2.30[\text{H}^+] = 10^{-2.30}$
Calculate the hydrogen ion concentration:
$dm−3[\text{H}^+] = 5.01 \times 10^{-3}\ \text{mol dm}^{-3}$
Use the 1:1 dissociation of HNO₃:
$HNO3(aq)→H+(aq)+NO3−(aq)\text{HNO}_3\text{(aq)} \to \text{H}^+\text{(aq)} + \text{NO}_3^-\text{(aq)}$
Therefore the concentration of HNO₃ is $5.01 \times 10^{-3}\ \text{mol dm}^{-3}$ .

Diluting a strong acid

When you dilute an acid, you add water. The amount of acid in mol stays the same, but the total volume increases, so the concentration decreases.

For dilution calculations, use:

c_1V_1 = c_2V_2

This works because the amount of solute is unchanged.

Example

Calculating pH after dilution

20.0 cm³ of 0.150 mol dm⁻³ HCl(aq) is diluted with water to a final volume of 250.0 cm³. Calculate the pH of the diluted solution.

Use the dilution equation, keeping both volumes in the same units:
$c2=c1V1V2c_2 = \frac{c_1V_1}{V_2}$
Substitute the values:
$dm−3c_2 = \frac{0.150 \times 20.0}{250.0} = 0.0120\ \text{mol dm}^{-3}$
Use complete dissociation of HCl:
$dm−3[\text{H}^+] = 0.0120\ \text{mol dm}^{-3}$
Calculate the pH:
$pH=−log⁡10(0.0120)=1.92\text{pH} = -\log_{10}(0.0120) = 1.92$

Tip

Sanity check for dilution

A tenfold dilution of a strong acid increases the pH by about one unit, provided the acid is not extremely dilute.

Common Mistake

Very dilute strong acids

For very dilute acids, around $dm−310^{-7}\ \text{mol dm}^{-3}$ or lower, the H⁺ from water itself becomes significant. The simple assumption that all $[H+][\text{H}^+]$ comes from the acid then breaks down.

A note on pH 7 and temperature

At 298 K, pure water is neutral and has pH 7.00 because:

dm−3[\text{H}^+] = [\text{OH}^-] = 1.00 \times 10^{-7}\ \text{mol dm}^{-3}

The familiar pH scale from 0 to 14 is a useful range for many dilute aqueous solutions at 298 K. It is not an absolute limit: very concentrated acids can have pH below 0.

Measuring pH practically

For approximate pH, universal indicator or pH paper is enough. For quantitative A-Level work, use a calibrated pH meter.

Tip

Good pH measurement

Calibrate the pH meter using buffer solutions, rinse the probe with distilled water between solutions, and remember that pH depends on temperature.

Exam technique

In the exam

Decide whether the acid is strong or weak, and whether it is monobasic or not.
Convert volumes into dm³ before using $n = c V$ , unless using $c_1V_1 = c_2V_2$ with both volumes in the same unit.
For a strong monobasic acid, use $[H+]=c[\text{H}^+] = c$ , then calculate $pH=−log⁡10[H+]\text{pH} = -\log_{10}[\text{H}^+]$ .
To work backwards, use $[H+]=10−pH[\text{H}^+] = 10^{-\text{pH}}$ .
Check your answer: a more concentrated strong acid should have a lower pH.

Self review

Check yourself

What is $[H+][\text{H}^+]$ in 0.0350 mol dm⁻³ HNO₃(aq)?
Calculate the pH of 0.00400 mol dm⁻³ HCl(aq).
A strong monobasic acid has pH 1.50. What is its concentration in mol dm⁻³?

What you'll learn

What pH measures and why it is a logarithmic scale.
What makes an acid “strong” in A-Level chemistry.
How to calculate pH from the concentration of a strong acid.
How to work backwards from pH to hydrogen ion concentration, including dilution questions.

Starting point: acids in water

In Brønsted–Lowry theory, acids are substances that donate protons. A proton is a hydrogen ion, H⁺, because a hydrogen atom has lost its electron.

In water, a bare H⁺ ion does not really float around on its own; it attaches to water molecules. At A-Level, we usually write H⁺(aq) as a convenient shorthand.

Definition

Acid and hydrogen ion concentration

An acid is a proton donor. In aqueous solution, acids increase the concentration of hydrogen ions, written as $[H+][\text{H}^+]$ , where square brackets mean “concentration in mol dm⁻³”.

The higher the value of $[H+][\text{H}^+]$ , the more acidic the solution.

Concentration reminders

For pH calculations, concentration is usually measured in mol dm⁻³. You will often need:

\frac{n}{V}

where:

$c$ is concentration in mol dm⁻³
$n$ is amount of substance in mol
$V$ is volume in dm³

Remember that 1000 cm³ = 1 dm³, so:

dm3250\ \text{cm}^3 = 0.250\ \text{dm}^3

Common Mistake

Forgetting to convert cm³ to dm³

If you use $\frac{n}{V}$ , the volume must be in dm³ when concentration is in mol dm⁻³. Using cm³ directly makes your concentration 1000 times too small.

