APPENDIX 205 



number of molecules which causes osmotic pressure to vary. The osmotic 

 pressure, however, of substances like sodium chloride, which are electrolytes, is 

 greater than what one would expect from the nrunber of molecules present. 

 This is because the molecules in solution are split into their constituent ions, 

 and an ion plays the same part as a molecule, in questions of osmotic pressure. 

 In dilute solutions of sodium chloride ionisation is more complete, and as the 

 total number of ions is then nearly double the number of original molecules, 

 the osmotic pressure is nearly double what would have been calculated from 

 the number of molecules. 



The analogy between osmotic pressure and the partial pressure of gases 

 is very complete, as may be seen from the following statements. 



1. At a constant temperature osmotic pressure is proportional to the 

 concentration of the solution (Boyle-Mariotte's law for gases). 



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

 proportional to the temperatrure (Gay-Lussac's law for gases). 



3. The osnaotic 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 take an example in the case of a non-electro- 

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

 dissociation of the molecules into ions. We will suppose we want to calcu- 

 late the osmotic pressure of a 1-per-cent. solution of cane sugar. 



One gramme of hydrogen at atmospheric pressure and 0° C. occupies a 

 voliune 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 wiU exert a gas pressure 

 equal to that of 22*38 litres compressed to 1 litre — that is, a pressure of 22-38 

 atmospheres. A granmie-molecular solution of cane sugar, since it contains the 

 same number of molecules in a litre, must therefore exert an osmotic pressiire 

 of 22*38 atmospheres also. A gramme-molecular solution of cane sugar 

 {C,.,Ho.,0„) 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 — x 22*38 



342 



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 

 electrolyte, because we should not know how many molecules had been 

 ionised. In the liquids of the body, both electroh-tes 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 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. 



