OSMOTIC PRESSURE 161 



that in equilibrium, there must always be equal concentration of non-dissociated 

 sodium chloride on both sides, since it is freely diffusible and there are no 

 electrostatic forces to prevent its equal distribution. To ensure this, the total 

 amount of sodium chloride present must be less inside, on account of the fact that 

 its dissociation is lowered by the presence of an ion (Na'), which is common to the 

 two salts within the membrane. 



At first sight it seems strange that salts which have no ion in common with 

 the dye are also affected in the same way. The reason is that, when equilibrium 

 is established, there are present, inside and out, both kinds of the diffusible cation 

 in the same ratio. The layer of Na' ions, arising from the dissociation of the dye 

 salt, and situated on the outside of the double layer at the membrane, must not 

 be thought to be composed of the same individual ions there is perpetual inter- 

 change with those in the body of the solution. Suppose now we place a solution 

 of potassium chloride outside ; the sodium ions, since they are kept in place merely 

 by virtue of their positive charges, will naturally interchange with potassium ions 

 of the outer solution, so that, to begin with, the outer layer at the membrane will 

 consist of both K- and Na' ions ; these, in their turn, interchange with the Na' 

 ions in the solution within the membrane, so that finally there will be the same 

 relative distribution of total diffusible salt as if sodium chloride had been taken. 

 Naturally there will also be present a certain proportion of the potassium salt of 

 the dye in place of a part of the sodium salt originally present. An important 

 point to be noticed is that the ratio of sodium to potassium will be the same inside 

 and outside, as indeed I have found experimentally to be the case. It follows, 

 as already pointed out, that a membrane impermeable merely to colloids will not 

 account for the unequal ratio of sodium and potassium inside and outside the red 

 blood corpuscles. The membrane must be impermeable to these also. 



This formation of a double layer at the membrane, as pointed out by Laqueur and Sackur 

 (1903, p. 203), should give rise to a considerable difference of potential between the two sides 

 of the membrane. Theoretical considerations show that it will be expressed* by the same 

 formula as that deduced by Nernst for the potential of metallic electrodes, viz. : 



5*log3, 



nq q 



where R and T have their usual significance, q is the charge on one gram-equivalent of the 

 diffusible ion concerned, n is the number of these gram-equiyalents, c. 2 is the concentration of 

 this ion inside the membrane, and Cj its concentration in the outside solution. Direct measure- 

 ments made by myself (1911, pp. 243-248) confirm the correctness of the formula as applied to 

 the case in question. The reader will recognise this formula as being the same as that for the 

 isothermal compression of a gas or the concentration of a solution, the only difference being 

 that, as we are dealing with electric charges, we have to introduce q, in order to give the 

 correct numerical values to our result. In other words, the number in gram-equivalents of the 

 ordinary formula has to be changed into the number of charges on these gram-equivalents. 

 R, the gas constant, must also be expressed in electrical units. The way in which the formula 

 is obtained is described below (Chapter XXII. ). 



It is not to be forgotten that the results given in the present section apply not 

 only to dyes, but to all salts of which one ion is held back by a membrane, 

 permeable to the opposite ion. They apply to salts of proteins and also to non- 

 colloidal electrolytes, if the membrane is impermeable to one only of their ions. 

 This latter case has been discussed by Ostwald (1890). The considerations with 

 regard to interchange of ions form also the explanation of the experiments of 

 W. A. Osborne (1906) on the interchange of ions between colloids and salts. 



Since dyes of the molecular weight of Congo-red give considerable osmotic pressures, 

 owing to the fact that their molecules are only just sufficiently large to be unable to pass 

 through parchment paper, they form very useful substances for the investigation of many 

 problems relating to osmotic pressure. The difficulty of preparing reliable copper ferrocyanide 

 membranes is avoided. A O'Ol molar solution of Congo-red has an osmotic pressure of 

 170 mm. of mercury, and that of Chicago blue is nearly double. There is one practical point 

 to be taken care about, if permanent readings are to be expected, when dyes with an 

 indiffusible anion are made use of. The free acid is insoluble, and although it forms a 

 colloidal solution when free from electrolytes, it is precipitated by traces of them. If the 

 outer water is exposed to the air, it will absorb carbon dioxide ; this, being diffusible, obtains 

 access to the interior of the osmometer, and, although a weaker acid than that of the dye, 

 it will slowly decompose the salt, by mass action, owing to the precipitation of the free acid 

 out of solution, while the sodium carbonate diffuses away to the outer water. The fact 



II 



