326 PHYSICAL CHEMISTRY [CH. XXIV. 



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 take an example in the case of a non-electrolyte 

 such as 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 '2 litres; two grammes of hydrogen will therefore occupy a volume of 22 '4 

 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 '4 litres 

 compressed to 1 litre that is, a pressure of 22 - 4 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*4 atmospheres also. A 

 gramme-molecular solution of cane sugar (C^H^On) contains 342 grammes of cane 

 sugar in a litre of water. 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 x22'4 atmospheres, or 0'65 of an atmosphere, 



which in terms of a 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 is seldom directly 

 measured by a manometer, because of the difficulty in obtaining perfect semi- 

 permeable membranes ; 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 1'87C. , and the osmotic pressure is, as we have seen, 

 equal to 22-4 atmospheres, that is, 22'4 x 760 - 17,024 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 = -- _- x 17,024. 

 1 "o/ 



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

 osmotic pressure is therefore 1-37' - 4 ' 3 mm., a number approximately 



equal to that we obtained by calculation. 



Mammalian blood serum gives A = 0'o6 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 =-^=f =5000 mm. of mercury approximately, or a pressure of nearly 



1 *o/ 



7 atmospheres. 



The osmotic pressure of solutions may also be compared by observing their 

 effect on red blood-corpuscles, or on vegetable cells such as those in Tradescantia. 



