The partial pressure of the dissolved substance in a solution has been measured by a similar plan, devised by the German botanist Pfeffer. It was necessary for this purpose to discover a " semi-permeable membrane," through the pores of which water could pass freely, but which would be impermeable to the dissolved substance. A slimy precipitate, produced by adding potassium ferrocyanide to copper sulphate, is not permeated by dissolved sugar, though water freely penetrates it. But a diaphragm of this nature is far too tender to withstand any pressure. Pfeffer succeeded in depositing the slimy ferro cyanide of copper in the interior of the walls of a pot of porous unglazed earthenware, and so constructing a vessel which could be closed with a glass stopper, with the help of cement. The stopper, which was hollow, was placed in connection with a gauge containing mercury ; and after the pot and stopper had been filled with a solution of sugar, the stopper was connected with the gauge, which thus registered the pressure upon, and consequently exerted by, the liquid. The pot was then immersed in a large vessel of water, which could be heated to any desired temperature, not too high to soften the cement. It was found that the water slowly entered the pot, and consequently raised the mercury in the gauge ; but after a certain quantity had entered, the ingress of water stopped, and the pressure ceased to rise.
The pressure thus raised has been termed " osmotic pressure." The numbers which follow were obtained by PfefFer :
Concentration. Pressure. Ratio.
1 percent. 53.5 cms. 53.5
2 101.6 50.8
4 99 99 2 8 ' 2 99 5 2 ' 1
6 37-5 99 5 l -$
When a gas occupying a certain volume is increased in quantity by pumping in an equal volume of gas, it is clear that the number of molecules in the volume is doubled ; and experiment shows that, in accordance with Boyle's law, the pressure is doubled. The concentration of a solution is expressed by the weight of dissolved substance in 100 parts of the solution ; and it is evident from PfefFer's numbers that, on doubling the number of molecules of sugar in a given volume of the solution, the osmotic pressure is also doubled. The osmotic pressure, in fact, increases directly as the concentration, exactly as with gases.
PfefTer also made experiments at different temperatures. Owing to the softening of the cement with which the semi permeable pot was closed, he was not able to use high temperatures ; but some of his results are given below :
273 = 287.2 = 288.5
51. 0 cms.
51. 0 cms.
35 = 309.0
54-4 5 6 -7
The results are meagre, but, so far as they go, in reasonably good accord. Experiments of this kind have seldom been made, owing to the difficulty in preparing satisfactory membranes. The calculation has been made on the assump tion that the osmotic pressure, like the gaseous pressure, increases directly as the absolute temperature.
A striking proof of the correctness of the analogy between osmotic and gaseous pressure is derived from the following consideration : A gram of oxygen gas, measured at o C. and 76 cms. Pressure, has been found to occupy
699. 4 cc. ; now, 32 grams of oxygen form a gram molecule, for the atomic weight of oxygen is 16, and there are two atoms of oxygen in a molecule of the gas, as we have seen on p. 13. The volume of 32 grams is accordingly 699.4x32 = 22,380 cc. The simplest formula for cane-sugar is C 12 H 22 O n , and as the atomic weight of carbon is 12, the molecular v/eight of sugar is at least (12 x 12) + (22 x i) + ( 1 1 x 16) = 342. If it were possible for cane-sugar to exist in the state of gas, it might be expected that 342 grams in 22,380 cc. Would exert the same pressure as 32 grams of oxygen, viz., 76 cms., since 342 grams of sugar are likely to contain as many molecules as 32 grams of oxygen. But sugar chars when heated, and decomposes. However, it is possible to calculate, by means of Boyle's and Gay Lussac's laws, the pressure which a i 1 per cent, solution of sugar ought to exert at 14.2 C. If there were
223. 8 grams in 22,380 cc., the solution would be one of I per cent. And the pressure which it should exert
22 3 8
would be x 76, or 51.66 cms. At o C., or 273
Abs. And at 14.2 C., or 287.2 Abs., this pressure should be increased in the proportion 273 : 287.2 ; giving a theoretical pressure of 52.5 cms.; the actual pressure measured was 51 cms. A fairly close approximation. It may, therefore, be taken that sugar in solution in water exerts the same osmotic pressure on the walls of a semi permeable vessel, as the same number of molecules would do, if it were in the state of gas, occupying the same volume, and at the same temperature.
Experiments with semi-permeable diaphragms arc very difficult ; the diaphragm seldom receives sufficient support from the pipe-clay walls of the pot, and is usually torn when the pressure rises to even a very moderate degree. But it is not necessary to attempt such measurements ; for the Dutch chemist, J. H. van't Hoff, now Professor of Physical Chemistry in Berlin, pointed out in 1887 that very simple relations exist between the osmotic pressure of solutions and the lowering of the freezing-point of the solvent, due to the presence of the dissolved substance, and also the rise of boiling-point of the solvent, produced by the same cause. A proof of this connection will not be attempted here, but the facts may be shortly stated.
