OSMOTIC PRESSURE.

129

solute must not be volatile at the boiling temperature of the solvent. But, just as gram-molecular weights of cane-sugar, grape-sugar, urea, etc., each dissolved in 1,000 grams of water, give solutions having the same freezing-point, so they give solutions of the same boiling temperature. While water boils at 100° C., under 760 mm., a solution containing a gram-molecular weight of solute in 1,000 grams of water boils at 100.52° C. Hence, by adding a solute of unknown molecular weight to 1,000 grams of water at 760 mm., until the boiling-point of the solution reaches 100.52° C., we can determine its gram-molecular weight.

149. Osmotic Pressure.

Under "hydrogen," § 52, we learned that if a porous cup of air (Fig. 14) is immersed in hydrogen, this gas enters the cup so much more rapidly than air can get out, that there is an increase of pressure inside the cup. Suppose the

99 cup were a closed vessel made of palladium, a metal which occludes hydrogen (cf. § 53), and through which hydrogen can pass while air cannot (Fig. 37). Assume that the air inside was under one atmosphere pressure. Hydrogen would enter until its pressure inside was equal to that outside, viz., one atmosphere. But, since the air originally in the palladium vessel had a pressure of one atmosphere, the total pressure inside would now be two atmospheres. If the vessel communicated with a column of mercury, the height to which the mercury was raised would indicate the excess of pressure inside the palladium vessel.

H

FIG. 37.

If we replace the palladium vessel of air by a water solution of sugar, and the surrounding hydrogen by pure water, we shall

have the corresponding phenomenon for solutions. We call it osmosis. The sugar solution may be in a thistle tube (Fig. 38), the thistle of which is covered water-tight with parchment paper. An egg-shell, with a tube attached, may be used instead; here the lining membrane of the shell replaces the parchment. The parchment and membrane are semi-permeable, i. e., they permit the water molecules to pass freely, but not the sugar molecules (or only a very little). Water enters the "cell" to make the pressure of water inside equal that without. The result is to increase the volume of liquid inside, and to force some of it up the tube. If the membrane is strong enough, and permits no sugar to pass outward, the column will rise until its hydrostatic pressure causes water to leave the cell as rapidly as it enters. When this condition of equilibrium is reached, the excess of inside pressure is the osmotic pressure of the solution. For accurate work osmotic pressure cells are made of strong earthenware into the pores of which cupric ferrocyanide, Cu,Fe(CN)6, has been precipitated. Now, if gram-molecular weights of cane-sugar, grape-sugar, urea, etc., are dissolved in 1,000 grams of water, the osmotic pressures of the solutions, like the boiling-point elevations and freezingpoint depressions, are equal. Osmotic pressure methods are not used much in getting molecular weights because the other methods are easier to carry out. Just as gas pressure is proportional to the density (cf. § 40), so the osmotic pressure is proportional to the concentration of the solution. Osmotic pressure is also proportional to the absolute temperature (Charles' Law).

FIG. 38.

150. Methods of Obtaining Exact Molecular Weights.

All the methods described give only approximate molecular weights; exact molecular weights are found by quantitative analysis.

The methods used may be illustrated by the case of acetic acid, HC2H3O2; the exact molecular weight of this substance may be found by a study of its silver salt, AgC2H3O2.

Silver acetate contains silver, carbon, hydrogen, and oxygen. The per cent of the silver being found by analysis to be 64.65, that of the remainder of the molecule must be 35.35. The atomic weight of silver, if we take the atomic weight of oxygen as exactly 16, is very nearly 107.94; the weight (x) of all of the silver acetate molecule except the silver is, therefore, found from the equation,

Since acetic acid is silver acetate with the silver replaced by hydrogen, we must add to 59.02 the number representing the weight of the hydrogen that 107.94 parts of silver replace. This is 1.008. Hence the exact molecular weight of acetic acid is 60.028.

151. Exercises.

1. If 1 volume of phosphorus vapor unites with 6 volumes of chlorine to give 4 volumes of phosphorus trichloride, how many atoms, at least, are there in a molecule of phosphorus?

2. If, at the boiling point of sulphur, 1 c.c. of the vapor unites with 8 c.c. of oxygen to give 8 c.c. of sulphur dioxide, calculate the number of sulphur atoms in a molecule.

3. If 275 c.c. of a gas at 25° C. and 715 mm. weigh 0.46 gram, calculate the molecular weight of the gas.

4. The molecular weight of a gas is 60. Calculate the weight of 290 c.c. of it at 13° C. and 800 mm.

5. A 500 c.c. flask of air weighed 40.495 grams at 18° C. and 740 mm. When filled with ether vapor at 50° C. and 740 mm.

it weighed 41.2605 grams. Calculate the weight of one liter of ether vapor at 50° C. and 740 mm. Calculate the molecular weight of ether.

6. In a Victor Meyer vapor density apparatus 0.1387 gram of a compound expelled 47.2 c.c. of dry air at 24° C. and 735 mm. What is the molecular weight of the compound?

CHAPTER XIII.

ATOMIC WEIGHTS.

152. Determination of Atomic Weights. As was stated in § 97, we were obliged to postpone the determination of atomic weights until we had learned how the molecular weights are obtained. Now, since the common methods of getting molecular weights, described in §§ 143 to 145, apply only to gases, the atomic weights of elements are determined primarily from the molecular weights of the gaseous compounds of the elements. The tables will show how the method works for chlorine and carbon.