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قراءة كتاب The Elements of Qualitative Chemical Analysis, vol. 1, parts 1 and 2. With Special Consideration of the Application of the Laws of Equilibrium and of the Modern Theories of Solution.
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The Elements of Qualitative Chemical Analysis, vol. 1, parts 1 and 2. With Special Consideration of the Application of the Laws of Equilibrium and of the Modern Theories of Solution.
the solution—that is, the tendency of the solute to expand into larger volumes of the solvent is satisfied exactly as in the experiment (Fig. 1) described above. In the second place, like all natural phenomena which proceed spontaneously, the change is in the direction of equilibrium; for when the hydrostatic pressure on the solution in the cell becomes sufficiently great, or if it is made sufficiently great at once by the application of some outside pressure, a point of equilibrium is reached, at which water will pass neither into the cell nor out of it. At that point, the tendency to expansion, both of the solute and of the solvent in the solution, is just overcome by the pressure on the solution.
Definition of Osmotic Pressure.
—The hydrostatic pressure which is necessary to bring the solution into equilibrium with the pure solvent, when the two are separated by a semipermeable membrane, may be defined, according to van 't Hoff, as the measure of what is called the osmotic pressure of the solution. We note that this definition still does not commit us to any theory as to the origin of the pressure, but merely formulates an experimental relation.
Measurement of Osmotic Pressure.
—More perfect semipermeable membranes can be produced. These make possible quantitative measurements of the hydrostatic pressure on a solution, when equilibrium between the solution and the pure solvent [p011] has been reached. Such membranes were first used by Pfeffer. They consist of certain gelatinous precipitates, notably copper ferrocyanide. Films of these precipitates may be formed, under proper conditions, which are permeable to water but not to certain solutes, such as cane sugar, glucose and galactose.
By precipitating these membranes in the pores of unglazed clay cells, especially by the process devised by Morse,7 we may make them sufficiently strong to resist enormous pressures—some used by the Earl of Berkeley were found to withstand a pressure of 130 atmospheres. The hydrostatic pressure required to produce equilibrium may then be measured in either of two ways. The first method, used originally by Pfeffer and more recently by Morse and Frazer8 and their collaborators in a wonderfully conscientious study of osmotic pressures, consists in allowing the hydrostatic pressure to establish itself by the passage of very small quantities of the solvent, through the membrane, into the tightly closed cell containing the solution. When the resulting pressure produces a condition of equilibrium, it is measured9 by a manometer connected with the solution, much as a gas pressure may be measured (Fig. 3).10 This process requires considerable time for exact measurements—weeks, during which the cell must be kept at a constant temperature. The second method, which has been used by Berkeley and Hartley,11 is very much more rapid and requires only a few hours for the measurement. It consists in having the pure solvent within the cell, instead of outside of it, and in [p012] exerting an external pressure on the solution outside of the cell, until a delicate manometer, communicating with the pure solvent, shows that water does not pass through the membrane in either direction—equilibrium having been reached.
Osmotic Pressure and the Laws of Gases.
—The work of van 't Hoff, which has proved of inestimable value to the development of chemistry, succeeded in demonstrating that, for dilute solutions, the osmotic pressure, as defined above, obeys the common laws of gases,12—that, in fact, a substance in a dilute solution has an osmotic pressure equal to the gas pressure which it would exert if it were a gas of the same volume and at the same temperature.13
Space does not permit the presentation of all the details of the evidence confirming this conclusion, but some of the most direct experimental proofs14 will be considered. [p013]
Boyle's Law.
—Boyle's law for gases states that, at a constant temperature, the pressure of a gas changes inversely as its volume, or directly as its concentration. Mathematically we have P : P′ = V′ : V or P V = P′ V′ = a constant, and P : P′ = C : C′ or P : C = P′ : C′ = a constant. When van 't Hoff published his first paper on the subject, Pfeffer's results from the direct measurement of the osmotic pressures of cane-sugar solutions were available, and even these, although experimentally not as exact as more recent determinations, showed plainly that, at a given temperature, the osmotic pressure of a sugar solution varies directly as the concentration, or inversely as the volume containing a given weight of the sugar. At 13–16° we have:
| Concentration. | Osmotic Pressure. mm. Mercury. |
Pressure/ Concentration. |
|---|---|---|
| 1.00% | 535 | 535 |
| 2.00% | 1016 | 508 |
| 2.74% | 1518 | 554 |
| 4.00% | 2082 | 521 |
| 6.00% | 3075 | 513 |
The ratio of pressure to concentration varies irregularly round a mean value of 526, and is approximately constant. The more recent, exceedingly careful measurements of Morse and Frazer confirm the conclusion, that Boyle's law holds for the osmotic [p014] pressures of dilute solutions; they find that the osmotic pressures of glucose and of cane-sugar solutions vary directly as