# Chapter XXXIV. Vapor Density and Molecular Weight.

Examine a liter measure, in the form of a cube,—cubic decimeter, —and a cubic centimeter.

171. Gaseous Weights and Volumes.—A liter of H, at 0 degrees and 760 mm., weighs nearly 0.09 g. This weight is called a crith. Find the weight of H in the following, in criths and in grams: 15 1., 0.07 1., 50.3 1., 0.035 1., 0.6 1..

It has been estimated that there are (10) 24. molecules of H in a liter. Does the number vary for different gases? The weight of a molecule of H in parts of a crith is 1/(10) 24.; in parts of a gram .09/(10) 24.. If the H molecule is composed of 2 atoms, what is the weight of its atom in fractions of a crith? What in fractions of a gram? The weight of the H atom is a microcrith. What part of a crith is a microcrith?

172. Vapor Density.—Vapor density, or specific gravity referred to H as the standard, (Physics) is the ratio of the weight of a given volume of a gas or vapor to the weight of the same volume of H. A liter of steam weighs nine times as much as a liter of H. Its vapor density is therefore nine. For convenience, a definite volume of H is usually taken as the standard, viz., the H atom. The volume of the H atom and that of the half-molecule of H2O, or of any gas are identical, each being represented by one square. If, then, the standard of vapor density is the H atom, half the molecular weight of a gas must be its vapor density, since it is evident that we thus compare the weights of equal volumes. The vapor density of H2O, steam, is found from the symbol as follows: (2 + 16) / 2 = 9. To obtain the vapor density of any compound from the formula, we have only to divide its molecular weight by two. Find the vapor density of HCl, N2O, NO, C12H22O11, Cl, CO2, HF, SO2. Explain each case.

The half-molecule, instead of the whole, is taken; because our standard is the hydrogen atom, the smallest portion of matter, by weight, known to science.

How many criths in a liter of HCl? How many grams? Compute the number of criths and of grams in one liter of the compounds whose symbols appear above.

PROBLEMS.

(1) A certain volume of H weighs 0.36 g. at standard temperature and pressure. How many liters does it contain? If one liter weighs 0.09 g., to weigh 0.36 g. it will take 0.36 / 0.09 = 4 liters.

(2) How many liters, or criths, of H in 63 g.? 2.7 g.? 1 g.? 5 g.? 250 g.? Explain each.

(3) Suppose the gas to be twice as heavy as H, how many liters in 0.36 g.? A liter of the gas will weigh 0.18 g. (0.09 X 2). In 0.36 g. there will be 0.36 / 0.18 = 2. Answer the question for 63 g., 2.7 g., etc.

(4) How many liters of Cl in each of the above numbers of grams?

(5) How many of HCl? H2O (steam)? CO2? Explain fully every case.

Vapor density is very easily determined from the formula by the method given above. But in practice the formula is obtained from the vapor density, and hence the method there given has to be reversed.

173. Vapor Density of Oxygen.—Suppose we were to obtain the vapor density of O. We should carefully seal and weigh a given volume, say a liter, at a noted temperature and barometric pressure, which are reducedto 0 degrees and 760 mm, and compare it with the weight of the same volume of H. This has been done repeatedly, and O has been found to weigh 16 times as much as H, volume for volume, or, more exactly, 15.96+. Now a liter of each gas has the same number of molecules, therefore the O molecule weighs 16 times the H molecule. The half-molecule of each has the same proportion, and the vapor density of O is 16. Atomic weight is obtained in a very different way.

PROBLEMS.

(1) A liter of Cl is found to weigh 3.195 g. Compute its vapor density, and explain fully.

(2) A liter of Hg vapor, under standard conditions, weighs 9 g. Find its vapor density, and explain.

The vapor density of only a few elements has been satisfactorily determined. See page 12. Some cannot be vaporized; others can be, but only under conditions which prevent weighing them. The vapor density of very many compounds also is unknown.

(3) A liter of CO2 weighs 1.98 g. Find the vapor density, and from that the molecular weight, remembering that the latter is twice the former. See whether it corresponds to that obtained from the formula, CO2. This is,in fact, the way a formula is ascertained, if the atomic weights of its elements are known.

(4) A liter of a compound gas weighs 2.88 g. Analysis shows that its weight is half S and half O. As the atomic weight of S is 32, and that of O is 16, what is the symbol for the gas?

Solution. Its molecular weight is 64, i.e. (2.88=0.09) X 2, of which 32 is S and 32 O. The atomic weight of S is 32, hence there is one atom of S, while of O there are two atoms. The formula is SO2.

(5) A liter of a compound gas, which is found to contain 1 C and 3 O by weight, weighs 1.26 g. What is its formula? Atomic weights are taken from page 12. Prove your answer.

(6) A liter of a compound of N and O weighs 1.98 g. The N is 7/11; and the O 4/11. What is the gas?

(7) A compound of N and H gas weighs 0.765 g. to the liter. The N is 14/17 of the whole, the H 3/17. What gas is it?