pH Formula
What is the pH Formula?
pH measures how acidic or basic a solution is, based on the concentration of hydrogen ions ([H⁺]) dissolved in it. Because [H⁺] can range over many orders of magnitude, the formula uses a logarithm to compress that huge range into a manageable scale, typically running from 0 to 14: 0–6 is acidic, 7 is neutral, and 8–14 is basic (alkaline).
Because of the logarithm, each whole-number change in pH represents a tenfold change in hydrogen ion concentration — a solution with pH 3 has ten times more H⁺ than one with pH 4, not just one more unit's worth.
What Each Variable Means
When to Use It
- Determining how acidic or basic a solution is from its hydrogen ion concentration
- Comparing the relative acidity of two solutions on a consistent scale
- Converting between pH and hydrogen ion concentration in acid-base chemistry
Step-by-Step Example
Problem: A solution has a hydrogen ion concentration of 1 × 10⁻³ mol/L. Find its pH.
The hydrogen ion concentration is given directly.
[H⁺] = 1 × 10⁻³ mol/LTake the negative base-10 logarithm.
pH = -log(1 × 10⁻³)Interactive Calculator
Common Mistakes
Mistake: Forgetting the negative sign.
Fix: pH = -log[H⁺], with a negative sign — since [H⁺] is typically less than 1, log[H⁺] alone would be negative, and the formula flips it positive.
Mistake: Treating pH differences as linear rather than logarithmic.
Fix: A change of 1 pH unit represents a tenfold change in [H⁺], not a simple additive difference — pH 3 is ten times more acidic than pH 4, not just "one more."
Practice Questions
A solution has [H⁺] = 1 × 10⁻⁷ mol/L. Find its pH.
Which is more acidic: a solution with pH 2 or pH 5?
Frequently Asked Questions
What does a pH of 7 mean?
It means the solution is neutral — neither acidic nor basic — which is the pH of pure water at 25°C.
Can pH be negative or greater than 14?
Yes, for extremely concentrated acids or bases — the 0–14 range is typical for common solutions, but the formula itself has no such hard limit.