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 ranging from 0 to 14 that quantifies the hydrogen ion concentration [\text{H}^+] in an aqueous solution, where values below 7 indicate acidic.

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: Each pH unit represents a 10\times change in \text{H}^+ concentration.

Common stuck point: pH 3 is 10\times more acidic than pH 4, not just 'one more.'

Sense of Study hint: When solving pH problems, remember the logarithmic relationship. First apply the formula \text{pH} = -\log[\text{H}^+] to convert between pH and hydrogen ion concentration. Then to find [\text{H}^+] from pH, use [\text{H}^+] = 10^{-\text{pH}}. Finally, remember that each pH unit is a factor of 10 — pH 3 is 100 times more acidic than pH 5.

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}.

Solution

  1. 1
    Recall the pH formula: \text{pH} = -\log[\text{H}^+], where [\text{H}^+] is the hydrogen ion concentration in mol/L.
  2. 2
    Identify the given value: [\text{H}^+] = 1.0 \times 10^{-4}\,\text{mol/L}.
  3. 3
    Apply the formula: \text{pH} = -\log(1.0 \times 10^{-4}) = -(-4) = 4

Answer

\text{pH} = 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}^-].

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.)

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?
← Back to pH Formula Explained Common Mistakes Practice Mode

Background Knowledge

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

acidbaseconcentration