Mole and Avogadro constant

A mole is a counting unit. $N_A$ is the number of particles in one mole. $N_A = 6.022\times10^{23}\ \text{mol}^{-1}$ Molecular mass in u = molar mass $M_m$ in g/mol (e.g. $CO_2$: 44 u → 0.044 kg/mol).

$N = \frac{m}{M_m}N_A$

ppm is a ratio of molecules, not mass: $\text{ppm}_X = \frac{N_X}{N_{atm}}\times10^6$ For two gases in the atmosphere: $\frac{M_X}{M_{CO_2}} = \frac{\text{ppm}_X}{\text{ppm}_{CO_2}}\frac{M_{m,X}}{M_{m,CO_2}}$

Related: GWP. Global warming potential