## Dumas vapor density

Jean-Baptiste Dumas devised a method of determining the molar mass of substances that can conveniently be turned into vapor. The Dumas method is still the subject of laboratory exercises in chemistry courses. It involves finding the mass, volume, temperature, and pressure of a substance in the vapor phase. The determination of molar mass in a modern Dumas method experiment uses the ideal gas law: knowing the pressure, volume, and temperature of a gas sample allows one to know the number of moles[1]; knowing the mass that corresponds to that number of moles allows computation of the molar mass. Alternatively,
pV = nRT = mRT/M
so
M = mRT/(pV) .
1) Dumas investigated mercury, finding that at 446°C and 765 torr, 0.812 g of mercury vapor filled a vessel of volume 0.235186 L. From these data, compute the molar mass of mercury.

2) Dumas reported results on a compound he called "liquor of Libavius." He carried out the experiment at 124°C, but he expressed the vapor density for standard conditions of 0°C and 1.00 atm. If this compound remained a vapor at 0°C and 1.00 atm, its density would be 11.9514 g/L.
a) What is the molar mass of "liquor of Libavius?"
b) "Liquor of Libavius" is a compound of tin and chlorine. Look at a modern periodic table and suggest a formula consistent with the molar mass.

3) The raw data that Dumas collected included temperature, pressure, and mass measurements. He measured the mass of a vessel when it was filled with air, when it was filled with the vapor he was investigating, and when it was filled with (liquid) water. For a certain compound of arsenic and chlorine, the data, all at 758 torr, were:

mass of vessel filled with dry air at 25°C = 97.432 g
mass of vessel filled with vapor at 175°C = 99.420 g
mass of vessel filled with water at 23°C = 638.740 g
a) Find the molar mass of this arsenic chloride. First, assume that the volume of the vessel in mL is the same as the mass of the water that fills the vessel. (The mass of the air that fills the vessel is negligible here.) The mass of the vapor is the difference between the mass of vessel filled with vapor and that of the empty vessel. (The mass of the air that fills the vessel is not negligible here.) Find the mass of the empty vessel from the reported mass of the vessel filled with air and the density of air at 25°C and 758 torr, which is 1.187 g/L.
b) Look at a modern periodic table and suggest a formula consistent with the molar mass.

4) Dumas reported results for sulfur that made him (and others) question the reliability of his method. "In the first experiment to which I submitted this element, I had no doubt that some error had escaped my attention," he wrote. However, he kept getting similar results. The average of several trials, carried out in different vessels and at different temperatures, was 8.49 g/L (converted to standard conditions of 0°C and 1.00 atm).
a) What is the molar mass of sulfur, according to his data?
b) Look at a modern periodic table; what does it suggest for the formula of sulfur vapor?

### Reference

J. Dumas, "Memoire sur quelques Points de la Théorie atomistique," Ann. Chim. Phys. 33, 337-391 (1826) [exercises 1-3]
J. Dumas, "Dissertation sur la Densité de la Vapeur de quelques corps simples," Ann. Chim. Phys. 50, 170-8 (1832) [exercise 4]
[1]The concept of the mole had not yet been developed in Dumas' day.
Copyright 2003 by Carmen Giunta. Permission is granted to reproduce for non-commercial educational purposes.