pH Formula

The Formula

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

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

Quick Example

Lemon juice: pH ~2 (acidic). Pure water: pH 7 (neutral). Bleach: pH ~13 (strongly basic).

Notation

\text{pH} is the negative log of hydrogen ion concentration [\text{H}^+] in mol/L. pH 7 is neutral; below 7 is acidic, above 7 is basic.

What This Formula Means

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).

Formal View

pH is defined as the negative base-10 logarithm of the hydrogen ion activity: \text{pH} = -\log_{10} a_{\text{H}^+}. For dilute solutions, activity approximates concentration: \text{pH} \approx -\log_{10}[\text{H}^+]. At 25°C, the ion product of water gives \text{pH} + \text{pOH} = 14.

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}^-].

Common Mistakes

  • Thinking pH is linear — a one-unit pH change means a tenfold change in [\text{H}^+], so pH 2 is 100 times more acidic than pH 4
  • Forgetting that pH can go below 0 or above 14 for very concentrated solutions — the 0-14 range applies to typical aqueous solutions
  • Confusing pH with pOH — pH measures [\text{H}^+], pOH measures [\text{OH}^-], and they sum to 14 at 25°C

Common Mistakes Guide

If this formula feels simple in isolation but keeps breaking during real problems, review the most common errors before you practice again.

pH Mistakes

Why This Formula Matters

pH affects everything from enzyme activity to environmental health. Blood must stay between pH 7.35 and 7.45 for survival, soil pH determines which crops can grow, and industrial processes require precise pH control for product quality and safety.

Frequently Asked Questions

What is the pH formula?

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.

How do you use the pH formula?

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

What do the symbols mean in the pH formula?

\text{pH} is the negative log of hydrogen ion concentration [\text{H}^+] in mol/L. pH 7 is neutral; below 7 is acidic, above 7 is basic.

Why is the pH formula important in Chemistry?

pH affects everything from enzyme activity to environmental health. Blood must stay between pH 7.35 and 7.45 for survival, soil pH determines which crops can grow, and industrial processes require precise pH control for product quality and safety.

What do students get wrong about pH?

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

What should I learn before the pH formula?

Before studying the pH formula, you should understand: acid, base, concentration.

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Related Formulas

Concentration Formula