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From pH to concentration

If you know the pH, you get the oxonium concentration by taking ten to the power of minus pH. Because the scale is logarithmic, two pH units mean a factor of one hundred, not a factor of two. pH 3 is therefore a hundred times the oxonium concentration of pH 5. It is easy to underestimate the difference if you only look at the numbers 3 and 5. The same rule applies upwards: pH 9 is ten times as basic as pH 8, measured in hydroxide.

[H3O+]=10−pH[\mathrm{H}_3\mathrm{O}^+] = 10^{-\mathrm{pH}}oxonium from pH

Symbols

pH\mathrm{pH}the stated acidity
[H3O+][\mathrm{H}_3\mathrm{O}^+]oxonium concentrationmol/L

Example

pH 3 gives [H3O+]=10−3=0.001[\mathrm{H}_3\mathrm{O}^+] = 10^{-3} = 0.001 mol/L.

From pH 5 to pH 3 the factor is 102=10010^{2} = 100.

Write the concentration with the unit mol/L. 0.001 mol/L is the same as 10⁻³ mol/L.
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Part of Chemistry 1: Acids, bases and pH.