mol/L to ppb Converter - Molar to Parts per billion

Conversion derivation

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

1. 1

   Rewrite mol/L in the base unit

   $$1mol/L=1mol/L$$
2. 2

   Rewrite ppb in the base unit

   $$1\mathrm{ppb}=1\times 10^{-9}mol/L$$
3. 3

   Forward conversion

   $$\begin{array}{rl}1mol/L& =\frac{1\cancel{mol/L}}{1\times 10^{-9}\cancel{mol/L}}\times 1\mathrm{ppb}\\ & =\frac{1}{1\times 10^{-9}}\mathrm{ppb}\\ & =1,000,000,000\mathrm{ppb}\end{array}$$
4. 4

   Reverse conversion

   $$\begin{array}{rl}1\mathrm{ppb}& =\frac{1\times 10^{-9}\cancel{mol/L}}{1\cancel{mol/L}}\times 1mol/L\\ & =\frac{1\times 10^{-9}}{1}mol/L\\ & =1\times 10^{-9}mol/L\end{array}$$