Humidity of PEMFC Air

The humidity of the air in a PEMFC must be carefully controlled. The air must be dry enough to evaporate the product water, but not so dry that it dries too much - it is essential that the electrolyte membrane retains a high water content. The humidity should be above about 80% to prevent excess drying, but must be below 100%, or liquid water would collect in the electrodes. 

What conditions are required to bring this about Higher airflow would obviously reduce humidity, as would raising the temperature. But is there some theory that can help us put some detail into the picture Fortunately, it is not too difficult to derive a simple formula for the humidity of the exit air of a fuel cell. 

The partial pressure of a gas is proportional to the number of molecules of that gas in the mixture - the molar fraction . If we consider the exit gas of a fuel cell, then we can 

Pw number of water molecules total number of molecules 

Where hw is the number of moles of water leaving the cell per second, fio2 is the number of moles of oxygen leaving the cell per second, 

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