ppb to molec/cm³ Converter - Parts per billion to Molecules per cubic centimeter

Conversion derivation

Express both ppb and molec/cm³ in the same base unit mol/L (molar), then cancel the shared base unit.

1. 1

   Rewrite ppb in the base unit

   $$1\mathrm{ppb}=1\times 10^{-9}mol/L$$
2. 2

   Rewrite molec/cm³ in the base unit

   $$1molec/c{\mathrm{m}}^3=1.66053907\times 10^{-27}mol/L$$
3. 3

   Forward conversion

   $$\begin{array}{rl}1\mathrm{ppb}& =\frac{1\times 10^{-9}\cancel{mol/L}}{1.66053907\times 10^{-27}\cancel{mol/L}}\times 1molec/c{\mathrm{m}}^3\\ & =\frac{1\times 10^{-9}}{1.66053907\times 10^{-27}}molec/c{\mathrm{m}}^3\\ & =6.02214076\times 10^{17}molec/c{\mathrm{m}}^3\end{array}$$
4. 4

   Reverse conversion

   $$\begin{array}{rl}1molec/c{\mathrm{m}}^3& =\frac{1.66053907\times 10^{-27}\cancel{mol/L}}{1\times 10^{-9}\cancel{mol/L}}\times 1\mathrm{ppb}\\ & =\frac{1.66053907\times 10^{-27}}{1\times 10^{-9}}\mathrm{ppb}\\ & =1.66053907\times 10^{-18}\mathrm{ppb}\end{array}$$