Boyle's Law.
| 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 the concentrations of the solutions, at a constant temperature.[15]
Gay-Lussac's Law.
Expressing the temperature in absolute degrees, we have more simply:
Pt = P0 (T / 273) or Pt / T = P0 / 273 = a constant.[16]
That is, the pressure of a gas varies directly as its absolute temperature, if the volume is kept constant.
Pfeffer's results, on the osmotic pressure of sugar solutions at different temperatures, were not sufficiently accurate to enable van 't Hoff to use them to confirm positively the rigorous thermodynamic proof (footnote 3, p. [12]), that the osmotic pressure must increase proportionally to the absolute temperature, as required by Gay-Lussac's law. But the data did show, uniformly, a marked increase of the osmotic pressure with the temperature and, frequently, excellent agreement between theory and experiment. More striking were the results obtained by van 't Hoff in testing the correctness of this extension of Gay-Lussac's law by means of Soret's results on the diffusion of a solute from a warmer to a colder place. It was found that the concentrations, obtained by Soret when equilibrium was reached, agreed closely with the demand that the osmotic pressures in the colder and the warmer parts of the solution should be equal, and that the osmotic pressure of a given weight of solute in a given volume should increase proportionally to the absolute temperature. An elevation of temperature, in a portion of a uniform solution, will increase the osmotic pressure of this part. Diffusion will follow, until the loss in concentration of the solute, and therefore the loss of osmotic pressure (Boyle's law), of the warmer part, and the increased concentration and increased pressure of the colder portion result in all parts of the solution having the same osmotic pressure. [p015] As an example, a concentration of 17.33% copper sulphate at 20° was found to be in equilibrium with a concentration of 14.03% at 80°. Now, if the 17.33% solution had an osmotic pressure of P mm. at 20°, a 14.03% solution at the same temperature would have a pressure of (14.03 / 17.33) × P mm. (Boyle's law), and this would increase to (14.03 / 17.33) × P × (353 / 293) mm. at 80° C., or 0.975 P mm.—a result showing that the osmotic pressure in the hot part was practically the same as that, (P), in the cold part of the solution.[17]
It is a source of great satisfaction, that the recent very exact and painstaking work of Morse and Frazer,[18] in measuring osmotic pressures directly, completely confirms this fundamentally important conclusion, that the osmotic pressure of a solution does increase proportionally to its absolute temperature.