Parts per Million as a Mass Ratio

Define ppm as mass of solute over mass of water and show why ppm equals mg/L for dilute aqueous solutions (1 L of water weighs close to 1,000,000 mg).

$$1\text{ppm}\approx \frac{1\text{mg}}{1,000,000\text{mg}}\approx 1\frac{\text{mg}}{\text{kg}}\approx 1\frac{\text{mg}}{\text{L}}$$

Variables

Symbol	Meaning	Unit
ppm	Parts per million by mass	dimensionless ratio

Worked example

Because 1 L of water weighs about 1,000,000 mg, 1 mg of solute in 1 L is about 1 ppm. This holds well for dilute solutions but loses accuracy as concentration rises and density departs from pure water.

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Part of The Blueprint of Water