Measurement of Osmotic Pressure by Lowering of Freezing-point
All pure substances have a perfectly definite melting-point ; thus, ice melts at o C., sulphur at 120, tin at 226, lead at 325, and so on. These temperatures are also the freezing-points of the liquids, provided some of the solid substance is present. If this is not the case, then it is possible to cool the liquid below its freezing-point without its turning solid. Accordingly, water freezes at o if there is a trace of ice present ; melted tin solidifies at 226 if there is a trace of solid tin added to the cooled liquid ; and if, for example, water be cooled without the presence of ice, until it has a temperature lower than o, say 0.5 below o, on addition of a spicule of ice a number of little crystals of ice begin to form in the liquid and the temperature rises to o. But if there is some substance dissolved in the liquid, as, for example, sugar in the water or lead in the tin, then the freezing-point is lowered below that of the pure substance. And when the solvent freezes, in general the solid consists of the solid solvent, none of the dissolved substance crystal lising out with it. It is owing to this fact that travelers in Arctic regions manage to get water to drink ; for the ice from salt water is fresh, and when melted yields fresh water. It has been observed that with the same solvent the freezing-point is lowered proportionally to the amount of dissolved substance present, provided the solution is a dilute one. Thus, a solution of cane-sugar in water, containing 3.42 grams of sugar in 100 grams of the solution, froze at 0.185 below zero; and one contain ing half that quantity, 1.71 grams, froze at 0.092 below zero. Again, the same lowering of the freezing-point is produced by quantities proportional to the molecular weights of the dissolved substances. Malic acid, an acid contained in sour apples, has the molecular weight 134, while it will be remembered that the molecular weight of cane-sugar is 342. Now, a solution of 1.34 grams of malic acid in water, made up with water so that the whole solution weighed 100 grams, froze at 0.187 below zero, a number almost identical with that found for sugar.
Solvents other than water may also be used ; but in that case the lowering of the freezing-point is different. Acetic acid, which is vinegar free from water, is often employed ; so also is benzene, a compound separated from coal-tar, produced in the manufacture of coal-gas. The freezing-point of acetic acid is 17; that of benzene is
4. 9. It was found in 1884 by Raoult, Professor of Chemistry in Grenoble in the South of France, that while
1. 52 grams of camphor (the hundredth part of its molecular weight) dissolved in benzene (100 grams of solution) lowered the freezing-point of the benzene by 0.514, the same quantity of camphor, forming a solution in acetic acid of the same strength, lowered the freezing-point of the latter by 0.39. And he also noticed that the lowering of the freezing-point is proportional, at least in some cases, to the molecular weights of the solvents. Thus, the molecular weights of acetic acid and benzene are respectively 60 and 78; and as 0.39 : 0.514 : : 60 : 79, the proportionality is very nearly exact.
It is possible by this means to determine the molecular weight of any substance which will dissolve in any solvent for which the depression produced in the freezing-point is known. Thus, for example, Beckmann, the deviser of the apparatus with which such determinations are made, found that a solution of naphthalene, a white compound of carbon and hydrogen contained in coal-tar, in benzene, the solution containing 0.452 per cent, of naphthalene, lowered the freezing-point of benzene by 0.140. A I per cent, solution would therefore cause a lowering of 0.309. And as 0.309 : 0.39 :: 100 : 126, this is therefore the molecular weight of naphthalene. The simplest formula for naphthalene is C 5 H 4 , for its percentage composition is carbon,
93. 75, hydrogen, 6.25; and to find the relative number of atoms, the percentage of carbon must be divided by the atomic weight of carbon, and that of hydrogen by its atomic
weight, thus : 25^75 = 7.81, and _ 5 = 6.25 ; and these numbers are to each other in the proportion 5 : 4. But a substance with the formula C 5 H 4 must have the molecular weight (5x 12) + (4 x i)=64; whereas the molecular weight found is 126. Now, 126 is nearly twice 64; hence the formula of naphthalene must be C 10 H g . The method is not exact, but it affords evidence which, taken in conjunction with the analysis of the compound, enables the molecular weight to be determined.
Measurement of Osmotic Pressure by Rise of Boiling-point
A method for determining the molecular weights of substances by the rise of boiling-point of their solutions was also devised by Beckmann, and it is frequently used. The process is analogous to that in which the depression of freezing-point is made use of. Every pure substance has a perfectly definite boiling-point, provided that pressure is constant ; but if any substance is dissolved in a pure liquid, the boiling-point of the latter is raised ; and it is found that the rise of boiling-point is proportional to the number of molecules of the dissolved substance present. As an example, let us calculate the molecular weight of iodine dissolved in ether from the rise in the boiling-point of the ether. The rise caused by the hundredth part of the molecular weight of a substance taken in grams, and dissolved in 100 grams of ether, is
0. 2105. Now, Beckmann found that 1.513 grams of iodine dissolved in 100 grams of ether raised the boiling-point of the ether by 0.126. And to raise the boiling-point by
0. 2105, 2.53 grams of iodine would have been necessary;
2. 53 is therefore the hundredth part of the molecular weight of iodine. It is possible to weigh iodine in the state of gas, for it is an easily volatilised element ; and its vapour has been found to be 126 times as heavy as hydro gen. We have seen that this statement implies that a molecule of iodine gas is 126 times as heavy as a molecule of hydrogen gas ; and as a molecule of hydrogen consists of two atoms, a molecule of iodine gas is 252 times as heavy as an atom of hydrogen, or its molecular weight is 252. The number obtained from the density of the gas is accordingly almost identical with that obtained from the rise in the boiling-point of ether.
We have now studied four methods by means of which the molecular weights of elements and compounds have been ascertained ; they are :
1 I ) By determining the density of the substance in the state of gas with reference to hydrogen, and doubling the number obtained ; for molecular weights are referred to the weight of an atom of hydrogen, while a molecule, it is believed, consists of two atoms.
(2) By measuring the osmotic pressure exerted by a solution of the substance, and comparing the pressure with that exerted by an equal number of molecules of hydrogen, occupying the same volume, at the same temperature.
( 3 ) By comparing the depression in freezing-point of a solvent containing the substance in solution, with the depression produced by the hundredth part of the molecular weight in grams of a substance of which the molecular weight is known, and by then making use of the known fact that equal numbers of molecules produce equal depression in the freezing-point of a solvent.
(4) By a similar method applied to the rise in boiling point of a solvent caused by the presence of a known weight of the substance of which the molecular weight is required.