Summary

This article details the most common methods to quantify the concentration of a component in a mixture, and details how to convert between these concentrations. Concentration is commonly expressed in moles per volume, mass per volume, mass percentage, volume percentage, mole percentage and parts per million. Using density and/or molecular weight properties it is possible to convert between any of the above measures.

Definitions

mm:Mass of component
MWMW:Molecular weight
ppmppm:Parts per million
ppm(w)ppm(w):Parts per million, weight basis
ppm(v)ppm(v):Parts per million, volume basis
ppm(mol)ppm(mol):Parts per million, mole basis
vv:Volume fraction
ww:Mass fraction
xx:Mole fraction
ρ\rho:Density or mass per volume concentration

Concentration Conversions

Below are tabulated the concentration conversions between many measures of concentration. In all cases we are describing the concentration of substance 1 in total substance, and this is used in subscripts in the formulae below.

Convert FromConvert ToTypical UnitsFormula
mol/molmass/mass–w=x×MW1MWtotw = x \times \frac{MW_{1}}{MW_{tot}}
mol/molvolume/volume–v=x×MW1MWtot×ρtotρ1v = x \times \frac{MW_{1}}{MW_{tot}} \times \frac{\rho_{tot}}{\rho_{1}}
mol/molmolar concentrationmol/Lc=x×ρtotMWtotc = x \times \frac{\rho_{tot}}{MW_{tot}}
mol/molmass/volumeg/Lm1vtot=x×MW1MWtot×ρtot\frac{m_{1}}{v_{tot}} = x \times \frac{MW_{1}}{MW_{tot}} \times \rho_{tot}
mol/molparts per million (ppm mol)μmol/molppm(mol)=x×1,000,000ppm(mol) = x \times 1{,}000{,}000
mol/molparts per million (ppm weight)mg/kgppm(w)=x×MW1MWtot×1,000,000ppm(w) = x \times \frac{MW_{1}}{MW_{tot}} \times 1{,}000{,}000
mol/molparts per million (ppm volume)μL/Lppm(v)=x×MW1MWtot×ρtotρ1×1,000,000ppm(v) = x \times \frac{MW_{1}}{MW_{tot}} \times \frac{\rho_{tot}}{\rho_{1}} \times 1{,}000{,}000
mass/massmol/mol–x=w×MWtotMW1x = w \times \frac{MW_{tot}}{MW_{1}}
mass/massvolume/volume–v=w×ρtotρ1v = w \times \frac{\rho_{tot}}{\rho_{1}}
mass/massmolar fractionmol/Lc=w×ρtotMW1c = w \times \frac{\rho_{tot}}{MW_{1}}
mass/massmass/volumeg/Lm1vtot=w×ρtot\frac{m_{1}}{v_{tot}} = w \times \rho_{tot}
mass/massparts per million (ppm mol)μmol/molppm(mol)=w×MWtotMW1×1,000,000ppm(mol) = w \times \frac{MW_{tot}}{MW_{1}} \times 1{,}000{,}000
mass/massparts per million (ppm weight)mg/kgppm(w)=w×1,000,000ppm(w) = w \times 1{,}000{,}000
mass/massparts per million (ppm volume)μL/Lppm(v)=w×ρtotρ1×1,000,000ppm(v) = w \times \frac{\rho_{tot}}{\rho_{1}} \times 1{,}000{,}000
volume/volumemol/mol–x=v×ρ1ρtot×MWtotMW1x = v \times \frac{\rho_{1}}{\rho_{tot}} \times \frac{MW_{tot}}{MW_{1}}
volume/volumemass/mass–w=v×ρ1ρtotw = v \times \frac{\rho_{1}}{\rho_{tot}}
