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The osmotic pressures of solutions of moderate concentrations are very considerable and have been measured up to 131 atm.
The following results were obtained by Pfeffer (1877) with dilute solutions of cane-sugar.
Osmotic Pressures of Sugar Solutions at 0°C
| Concentration, C, gm./lit. soln. | 10.03 | 20.14 | 40.60 | 61.38 | | Pressure, P, atm. | 0.686 | 1.34 | 2.75 | 4.04 | | Ratio, P/C | 0.068 | 0.067 | 0.068 | 0.066 |
The ratio is practically constant, hence the osmotic pressure at a constant temperature is proportional to the concentration. This is the exact analogue of Boyle's law for gaseous pressures.
Osmotic Pressures of 1 per cent. Cane-sugar Solutions
| Absolute temp., T° | 273 | 279.8 | 286.7 | 287.2 | 288.5 | 295.0 | 305.0 | 309.0 | | Pressure, P (atm.) | 0.648 | 0.664 | 0.691 | 0.671 | 0.684 | 0.721 | 0.716 | 0.746 | | Ratio P/T. 103 | 2.38 | 2.37 | 2.41 | 2.33 | 2.37 | 2.44 | 2.35 | 2.41 |
The ratio is constant, hence the osmotic pressure for a given concentration is proportional to the absolute temperature. This is the exact analogue of Gay-Lussac's law for gaseous pressures.
The mean value of P/C at 0° C. is 0.066; this is the osmotic pressure in atm. exerted by 1 gram of sugar in 1 litre of solution. Since the molecular weight of sugar is 342, this is also the pressure exerted by 1 gram molecule of sugar in 342 litres. The pressure is proportional to the concentration, hence the pressure becomes 1 atm. when the volume containing 1 gram molecule (mol) is 342 x 0.066 = 22.6 litres.
If 1 mol of ideal gas is confined in a space of 22.4 litres at 0° it will exert a pressure of 1 atm. The value 22.6 for a molar solution is nearly equal to 22.4, hence solutions obey Avogadro’s law. Van’t Hoff in 1886 summarised these results in the statement that dissolved substances obey the gas laws. The osmotic pressure of a solution is equal to the gas pressure which the solute would exert if all the solvent were removed, and the dissolved substance were left in the space in the condition of an ideal gas. This is known as van't Hoff's gaseous theory of solution; accurate experiments show that it is only approximate, but becomes more exact in the limiting case of extreme dilution, just as the gas laws are exact only at small pressures. The gaseous theory of solution is the basis of modern physical chemistry; its consequences have had a most remarkable influence on the progress of the science and especially in its applications to biology.
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