DON NAN ECiUl LIBRIUM 1-13 



Water passes through the membrane in the reverse way when 

 the sokition on both sides of the membrane is alkahne. A dihite 

 acid sohition separated from a dihitc alkahne sohition of the same 

 relative strength by an amphoteric membrane will produce a 

 passage of water from the anodal to the cathodal side due to the 

 greater speed of the positive ion. 



Whatever causes may be assigned to the \'ariations in permea- 

 bility of plasma membranes, we can definitely exclude (a) mere 

 variations in the size of the molecules presented to the membrane. 

 Metallic cations, we have seen, are not allowed to pass through, 

 while relatively large molecules like those of amino acids and 

 glucose are able to make their way into the cell, and urea easily 

 passes in or out, depending on which side of the membrane it is 

 most concentrated. Hamburger and others thought that they 

 had disproved Ciiirber's work on the lack of penetration of sodium 

 and potassium. Recent work, however, has confirmed the view 

 given above. 



Bayliss separated a concentrated from a dilute solution of the 

 sodium salt, congo red, by a membrane of parchment paper which 

 is permeable to the sodium ion but not to the anion. He found 

 that the dilute side became electro-positive on account of the 

 preponderance of cations on that side. 



Donnan (1911) propounded a theory of membrane equilibrium 

 which is now classical. He studied a system such as that above 

 where a membrane separated two liquids, in one of which was an 

 ion (like the anion of congo red) which could not pass through 

 the membrane. From thermodynamic considerations, he deduced 

 formulae quantitatively connecting the ion concentrations on 

 either side of the membrane (when equilibrium had been reached) 

 and, by pure reasoning, predicted the presence of a potential 

 difference across the membrane, the magnitude of which depends 

 on the difference in the concentrations of the dijfusihle ions on both 

 sides of the membrane. That is, if a solution of congo red (XaR) 

 is separated from a solution of sodium chloride (NaCl) by a mem- 

 brane impermeable to the anion of the dye (HR), the Na coming 

 from the NaR would be prevented by electrostatic attraction from 

 wandering far from its anion, i.e. it could not pass through a 

 membrane except in minute quantities. The anion may be 

 likened to a large dog attached by a short leash to a terrier (cation). 

 The terrier could (and probably does) pass through between the 

 rails of a fence, but is prevented by its large companion from 

 penetrating far from the boundary. If we had a large mnnber of 

 such pairs, the chance of finding (at any particular time) a fair 

 proportion of terriers in the field would be small. Two small dogs, 



