Formula
\(n_i = \frac{w_i}{M_i} \qquad y_i = \frac{n_i}{\sum_j n_j} \qquad M = \frac{1}{\sum_i w_i / M_i}\)
Variables
| Symbol | Meaning | SI unit |
|---|---|---|
| \(w_i\) | mass fraction of species i: \(w_{O_2}\), \(w_{N_2}\), \(w_{CO_2}\), \(w_{H_2O}\), \(w_{SO_2}\), \(w_{CO}\), \(w_{H_2}\), \(w_{Ar}\) | – |
| \(M_i\) | molar mass of species i | kg/kmol |
| \(n_i\) | moles of species i per kilogram of mixture | kmol/kg |
| \(y_i\) | mole (volume) fraction of species i: \(y_{O_2}\), \(y_{N_2}\), \(y_{CO_2}\), \(y_{H_2O}\), \(y_{SO_2}\), \(y_{CO}\), \(y_{H_2}\), \(y_{Ar}\) | – |
| \(M\) | molar mass of the mixture | kg/kmol |
Method and standards
Molar masses from IUPAC 2013 conventional atomic weights. Exact for ideal-gas mixtures.
Assumptions and limits
- Ideal gas: mole fraction equals volume fraction.
- Fractions that do not sum to 1 are normalised; the page reports the original sum.
References
- IUPAC 2013 standard atomic weights
Questions and answers
Why do light gases such as hydrogen take so much more volume than mass?
Volume fraction follows moles, and a kilogram of hydrogen is about 496 moles while a kilogram of CO₂ is about 23 moles. The same mass of hydrogen occupies 22 times the volume.