Fuel Cell Proportions In Engineering Thermodynamics (beginning level) we avoid involvement with moles of gases by always writing the gas constant as R/M. Inevitably, however, one must relate moles to mass and vice versa. To that purpose we include this simple illustration that mass is conserved in the hydrogen and oxygen reaction that forms water. This calculation serves well as an introduction to chemical equations.

In a fuel cell, hydrogen is oxidized (by oxygen) in the following ideal reaction of moles of matter:

2H₂ + O₂ = 2H₂O

The equation implies a perfect reaction in which two molecules of hydrogen (M = 2.0) react with one oxygen molecule (M = 32) to produce 2 water molecules (M = 18).

If the mass of hydrogen is two kilograms, how many kilograms of oxygen are needed for complete reaction and how much water is produced?

Multiply each number of moles by its molecular weight, M. Since m = η M, this will change the equation to a mass basis. The units of M are kg/kgmol.

So 16 kilograms of oxygen are needed and 18 kilograms of water will result.