pH Examples in Chemistry

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of pH.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Chemistry.

Concept Recap

A logarithmic scale (typically 0 to 14) that quantifies the hydrogen ion concentration $[\text{H}^+]$ in an aqueous solution: at 25°C, values below 7 are acidic, 7 is neutral, and above 7 is basic.

A number that tells you: acid (low), neutral (7), base (high).

Read the full concept explanation →

How to Use These Examples

Read the first worked example with the solution open so the structure is clear.
Try the practice problems before revealing each solution.
Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: pH starts by identifying the acid/base species, ions produced or transferred, and pH evidence.

Common stuck point: Students often know a formula related to ph but skip the recognition step: Am I tracking acid/base identity, pH, ions in solution, neutralization, buffer behavior, or salt formation? That leads to a correct-looking substitution attached to the wrong chemical model.

Sense of Study hint: Ask: Am I tracking acid/base identity, pH, ions in solution, neutralization, buffer behavior, or salt formation?

Common Mistakes to Watch For

Before you work through the examples, skim the mistake guide so you know which shortcuts and sign errors to avoid.

pH Mistakes

Worked Examples

Example 1

easy

Calculate the pH of a solution with

[\text{H}^+] = 1.0 \times 10^{-4}\,\text{M}

The solution sits in the acidic zone at pH 4.

Answer

\text{pH} = 4

First step

Recall the pH formula:

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

, where

[\text{H}^+]

is the hydrogen ion concentration in mol/L.

Full solution

2
Identify the given value: $[\text{H}^+] = 1.0 \times 10^{-4}\,\text{mol/L}$ .
3
Apply the formula: $\text{pH} = -\log(1.0 \times 10^{-4}) = -(-4) = 4$

The pH scale is logarithmic — each unit change in pH represents a tenfold change in hydrogen ion concentration. A pH of 4 means the solution is acidic.

Example 2

medium

A solution has pH = 9. Calculate

[\text{H}^+]

and

[\text{OH}^-]

Example 3

medium

Find the pH of

0.0010\,\text{M}

NaOH at 25°C.

Strong base 0.0010 M NaOH gives pH 11.

Example 4

hard

Equal volumes of pH 2 and pH 4 strong-acid solutions are mixed. Find the pH of the mixture (use

\log 2 \approx 0.30

Example 5

challenge

50\,\text{mL}

0.10\,\text{M}

HCl is mixed with

50\,\text{mL}

0.05\,\text{M}

NaOH. Find the pH after mixing (strong acid/strong base).

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

medium

What is the pH of a

0.001\,\text{M}

HCl solution? (HCl is a strong acid.)

Strong acid fully dissociates: 0.001 M HCl lands at pH 3.

Example 2

medium

Compare a solution with pH 2 and a solution with pH 5. How many times greater is the hydrogen-ion concentration in the pH 2 solution?

How many times more acidic is solution A (pH 2) than solution B (pH 5)?

Example 3

easy

Write the formula for pH in terms of

[\text{H}^+]

Example 4

easy

A solution has

[\text{H}^+]=10^{-3}\,\text{M}

. Find the pH.

Example 5

easy

A solution has pH 5. Find

[\text{H}^+]

Example 6

easy

Is pH 3 acidic, neutral, or basic?

Where does pH 3 fall on the scale — acidic, neutral, or basic?

Example 7

easy

How many times more acidic is a pH 2 solution than a pH 4 solution?

Example 8

easy

At 25°C, what is the pH of a neutral solution?

Pure water at 25°C sits exactly at the neutral point.

Example 9

easy

At 25°C, pH

+

pOH

=

Example 10

easy

Which is more acidic: a solution of pH 1 or pH 6?

Which solution — A (pH 1) or B (pH 6) — is more acidic?

Example 11

medium

A solution has

[\text{H}^+]=10^{-9}\,\text{M}

. Find the pH and state whether it is acidic or basic.

pH 9 falls in the basic zone — above 7.

Example 12

medium

At 25°C a solution has

[\text{OH}^-]=10^{-4}\,\text{M}

. Find the pH.