volume/volumemolar fractionmol/Lc=v×ρ1MW1c = v \times \frac{\rho_{1}}{MW_{1}}
volume/volumemass/volumeg/Lm1vtot=v×ρ1\frac{m_{1}}{v_{tot}} = v \times \rho_{1}
volume/volumeparts per million (ppm mol)μmol/molppm(mol)=v×ρ1ρtot×MWtotMW1×1,000,000ppm(mol) = v \times \frac{\rho_{1}}{\rho_{tot}} \times \frac{MW_{tot}}{MW_{1}} \times 1{,}000{,}000
volume/volumeparts per million (ppm weight)mg/kgppm(w)=v×ρ1ρtot×1,000,000ppm(w) = v \times \frac{\rho_{1}}{\rho_{tot}} \times 1{,}000{,}000
volume/volumeparts per million (ppm volume)μL/Lppm(v)=v×1,000,000ppm(v) = v \times 1{,}000{,}000
Molar Concentration (c)mol/mol–x=c×MWtotρtotx = c \times \frac{MW_{tot}}{\rho_{tot}}
Molar Concentration (c)mass/mass–w=c×MW1ρtotw = c \times \frac{MW_{1}}{\rho_{tot}}
Molar Concentration (c)volume/volume–v=c×MW1ρ1v = c \times \frac{MW_{1}}{\rho_{1}}
Molar Concentration (c)mass/volumeg/Lm1vtot=c×MW1\frac{m_{1}}{v_{tot}} = c \times MW_{1}
Molar Concentration (c)parts per million (ppm mol)μmol/molppm(mol)=c×MW1×1,000,000ppm(mol) = c \times MW_{1} \times 1{,}000{,}000
Molar Concentration (c)parts per million (ppm weight)mg/kgppm(w)=c×MW1ρtot×1,000,000ppm(w) = c \times \frac{MW_{1}}{\rho_{tot}} \times 1{,}000{,}000
Molar Concentration (c)parts per million (ppm volume)μL/Lppm(v)=c×MW1MW1×1,000,000ppm(v) = c \times \frac{MW_{1}}{MW_{1}} \times 1{,}000{,}000
mass/volumemol/mol–x=m1vtot×1ρtot×MWtotMW1x = \frac{m_{1}}{v_{tot}} \times \frac{1}{\rho_{tot}} \times \frac{MW_{tot}}{MW_{1}}
mass/volumemass/mass–w=m1vtot×1ρtotw = \frac{m_{1}}{v_{tot}} \times \frac{1}{\rho_{tot}}
mass/volumevolume/volume–v=m1vtot×1ρ1v = \frac{m_{1}}{v_{tot}} \times \frac{1}{\rho_{1}}
mass/volumemolar fractionmol/Lc=m1vtot×1MW1c = \frac{m_{1}}{v_{tot}} \times \frac{1}{MW_{1}}
mass/volumeparts per million (ppm mol)μmol/molppm(mol)=m1vtot×1ρtot×MWtotMW1×1,000,000ppm(mol) = \frac{m_{1}}{v_{tot}} \times \frac{1}{\rho_{tot}} \times \frac{MW_{tot}}{MW_{1}} \times 1{,}000{,}000
mass/volumeparts per million (ppm weight)mg/kgppm(w)=m1vtot×1ρtot×1,000,000ppm(w) = \frac{m_{1}}{v_{tot}} \times \frac{1}{\rho_{tot}} \times 1{,}000{,}000
mass/volumeparts per million (ppm volume)μL/Lppm(v)=m1vtot×1ρ1×1,000,000ppm(v) = \frac{m_{1}}{v_{tot}} \times \frac{1}{\rho_{1}} \times 1{,}000{,}000
parts per million (ppm mol)mol/molμmol/molx=ppm(mol)×11,000,000x = ppm(mol) \times \frac{1}{1{,}000{,}000}
parts per million (ppm mol)mass/mass–w=ppm(mol)×11,000,000×MW1MWtotw = ppm(mol) \times \frac{1}{1{,}000{,}000} \times \frac{MW_{1}}{MW_{tot}}
parts per million (ppm mol)volume/volume–v=ppm(mol)×11,000,000×MW1MWtot×ρtotρ1v = ppm(mol) \times \frac{1}{1{,}000{,}000} \times \frac{MW_{1}}{MW_{tot}} \times \frac{\rho_{tot}}{\rho_{1}}
