parts per million
Concentrationexact by definition
Parts per million is one part in 1e6, or exactly 1e-4 percent, and the factor is exact by definition. It is the standard reporting unit for dissolved minerals, hardness, alkalinity, chlorides and treatment chemical residuals in water. In dilute aqueous solution 1 ppm by mass is taken as 1 milligram per litre, an equivalence that rests on the density of water being close to 1 kg/L.
Watch out: ppm by mass and ppm by volume are different quantities and the distinction is not cosmetic. In water, ppm normally means mg/kg by mass and is treated as mg/L. In air and gas analysis, ppm almost always means ppmv, a volume or mole fraction, and converting ppmv to mg/m³ requires the gas's molar mass and the temperature and pressure. Separately, ppm as CaCO3 is not the same as ppm of the actual ion: it is a common-currency expression that recasts a hardness or alkalinity into the equivalent mass of calcium carbonate.
| 1 ppm | 0.0001 % |
About the parts per million
A part per million is one milligram in a kilogram, one gram in a tonne, one second in about eleven and a half days. In water treatment it is the unit almost everything is reported in, and the working convention is that 1 ppm equals 1 mg/L. That equivalence is not a definition, it is a consequence: one litre of water weighs one kilogram, so one milligram of solute in that litre is one milligram per kilogram, which is one part per million by mass. It is accurate to a fraction of a percent for ordinary fresh water and it starts to drift for brines and for hot water, where the density is no longer 1.000 kg/L.
The second thing to know is the "as CaCO3" convention. Hardness, alkalinity and several other parameters are reported not as the mass of the actual species but as the mass of calcium carbonate that would be chemically equivalent. The reason is arithmetic: calcium carbonate has a molar mass of 100.09 g/mol and an equivalent weight of 50.04, so expressing everything on that basis lets you add calcium and magnesium hardness together, or compare alkalinity against hardness, without converting each ion separately. To convert an actual ion concentration to CaCO3 equivalent, multiply by 50.04 and divide by the ion's equivalent weight: 40 ppm of calcium ion, equivalent weight 20.04, is \(40 \times 50.04/20.04 = 100\) ppm as CaCO3. A report that says 100 ppm hardness contains 40 ppm of actual calcium, and confusing the two is a real and frequent error.
Finally, ppm in a gas is a different animal. Air-quality and combustion figures are ppm by volume, which is the same as a mole fraction for an ideal gas, and converting to a mass concentration needs the molar mass and the state: 1 ppmv of carbon monoxide is about 1.15 mg/m³ at 25 °C and 101.325 kPa, while 1 ppmv of nitrogen dioxide is about 1.88 mg/m³. There is no universal factor, and a gas reading transcribed into a water-style ppm is meaningless.