ELECTROLYTES AND THEIR ACTION 



177 



We may conclude, then, that the conductivity of a highly diluted solution is 

 made up of the independent conductivities of the individual ions and, if this is 

 so, these ions must be present as separate entities. Kohlrausch expresses this 

 in what is generally known as his law of the independent migration of the ions. 

 The symbol u is given to the part contributed by the cation and v to that 

 contributed by the anion, so that the molecular conductivity at infinite dilution 

 of a binary electrolyte (that is, one that dissociates into two univalent ions) is 

 u + v. These are constant values for the same ions, whatever salts they may form 

 constituents of. 



Referring back to the table on page 176, we notice that the conductivity of the 

 Li ion is less than that of the Na ion and this again is less than that of the K ion. 

 Since each of these ions carries the same charge, it follows that they must travel 

 at different rates. A little consideration will show that, if this be so, after 

 electrolysis by passage of a current has gone on for some time, there will be 

 a different concentration of the electrolyte around the two electrodes and, by this 

 means, measurements of the rates of the various ions have been made by Hittorf. 

 Details of these measurements will be found in the textbooks (Philip, 1910, pp. 

 143, etc. ; Nernst, 1911, pp. 362, etc.). 



The following table gives the molecular conductivities of a number of ions at 

 the temperature of 18 (Nernst, 1911, p. 366). 



K NH Na Li Ag 

 44-4 35-5 55'7 



01 



NH 4 



64-2 



Br 



66-7 



I 



66-7 



NO 3 C1O 3 

 60-8 56-5 



H 



318 

 CO H 



45 



C. 2 H 3 2 

 33-7 



OH 

 174 



In the case of large organic ions it is interesting to note that the rate of 

 migration diminishes comparatively little with increasing size. Thus, according 

 to Bredig (1894), at 25, the values of certain anions are as follows : 



The practical use of these facts is that we can calculate the values of the 

 molecular conductivity at infinite dilution in cases where it cannot be obtained 

 experimentally. Thus ammonium hydroxide, even when diluted so far that the 

 accuracy of the measurements becomes uncertain, is a considerable distance 

 from complete dissociation. But from the law of Kohlrausch we can obtain 

 the value as the sum of those of the constituents, NH 4 ' and OH', viz. : 



64-2 + 174 = 238-2. 



Knowing the conductivity of salts when completely dissociated, we can thus 

 determine the degree of dissociation at any concentration from measurements 

 of its conductivity at that concentration. Suppose that we find that a binary 

 salt at a known concentration has a molecular conductivity half that which we 

 obtain from Kohlrausch's law as the limiting value at infinite dilution, we know 

 that only half of its molecules are taking part in the conduction of the current. 



The actual rate of movement of the various ions is of some interest. As Nernst 

 points out (1911, p. 363), the small dimensions of ions would lead us to expect 

 that the frictional resistance to their movements is very great. Their velocity is 

 therefore proportional to the force acting on them. If the fall of potential in the 

 solution is 1 volt per centimetre, that is, if the electrodes are 10 cm. apart and a 

 potential difference of 10 volts exists between them, the hydrogen ion moves at the 

 rate of 0'0033 cm. per second and the potassium ion at 0-00067 cm. per second. 

 The actual manner in which this is determined is beyond the scope of this book. 



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