Strong acids

A strong acid is not just an acid with a low pH. It has a specific meaning: it dissociates completely in water.

Definition

Strong acid

A strong acid is an acid that fully dissociates in aqueous solution. Dissociation means the acid particles split to form ions in solution.

For example:

HCl(aq)→H+(aq)+Cl−(aq)HNO3(aq)→H+(aq)+NO3−(aq)\begin{aligned} \text{HCl(aq)} &\to \text{H}^+\text{(aq)} + \text{Cl}^-\text{(aq)} \\ \text{HNO}_3\text{(aq)} &\to \text{H}^+\text{(aq)} + \text{NO}_3^-\text{(aq)} \end{aligned}

Hydrochloric acid and nitric acid are both monobasic strong acids.

Definition

Monobasic acid

A monobasic acid donates one proton per acid molecule.

So, for a strong monobasic acid:

concentration[\text{H}^+] = \text{acid concentration}

For example, 0.100 mol dm⁻³ HCl(aq) gives $dm−3[\text{H}^+] = 0.100\ \text{mol dm}^{-3}$ .

Key Idea

Strong monobasic acids

For a strong monobasic acid such as HCl or HNO₃, complete dissociation means every acid molecule forms one H⁺ ion, so $[H+]=c[\text{H}^+] = c$ .

Common Mistake

Strong does not mean concentrated

Strong describes the extent of dissociation. Concentrated describes how many moles of acid are dissolved per dm³. A dilute strong acid can still be fully dissociated.

What pH means

pH is a mathematical way of expressing hydrogen ion concentration.

Definition

pH is defined by the equation $pH=−log⁡10[H+]\text{pH} = -\log_{10}[\text{H}^+]$ . In A-Level calculations, use the numerical value of $[H+][\text{H}^+]$ in mol dm⁻³.

The diagram shows why pH changes are not linear: each decrease of one pH unit means the hydrogen ion concentration is 10 times larger.

Diagram showing the logarithmic relationship between hydrogen ion concentration and pH

Tip

Calculator buttons

Use the base-10 log button, usually labelled log, not the natural log button ln.

Calculating pH of a strong acid

The full method is:

Find the acid concentration in mol dm⁻³.
Use the dissociation ratio to find $[H+][\text{H}^+]$ .
Substitute into $pH=−log⁡10[H+]\text{pH} = -\log_{10}[\text{H}^+]$ .

Example

Calculating pH from a prepared HCl solution

0.365 g of hydrogen chloride, HCl, is dissolved in water and made up to 500 cm³ of solution. Calculate the pH of the solution. Use $Mr(HCl)=36.5M_r(\text{HCl}) = 36.5$ .

Calculate the amount of HCl dissolved:
$\frac{m}{M} = \frac{0.365}{36.5} = 0.0100\ \text{mol}$
Convert the volume into dm³ and calculate the concentration:
$dm3500\ \text{cm}^3 = 0.500\ \text{dm}^3$ $\frac{n}{V} = \frac{0.0100}{0.500} = 0.0200\ \text{mol dm}^{-3}$
Use the fact that HCl is a strong monobasic acid:
$dm−3[\text{H}^+] = 0.0200\ \text{mol dm}^{-3}$
Calculate pH:
$pH=−log⁡10(0.0200)=1.70\text{pH} = -\log_{10}(0.0200) = 1.70$

The pH scale is logarithmic

A pH difference of one unit means a tenfold difference in $[H+][\text{H}^+]$ .

So:

pH 1 has 10 times greater $[H+][\text{H}^+]$ than pH 2.
pH 2 has 100 times greater $[H+][\text{H}^+]$ than pH 4.
pH 3 has 1000 times greater $[H+][\text{H}^+]$ than pH 6.

Example

Comparing acidity using pH

Compare the hydrogen ion concentrations of two solutions: solution A has pH 2.00 and solution B has pH 5.00.

Convert each pH into a hydrogen ion concentration:
$[H+]A=10−2.00[\text{H}^+]_\text{A} = 10^{-2.00}$ $[H+]B=10−5.00[\text{H}^+]_\text{B} = 10^{-5.00}$
Find the ratio:
$[H+]A[H+]B=10−210−5=103\frac{[\text{H}^+]_\text{A}}{[\text{H}^+]_\text{B}} = \frac{10^{-2}}{10^{-5}} = 10^3$
Interpret the result:

Solution A has 1000 times greater hydrogen ion concentration than solution B.

Common Mistake

Treating pH as a linear scale

A solution with pH 2 is not “twice as acidic” as pH 4. It has 100 times greater $[H+][\text{H}^+]$ .

Working backwards from pH

You can rearrange the pH equation:

[H+]=10−pH[\text{H}^+] = 10^{-\text{pH}}

This is useful when you are given pH and asked for hydrogen ion concentration, or the concentration of a strong monobasic acid.

