pH is a measure of the acidity or alkalinity of an aqueous solution. It indicates how many hydrogen ions are present in the solution and lets you quickly judge whether a substance is an acid, a base, or neutral. In this article we explain the pH formula, the pH scale, and we show the calculations using an example.
The pH formula
We define pH as the negative decimal logarithm of the hydrogen ion concentration:
- pH = -log[H⁺] — where [H⁺] is the hydrogen ion concentration in mol/dm³
- [H⁺] = 10⁻ᵖᴴ — the inverse formula lets you calculate the concentration from a known pH
The square brackets denote the molar concentration of a given ion.
The pH scale
The pH scale usually spans the range from 0 to 14:
- pH below 7 — acidic (more hydrogen ions)
- pH equal to 7 — neutral (pure water)
- pH above 7 — alkaline (fewer hydrogen ions)
The scale is logarithmic, so a change of one pH unit means a tenfold change in the hydrogen ion concentration. A solution with a pH of 4 is ten times more acidic than a solution with a pH of 5.
Worked example
The hydrogen ion concentration in a solution is [H⁺] = 0.001 mol/dm³, that is 10⁻³. We calculate the pH.
- We apply the formula pH = -log[H⁺].
- We substitute: pH = -log(10⁻³).
- The logarithm: log(10⁻³) = -3.
- Result: pH = -(-3) = 3.
The solution has a pH of 3, so it is acidic.
Calculating the concentration from a known pH
If we know the pH and want to calculate the hydrogen ion concentration, we use the inverse formula. For pH = 5 we have [H⁺] = 10⁻⁵ = 0.00001 mol/dm³. The lower the pH, the higher the hydrogen ion concentration.
Acid-base indicators
To estimate the pH without calculations, we use indicators, that is substances that change colour depending on the reaction. Phenolphthalein stays colourless in acidic and neutral environments and turns raspberry pink in an alkaline one. Methyl orange is red in acid and yellow in a base. The most popular universal paper covers the whole range of the scale and, when dipped into a solution, takes on a colour matching the given pH value. Indicators are quick and convenient but less accurate than calculations or a measurement with a pH meter.
pOH and its link to pH
Alongside pH we define pOH for hydroxide ions. At a temperature of 25°C a simple relationship holds:
- pH + pOH = 14
So if the pOH of a solution is 4, then pH = 14 - 4 = 10, meaning the solution is alkaline.
Examples of the pH of everyday substances
For reference it is worth knowing the approximate pH values:
- Lemon juice — about 2 (strongly acidic)
- Vinegar — about 3
- Black coffee — about 5
- Pure water — 7 (neutral)
- Seawater — about 8
- Baking soda solution — about 9
- Bleach — about 12.5 (strongly alkaline)
These values help judge whether a calculated result makes sense.
Second example: calculating the pH of a base
A solution has a hydroxide ion concentration of [OH⁻] = 0.01 mol/dm³, that is 10⁻². We calculate the pH.
- First pOH = -log[OH⁻] = -log(10⁻²) = 2.
- We use the relationship pH + pOH = 14.
- Hence pH = 14 - 2 = 12.
The solution has a pH of 12, so it is strongly alkaline.
Most common mistakes
- Omitting the minus sign — pH is a negative logarithm, so acidic solutions have a positive but low pH.
- Confusing the natural logarithm with the decimal one — in the formula we use the logarithm to base 10.
- Wrong concentration — the value of [H⁺] must be expressed in mol/dm³.
- Confusing pH with pOH — pH refers to hydrogen ions, while pOH refers to hydroxide ions.
Frequently asked questions
- How can I measure pH without calculations? Indicator papers or electronic pH meters are used, which show the value directly.
- Can pH be negative? Yes, for very concentrated acids the hydrogen ion concentration can exceed 1 mol/dm³, giving a pH below zero.
- Why is the scale logarithmic? Because ion concentrations vary over many orders of magnitude, and the logarithm reduces them to a convenient range of numbers.
Summary
pH = -log[H⁺] is a measure of the acidity of a solution. Values below 7 mean an acid, 7 means neutral, and above 7 means a base. The scale is logarithmic, so a small change in pH means a large change in the hydrogen ion concentration.
Work out the pH of a solution at once: pH Calculator →