APPENDIX 241 



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 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-molecular solution of cane sugar, since it contains 

 the same number of molecules in a litre, must therefore exert an osmotic pres- 

 sure of 22'4 atmospheres also. A gramme-molecular solution of cane sugar 

 (C 12 H 2 . J 1] ) 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 of 

 water ; hence the osmotic pressure of a 1-per-cent. solution of cane sugar is 



- x 22'4 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 

 electrolyte, 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 the difficulty of directly measuring osmotic pressure by a 

 manometer ; we now see that mere arithmetic often fails us ; and so we come 

 to the question to which we have been 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 dis- 

 solved 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 1'87 C., 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*87 



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



its osmotic pressure is therefore r-^' =473 mm., a number approxi- 



1*87 



mately 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 