Example

Finding acid concentration from pH

A solution of nitric acid has pH 2.30. Calculate the concentration of HNO₃(aq), assuming complete dissociation.

Use the rearranged pH equation:
$[H+]=10−2.30[\text{H}^+] = 10^{-2.30}$
Calculate the hydrogen ion concentration:
$dm−3[\text{H}^+] = 5.01 \times 10^{-3}\ \text{mol dm}^{-3}$
Use the 1:1 dissociation of HNO₃:
$HNO3(aq)→H+(aq)+NO3−(aq)\text{HNO}_3\text{(aq)} \to \text{H}^+\text{(aq)} + \text{NO}_3^-\text{(aq)}$
Therefore the concentration of HNO₃ is $5.01 \times 10^{-3}\ \text{mol dm}^{-3}$ .

Diluting a strong acid

When you dilute an acid, you add water. The amount of acid in mol stays the same, but the total volume increases, so the concentration decreases.

For dilution calculations, use:

c_1V_1 = c_2V_2

This works because the amount of solute is unchanged.

Example

Calculating pH after dilution

20.0 cm³ of 0.150 mol dm⁻³ HCl(aq) is diluted with water to a final volume of 250.0 cm³. Calculate the pH of the diluted solution.

Use the dilution equation, keeping both volumes in the same units:
$c2=c1V1V2c_2 = \frac{c_1V_1}{V_2}$
Substitute the values:
$dm−3c_2 = \frac{0.150 \times 20.0}{250.0} = 0.0120\ \text{mol dm}^{-3}$
Use complete dissociation of HCl:
$dm−3[\text{H}^+] = 0.0120\ \text{mol dm}^{-3}$
Calculate the pH:
$pH=−log⁡10(0.0120)=1.92\text{pH} = -\log_{10}(0.0120) = 1.92$

Tip

Sanity check for dilution

A tenfold dilution of a strong acid increases the pH by about one unit, provided the acid is not extremely dilute.

Common Mistake

Very dilute strong acids

A note on pH 7 and temperature

At 298 K, pure water is neutral and has pH 7.00 because:

dm−3[\text{H}^+] = [\text{OH}^-] = 1.00 \times 10^{-7}\ \text{mol dm}^{-3}

The familiar pH scale from 0 to 14 is a useful range for many dilute aqueous solutions at 298 K. It is not an absolute limit: very concentrated acids can have pH below 0.

Measuring pH practically

For approximate pH, universal indicator or pH paper is enough. For quantitative A-Level work, use a calibrated pH meter.

Tip

Good pH measurement

Calibrate the pH meter using buffer solutions, rinse the probe with distilled water between solutions, and remember that pH depends on temperature.

Exam technique

In the exam

Decide whether the acid is strong or weak, and whether it is monobasic or not.
Convert volumes into dm³ before using $n = c V$ , unless using $c_1V_1 = c_2V_2$ with both volumes in the same unit.
For a strong monobasic acid, use $[H+]=c[\text{H}^+] = c$ , then calculate $pH=−log⁡10[H+]\text{pH} = -\log_{10}[\text{H}^+]$ .
To work backwards, use $[H+]=10−pH[\text{H}^+] = 10^{-\text{pH}}$ .
Check your answer: a more concentrated strong acid should have a lower pH.

Self review

Check yourself

What is $[H+][\text{H}^+]$ in 0.0350 mol dm⁻³ HNO₃(aq)?
Calculate the pH of 0.00400 mol dm⁻³ HCl(aq).
A strong monobasic acid has pH 1.50. What is its concentration in mol dm⁻³?

What you'll learn

Starting point: acids in water

Concentration reminders

Strong acids

What pH means

Calculating pH of a strong acid

The pH scale is logarithmic

Working backwards from pH

Diluting a strong acid

A note on pH 7 and temperature

Measuring pH practically

Review pH and strong acids by teaching Genie

Remember key concepts with flashcards

pH and strong acids

What you'll learn

Starting point: acids in water

Concentration reminders

Strong acids

What pH means

Calculating pH of a strong acid

The pH scale is logarithmic

Working backwards from pH

Diluting a strong acid

A note on pH 7 and temperature

Measuring pH practically

Review pH and strong acids by teaching Genie

Remember key concepts with flashcards

pH and strong acids

What you'll learn

Starting point: acids in water

Concentration reminders

Strong acids

What pH means

Calculating pH of a strong acid

The pH scale is logarithmic

Working backwards from pH

Diluting a strong acid

A note on pH 7 and temperature

Measuring pH practically

Review pH and strong acids by teaching Genie

Remember key concepts with flashcards

pH and strong acids Revision Guide

pH and strong acids

What you'll learn

Starting point: acids in water

Concentration reminders

Strong acids

What pH means

Calculating pH of a strong acid

The pH scale is logarithmic

Working backwards from pH

Diluting a strong acid

A note on pH 7 and temperature

Measuring pH practically

Review pH and strong acids by teaching Genie

Remember key concepts with flashcards

pH and strong acids Revision Guide