# Dumas method of molecular weight determination

For the method for quantitative determination of nitrogen, see Dumas method.

The Dumas method of molecular weight determination was historically a procedure used to determine the molecular weight of an unknown substance. The Dumas method is appropriate to determine the molecular weights of volatile organic substances that are liquids at room temperature.[1][2]

The method was designed by a French chemist named Jean Baptiste André Dumas, after whom the procedure is now named. Even though, during the nineteenth century the science of chemistry was at a relatively early state, Dumas was able to show that the vapor densities of some organic compounds are directly proportional to their molecular weights.

Today, modern methods such as mass spectrometry and elemental analysis are used to determine the molecular weight of a substance.

## Determination

The procedure entailed placing a small quantity of the unknown substance into a tared vessel of known volume. The vessel is then heated in a boiling water bath; all the air within the flask would be expelled, replaced by the vapor of the unknown substance. When no remaining liquid can be observed, the vessel may be sealed (e.g. with a flame), dried, and weighed.

By subtracting the tare of the vessel, the actual mass of the unknown vapor within the vessel can be calculated. Assuming the unknown compound obeyed the ideal gas equation, the number of moles of the unknown compound, n, can be determined by

[itex]PV=nRT\,[/itex]

where the pressure, P, is the atmospheric pressure, V is the measured volume of the vessel, T is the absolute temperature of the boiling water bath, and R is the ideal gas constant.

By dividing the mass in grams of the vapor within the vessel by the calculated number of moles, the molecular weight may be obtained.

## Assumptions

Two major assumptions are used in this method:

1. The compound vapor behaves ideally
2. Either the volume of the vessel does not vary significantly between room and the working temperature, or the volume of the vessel may be accurately determined at the working temperature