Avogadro's hypotheses

Amedeo Avogadro's principal contribution to chemistry was a paper in which he advanced two hypotheses: (1) that equal volumes of gas contain equal numbers of molecules and (2) that elementary gases such as hydrogen, nitrogen, and oxygen were composed of two atoms.[1] For simplicity, let us call the first the "volumes" hypothesis and the second the "diatomics" hypothesis. Avogadro was correct in both of these hypotheses, which he used to reconcile and correct Dalton's atomic hypothesis with Gay-Lussac's results on combining volumes.

1) If the volumes hypothesis is correct, then the relative masses of gas molecules can be computed from gas densities. (After all, the density is the mass of a unit volume, and that volume contains the same number of molecules, whatever the gas.) Construct a table of relative molecular masses based on the gas densities reported by Avogadro and using hydrogen as the unit molecular mass.

moleculegas density (air = 1)
oxygen1.10359
hydrogen0.07321
nitrogen0.96913
oxymuriatic acid2.470
water vapor0.625
nitrous gas1.03636
nitrous oxide1.52092
muriatic acid gas1.278
(Hint: The molecular mass of "nitrous gas" relative to hydrogen is the ratio of the mass of a "nitrous gas" molecule to a hydrogen molecule.)

2) The mass scale computed in the previous exercise has the hydrogen molecule as its unit mass. It might make more sense to take the hydrogen atom as the unit. What is the mass of the hydrogen molecule if the hydrogen atom is one mass unit? On this sacle, what is the mass of the oxygen molecule, nitrous gas, etc.?

3) Hydrogen, oxygen, nitrogen, and "oxymuriatic acid" are all diatomic elements. (Nowadays we call "oxymuriatic acid" chlorine.) On this scale where a hydrogen atom is one mass unit, what are the atomic masses of these elements?

4) Assume that molecules are made of small whole numbers of atoms. The masses of all of the constituent atoms ought to add up to the mass of a molecule.
a) Water vapor is a compound of hydrogen and oxygen. How many atoms of each element in one molecule of water vapor? Show that the molecular mass of water vapor is consistent with the atomic masses of the atoms and your proposed formula. (For example, Dalton thought that the formula for water was HO. If that were correct, then the molecular mass of water vapor ought to equal the atomic mass of hydrogen plus that of oxygen.)
b) Nitrous gas is a compound of nitrogen and oxygen. How many atoms of each element in one molecule of nitrous gas? Show that the molecular mass is consistent with the formula.
c) Nitrous oxide is another compound of nitrogen and oxygen. How many atoms of each element in one molecule of nitrous oxide? Show that the molecular mass is consistent with the formula.
d) Muriatic acid gas is a compound of hydrogen and oxymuriatic acid. How many atoms of each element in one molecule of muriatic acid gas? Show that the molecular mass is consistent with the formula.

5) Write balanced chemical equations for the formation of water vapor, nitrous gas, nitrous oxide, and muriatic acid from their diatomic elements.

Reference

Amedeo Avogadro, "Essay on a Manner of Determining the Relative Masses of the Elementary Molecules of Bodies, and the Proportions in Which They Enter into These Compounds," Journal de Physique 73, 58-76 (1811)
[1]Actually, Avogadro proposed that these gases were composed of two parts or a multiple of two.
Copyright 2003 by Carmen Giunta. Permission is granted to reproduce for non-commercial educational purposes.

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