2 lotka: discontinuous evolution 



of its normal alkalinity is essential. Calculations based on the 

 generally accepted theory of hydrolysis, using the most probable 

 values of the dissociation constants, indicate, that in a decimolar 

 solution of sodium oxalate, [H+] 18 ° = 2.0- 10~ 9 . In such a 

 solution phenolphthalein should be converted into its pink salt 

 to the extent of 7.8 per cent, if we accept the simple theory of 

 indicators, and employ the value 1.7- 10 -10 as the dissociation 

 constant of phenolphthalein. Pure sodium oxalate was pre- 

 pared by recrystallization in platinum of two samples, contain- 

 ing respectively slight excess of acid and alkali. After two 

 crystallizations, products of uniform and constant alkalinity 

 were obtained; which was accepted as the criterion of purity. 

 This material was found to produce a color equal to only 4 per 

 cent transfromation of phenolphthalein instead of the calculated 

 7.8 per cent. Calorimetric comparisons with solutions based 

 based upon Sorensen's E.M.F. measurements indicate that 

 [i/ + ]is° for 0.1 M sodium oxalate is 2.5- 10 -9 , and that the salt 

 is hydrolyzed at 18° to the extent of 0.0024 per cent. The 

 error involved in a titration for neutrality, if this "normal 

 alkalinity" is neglected, is only about 0.02 per cent, which is 

 practically negligible in all analytical work. It was found that, 

 contrary to statements of Sorensen, sodium oxalate solutions 

 do not decompose on boiling, but that in glass they do become 

 more alkaline, due to the attack of the vessel. Of various 

 kinds of glass tested, "Durax" was found to be most resistant 

 to such solutions. It was also found that commercial samples 

 of sodium oxalate may contain "excess C0 2 ," either as NaHC0 3 

 or as occluded C0 2 ; which is not readily expelled at 240°C. 

 Before testing the neutrality of sodium oxalate it is therefore 

 necessary to boil the solutions in quartz or Durax to expel 

 such C0 2 . 



EVOLUTION. — Evolution in discontinuous systems. 1 I. Alfred 

 J. Lotka. Communicated by J. A. Fleming. 

 In the minds of most of us the term "evolution" is associated 

 probably more closely with the biological than with the physical 



1 Paper read before the Philosophical Society of Washington on November 11, 1911. 



