CH. XXII.] OSMOTIC PRESSURE 325 



2. With constant concentration, the osmotic pressure rises with and is propor- 

 tional to the temperature (Gay-Lussac's law for gases). 



3. The osmotic pressure of a solution of different substances is equal to the sum 

 of the pressures which the individual substances would exert if they were alone in 

 the solution (Henry-Dalton law for partial pressure of gases). 



4. The osmotic pressure is independent of the nature of the substance in 

 solution, and depends only on the number of molecules or ions in solution 

 (Avogadro's law for gases). 



Calculation of Osmotic Pressure. We may best illustrate this by an example, 

 and to simplify matters we will takje an example in the case of a non-electrolyte 

 like sugar. We shall then not have to take into account any electrolytic dissocia- 

 tion of the molecules into ions. We will suppose we want to calculate the osmotic 

 pressure of a 1 per cent, solution of cane sugar. 



One gramme of hydrogen at atmospheric pressure and C. occupies a volume 

 of 11 '19 litres ; two grammes of hydrogen will therefore occupy a volume of 22 '38 

 litres. A gramme-molecule of hydrogen that is, 2 grammes of hydrogen when 

 brought to the volume of 1 litre, will exert a gas pressure equal to that of 22*38 litres 

 compressed to 1 litre that is, a pressure of 22 '38 atmospheres. A gramme-mole- 

 cular solution of cane sugar, since it contains the same number of molecules in a 

 litre, must therefore exert an osmotic pressure of 22*38 atmospheres also. A 

 gramme-molecular solution of cane sugar (Cj.2H.22On) contains 342 grammes of cane 

 sugar in a litre. A 1 per cent, solution of cane sugar contains only 10 grammes of 

 cane sugar in a litre ; hence the osmotic pressure of a 1 per cent, solution of cane 



sugar is r x 22 '38 atmospheres, or 0'65 of an atmosphere, which in terms of a 



o4. 



column of mercury = 760 x 0'65 = 494 mm. 



It would not be possible to make such a calculation in the case of an electro- 

 lyte, because we should not know how many molecules had been ionised. In the 

 liquids of the body, both electrolytes and non-electrolytes are present, and so a 

 calculation is here also impossible. 



We have seen that for such liquids the osmotic pressure cannot be directly 

 measured by a manometer, because there are no perfect semi-permeable mem- 

 branes ; we now see that mere arithmetic often fails us ; and so we come to the 

 question to which we have been so long leading up, viz., how osmotic pressure is 

 actually determined. 



Determination of Osmotic Pressure by means of the Freezing-point. 

 This is the method which is almost universally employed. A very simple apparatus 

 (Beckmann's differential thermometer) is all that is necessary. The principle on 

 which the method depends is the following : The freezing-point of any substance 

 in solution in water is lower than that of water ; the lowering of the freezing-point 

 is proportional to the molecular concentration of the dissolved substance, and that, 

 as we have seen, is proportional to the osmotic pressure. 



When a gramme-molecule of any substance is dissolved in a litre of water, the 

 freezing-point is lowered by l'S7C. , and the osmotic pressure is, as we have seen, 

 equal to 22*38 atmospheres, that is, 22'38 x 760 = 17,008 mm. of mercury. 



We can, therefore, calculate the osmotic pressure of any solution if we know 

 the lowering of its freezing-point in degrees Centigrade ; the lowering of the 

 freezing-point is usually expressed by the Greek letter A. 



Osmotic pressure = r^p x 17,008. 



For example, a 1 per cent, solution of sugar would freeze at -0'052 C. ; its 



052 x 17,008 

 osmotic pressure is therefore gr . = 4/3 mm., a number approximately 



equal to that we obtained by calculation. 



Mammalian blood serum gives A =0'56 C. A 0'9 per cent, solution of sodium 

 chloride has the same A ; hence serum and a 0'9 per cent, solution of common salt 

 have the same osmotic pressure, or are isotonic. The osmotic pressure of blood 



serum is - r 7 4987 mm. of mercury, or a pressure of nearly 7 atmospheres, 