Example 13

medium

A solution of pH 8.0 is changed to pH 6.0. By what factor does

[\text{H}^+]

change?

Example 14

medium

A strong acid solution has

[\text{H}^+]=2\times10^{-3}\,\text{M}

. Find the pH (use

\log 2\approx0.30

Example 15

medium

Two solutions have pH 3 and pH 5. Find each

[\text{H}^+]

and the ratio of acidities.

Example 16

medium

Water's pH rises from 7 toward 8 when a base is added. Did

[\text{H}^+]

increase or decrease, and by what factor for one unit?

Example 17

medium

A solution has pOH 2 at 25°C. Find its pH and

[\text{H}^+]

Example 18

medium

A solution has

[\text{H}^+]=10^{-2}\,\text{M}

. Find the pH and classify the solution.

Classify this solution: pH 2 is acidic.

Example 19

medium

A solution has pH 11. Find

[\text{H}^+]

and

[\text{OH}^-]

at 25°C.

Example 20

challenge

0.0050\,\text{mol}

of HCl is dissolved to make

0.50\,\text{L}

of solution. Find

[\text{H}^+]

and pH.

Example 21

challenge

50\,\text{mL}

0.10\,\text{M}

HCl is mixed with

50\,\text{mL}

of water. Find the resulting pH (strong acid).

Example 22

challenge

Equal volumes of pH 3 and pH 5 strong-acid solutions are mixed. Estimate the pH of the mixture.

Example 23

easy

A solution has

[\text{H}^+] = 10^{-6}\,\text{M}

. Find the pH.

Example 24

easy

A solution has pH = 10. What is

[\text{H}^+]

Example 25

easy

What is the pOH of a solution with pH 4 at 25°C?

Example 26

easy

Which is more basic: pH 9 or pH 12?

Which solution — X (pH 9) or Y (pH 12) — is more basic?

Example 27

easy

What is the pH of

0.01\,\text{M}

HCl? (HCl is strong)

Example 28

medium

A solution has pOH = 5. Find its pH and

[\text{H}^+]

at 25°C.

Example 29

medium

A solution changes from pH 4 to pH 7. By what factor did

[\text{H}^+]

change?

Example 30

medium

A strong acid has

[\text{H}^+] = 5 \times 10^{-3}\,\text{M}

. Estimate the pH (use

\log 5 \approx 0.70

Example 31

medium

[\text{H}^+] = 4 \times 10^{-5}\,\text{M}

. Find the pH (use

\log 4 \approx 0.60

Example 32

medium

A solution has pH 12. Find

[\text{H}^+]

and

[\text{OH}^-]

at 25°C.

Example 33

medium

How many times more acidic is a pH 1 solution than a pH 4 solution?

Example 34

medium

A solution of NaOH has

[\text{OH}^-] = 10^{-3}\,\text{M}

. Find the pH.

Example 35

hard

0.020\,\text{mol}

of HCl is dissolved in

200\,\text{mL}

of solution. Find

[\text{H}^+]

and pH.

Example 36

hard

100\,\text{mL}

0.020\,\text{M}

HCl is diluted to

200\,\text{mL}

. Find the new pH.

Example 37

hard

A solution has pH 3.7. Estimate

[\text{H}^+]

to one significant figure.

Example 38

hard

A strong base solution has

[\text{OH}^-] = 2 \times 10^{-4}\,\text{M}

. Find the pH at 25°C (use

\log 2 \approx 0.30

Example 39

hard

25\,\text{mL}

0.10\,\text{M}

HCl is mixed with

25\,\text{mL}

0.10\,\text{M}

NaOH. Find the pH of the resulting solution at 25°C.

Example 40

challenge

Concentrated HCl can have

[\text{H}^+] = 12\,\text{M}

. Estimate the pH (use

\log 12 \approx 1.08

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Related Concepts

Acid Base Concentration Neutralization Buffer

Background Knowledge

These ideas may be useful before you work through the harder examples.

acidbaseconcentration