ppm to molec/nm3 Converter - Parts per million to Molecules per cubic nanometer

Conversion derivation

Express both ppm and molec/nm3 in the same base unit mol/L (molar), then cancel the shared base unit.

1. 1

   Rewrite ppm in the base unit

   $$1\mathrm{ppm}=0.000001mol/L$$
2. 2

   Rewrite molec/nm3 in the base unit

   $$1molec/nm3=1.66053907\times 10^{-48}mol/L$$
3. 3

   Forward conversion

   $$\begin{array}{rl}1\mathrm{ppm}& =\frac{0.000001\cancel{mol/L}}{1.66053907\times 10^{-48}\cancel{mol/L}}\times 1molec/nm3\\ & =\frac{0.000001}{1.66053907\times 10^{-48}}molec/nm3\\ & =6.02214076\times 10^{41}molec/nm3\end{array}$$
4. 4

   Reverse conversion

   $$\begin{array}{rl}1molec/nm3& =\frac{1.66053907\times 10^{-48}\cancel{mol/L}}{0.000001\cancel{mol/L}}\times 1\mathrm{ppm}\\ & =\frac{1.66053907\times 10^{-48}}{0.000001}\mathrm{ppm}\\ & =1.66053907\times 10^{-42}\mathrm{ppm}\end{array}$$