Formula
\(M = \sum_i y_i M_i \qquad w_i = \frac{y_i\,M_i}{M}\)
Variables
| Symbol | Meaning | SI unit |
|---|---|---|
| \(y_i\) | mole (volume) fraction of species i: \(y_{O_2}\), \(y_{N_2}\), \(y_{CO_2}\), \(y_{H_2O}\), \(y_{SO_2}\), \(y_{CO}\), \(y_{H_2}\), \(y_{Ar}\) | – |
| \(M_i\) | molar mass of species i | kg/kmol |
| \(M\) | molar mass of the mixture | kg/kmol |
| \(w_i\) | mass fraction of species i: \(w_{O_2}\), \(w_{N_2}\), \(w_{CO_2}\), \(w_{H_2O}\), \(w_{SO_2}\), \(w_{CO}\), \(w_{H_2}\), \(w_{Ar}\) | – |
Method and standards
Molar masses are computed from the IUPAC 2013 conventional atomic weights (C 12.011, H 1.008, O 15.999, N 14.007, S 32.06, Ar 39.948 kg/kmol). The conversion is exact for ideal-gas mixtures.
Assumptions and limits
- Ideal gas: volume fraction equals mole 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
Are volume percent and mole percent the same?
For an ideal gas, yes (Avogadro's law). Flue gas and fuel gas at atmospheric pressure are close enough to ideal for this to hold within 0.1 %.
My analysis does not add up to 100 %. What happens?
The calculator normalises the fractions to 100 % and tells you by how much they were off. Check for a missing component such as water vapour or nitrogen.