no PHYSIOLOGY OF NUTRITION 



tion of KNO3 ought, according to this theory, to give a pressure of 0.235 atmos- 

 pheres, but it actually gives one of 0.352 atmospheres. If the value derived 

 directly from the van't Hoff theory be multiplied by %, the isosmotic coeffi- 

 cient of this salt (considering the coefficient of cane sugar as unity), the value 

 0.352 is obtained, which is the same as that found experimentally. Equimole- 

 cular solutions of potassium nitrate and of organic substances are thus not 

 isosmotic. To obtain a solution of potassium nitrate that shall produce the 

 same osmotic pressure as does a o.i-molecular cane-sugar solution it is necessary 

 to prepare a J^s {% X Mo) molecular solution of the salt. Salts with other 

 isosmotic coefficients must be employed in corresponding concentrations. Thus, 

 a 0.05-molecular solution of potassium sulphate is isosmotic with a o.i-molecular 

 solution of cane sugar. The osmotic pressure of a weak solution of an electrolyte 

 is thus "equal to the theoretical pressure multiplied by the isosmotic coefficient 

 of the electrolyte in question. This departure from the theory is explained by 

 Arrhenius' hypothesis, which supposes that electrolytes in solution dissociate 

 into ions. In a sodium chloride solution, for example, sodium and chlorine ions 

 are both present as well as molecules of sodium chloride. The more dilute the 

 solution, the greater is the degree of dissociation. 



According to the Arrhenius theory of electrolytic dissociation, the isosmotic 

 coefficient of potassium nitrate indicates that the number of particles in a solu- 

 tion of this salt is increased by dissociation, and if half of the molecules be con- 

 sidered as dissociated the total number of particles ought to be % of what it 

 would be without dissociation, and the osmotic pressure should be correspond- 

 ingly increased. A dissociated molecule of KNO3, in the form of two ions, K and 

 NO3, produces twice as much osmotic pressure as does an un dissociated molecule. 



Potassium sulphate has an isosmotic coefficient of 2 at the concentrations 

 employed by de Vries, the molecule of this electrolyte dissociates into three ions, 

 K, K and SO4, and the coefficient 2 indicates, in this case also, that half the total 

 number of molecules are to be considered as dissociated. The number of par- 

 ticles in solution would thus be about doubled, for }-^ -f- 3 X } 2 = 2-' 



De Vries used salt solutions of about o.i -volume-molecular concentration, 

 these being about half dissociated. The degree of dissociation varies with the 

 concentration, and so the osmotic coefficients obtained by deVries cannot be 

 used for solutions of other concentrations, the coefficients for which must be 

 obtained through the use of isosmotic solutions,^ employing a solution of an 

 undissociated and unhydrated substance as a standard. 



Errera^ proposed the myriotonie as a unit for the measurement of osmotic 



» Hamburger, H. J., Osmotisoher Druck und lonenlehre in den medicinischen Wissenschaften. 3 v. 

 Wiesbaden, 1902-1904. H6ber, Rudolf, Physikalisohe Chemie der Zelle und der Gewebe. 2 Aufl. Leipzig, 

 1906. [4 Aufl. Leipzig, 1914.] Brasch, Richard, Die Anwendung der physikalischen Chemie au£ die Phy- 

 siologie und Pathologie. Wiesbaden, 1901. 



' Errera, L., Sur la myriotonie comme unitfi dans les mesures osmotiques. Recueil Inst. Bot. Brujtelles 

 5: 193-208. 1902. 



^ ' The degrees of dissociation are actually much greater, however, than are assumed in 

 this discussion. DeVries's isosmotic coefficients are now to be regarded as of historical 

 interest only. The best discussion of the calculation of osmotic values of solutions is that 

 of Washburn, 1915. [See note e, p. loi.] — Ed. 



