Section: 8 | Mass- and Volume-Based Concentration Units |

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MASS- AND VOLUME-BASED CONCENTRATION UNITS

Thomas J. Bruno and Paris D. N. Svoronos

A variety of concentration units are used in analytical chemistry, and the most common are provided in this table (Ref. 1). The reference below provides additional details.

Reference

Bruno, T. J., and Svoronos, P. D. N., CRC Handbook of Basic Tables for Chemical Analysis – Data-Driven Methods and Interpretation, Fourth Edition, CRC Press/Taylor & Francis, Boca Raton, FL, 2021. [https://doi.org/10.1201/b22281]

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TABLE 1. Concentration Units Conversion – Parts per Million

Parts per Million		Percent
1 ppm	=	0.0001 %
10 ppm	=	0.001 %
100 ppm	=	0.01 %
1000 ppm	=	0.1 %
10 000 ppm	=	1.0 %
100 000 ppm	=	10.0 %
1 000 000 ppm	=	100.0 %

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TABLE 2. Concentration Units Conversion – Parts per Billion

Parts per Billion		Percent
10	=	0.000 001 %
100	=	0.000 01 %
1000	=	0.0001 %
10 000	=	0.001 %
100 000	=	0.01 %
1 000 000	=	0.1 %

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TABLE 3. Concentration Units Conversion – Parts per Trillion

Parts per Trillion		Percent
100	=	1 × 10^–8 %
10 000	=	0.000 001 %
1 000 000	=	0.0001 %
100 000 000	=	0.01 %

Because the mass of one liter of water is approximately one kg, mg/L units of dilute aqueous solution are nearly equal to ppm units. The precise equivalence is obtained by dividing by the density, ρ:

ppm = (mg/L)/ρ

where the solution density, ρ, is in g cm^–3. Some sources will substitute specific gravity for density in the above equation. The specific gravity is the ratio of the solution density to that of the density of pure water at 4 °C. Because the density of pure water at 4 °C is very nearly 1 g cm^–3, the specific gravity is numerically equal (within an uncertainty of 25 ppm) to the solution density when the latter is expressed in units of g cm^–3.

Concentration Units Nomenclature

The following table provides guidance in the use of base-10 concentration units (presented in the three preceding tables), since there are differences in usage worldwide.

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TABLE 4. Notation for Large Numbers in Different Countries

Number	Number of Zeros	Name (Scientific Community)	Name (United Kingdom, France, Germany)
1000.	3	thousand	thousand
1 000 000.	6	million	million
1 000 000 000.	9	billion	milliard, or thousand million
1 000 000 000 000.	12	trillion	billion
1 000 000 000 000 000.	15	quadrillion	thousand billion

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TABLE 5. Molar-Based Concentration Units


Molarity *, M:	(moles of solute)/(liters of solution)
Molality, m:	(moles of solute)/(kilograms of solvent)
Normality, N:	(equivalents* of solute)/(liters of solution)
Formality, F:	(moles of solute)/(kilograms of solution)

^{* This unit is temperature dependent.}

To convert from ppm to formality units:

F = ppm/(1000 RMM)

where RMM is the relative molecular mass of the solute i.

To convert from ppm to molality units:

m = [ppm/(1000 RMM)] [1/(1 – tds/1 000 000)]

where tds is the total dissolved solids in ppm in the solution.

To convert from ppm to molarity units:

M = [ppm/(1000 RMM)] ρ

where ρ is the solution density.

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MASS- AND VOLUME-BASED CONCENTRATION UNITS

Reference

TABLE 1. Concentration Units Conversion – Parts per Million

TABLE 2. Concentration Units Conversion – Parts per Billion

TABLE 3. Concentration Units Conversion – Parts per Trillion

Concentration Units Nomenclature

TABLE 4. Notation for Large Numbers in Different Countries

TABLE 5. Molar-Based Concentration Units

To convert from ppm to formality units:

To convert from ppm to molality units:

To convert from ppm to molarity units:

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