parts per million (ppm mol)molar fractionmol/Lc=ppm(mol)×ρtotMWtot×11,000,000c = ppm(mol) \times \frac{\rho_{tot}}{MW_{tot}} \times \frac{1}{1{,}000{,}000}
parts per million (ppm mol)mass/volumeg/Lm1vtot=ppm(mol)×11,000,000×MW1MWtot×ρtot\frac{m_{1}}{v_{tot}} = ppm(mol) \times \frac{1}{1{,}000{,}000} \times \frac{MW_{1}}{MW_{tot}} \times \rho_{tot}
parts per million (ppm mol)parts per million (ppm weight)mg/kgppm(w)=ppm(mol)×MW1MWtotppm(w) = ppm(mol) \times \frac{MW_{1}}{MW_{tot}}
parts per million (ppm mol)parts per million (ppm volume)μL/Lppm(v)=ppm(mol)×MW1MWtot×ρtotρ1ppm(v) = ppm(mol) \times \frac{MW_{1}}{MW_{tot}} \times \frac{\rho_{tot}}{\rho_{1}}
parts per million (ppm weight)mol/mol–x=ppm(w)×11,000,000×MWtotMW1x = ppm(w) \times \frac{1}{1{,}000{,}000} \times \frac{MW_{tot}}{MW_{1}}
parts per million (ppm weight)mass/mass–w=ppm(w)×11,000,000w = ppm(w) \times \frac{1}{1{,}000{,}000}
parts per million (ppm weight)volume/volume–v=ppm(w)×11,000,000×ρtotρ1v = ppm(w) \times \frac{1}{1{,}000{,}000} \times \frac{\rho_{tot}}{\rho_{1}}
parts per million (ppm weight)molar fractionmol/Lc=ppm(w)×ρtotMW1×11,000,000c = ppm(w) \times \frac{\rho_{tot}}{MW_{1}} \times \frac{1}{1{,}000{,}000}
parts per million (ppm weight)mass/volumeg/Lm1vtot=ppm(w)×11,000,000×ρtot\frac{m_{1}}{v_{tot}} = ppm(w) \times \frac{1}{1{,}000{,}000} \times \rho_{tot}
parts per million (ppm weight)parts per million (ppm mol)μmol/molppm(mol)=ppm(w)×MWtotMW1ppm(mol) = ppm(w) \times \frac{MW_{tot}}{MW_{1}}
parts per million (ppm weight)parts per million (ppm volume)μL/Lppm(v)=ppm(w)×ρtotρ1ppm(v) = ppm(w) \times \frac{\rho_{tot}}{\rho_{1}}
parts per million (ppm volume)mol/mol–x=ppm(v)×11,000,000×ρ1ρtot×MWtotMW1x = ppm(v) \times \frac{1}{1{,}000{,}000} \times \frac{\rho_{1}}{\rho_{tot}} \times \frac{MW_{tot}}{MW_{1}}
parts per million (ppm volume)mass/mass–w=ppm(v)×11,000,000×ρ1ρtotw = ppm(v) \times \frac{1}{1{,}000{,}000} \times \frac{\rho_{1}}{\rho_{tot}}
parts per million (ppm volume)volume/volume–v=ppm(v)×11,000,000v = ppm(v) \times \frac{1}{1{,}000{,}000}
parts per million (ppm volume)molar fractionmol/Lc=ppm(v)×11,000,000×ρ1MW1c = ppm(v) \times \frac{1}{1{,}000{,}000} \times \frac{\rho_{1}}{MW_{1}}
parts per million (ppm volume)parts per million (ppm mol)μmol/molppm(mol)=ppm(v)×ρ1ρtot×MWtotMW1ppm(mol) = ppm(v) \times \frac{\rho_{1}}{\rho_{tot}} \times \frac{MW_{tot}}{MW_{1}}
parts per million (ppm volume)mass/volumeg/Lm1vtot=ppm(v)×11,000,000×ρ1\frac{m_{1}}{v_{tot}} = ppm(v) \times \frac{1}{1{,}000{,}000} \times \rho_{1}
parts per million (ppm volume)parts per million (ppm weight)mg/kgppm(w)=ppm(v)×ρ1ρtotppm(w) = ppm(v) \times \frac{\rho_{1}}{\rho_{tot}}