198 JOURNAL OF THE WASHINGTON ACADEMY OF SCIENCES VOL. 11, NO. 9 



The usefulness of methods in which computation begins at the 

 neutral point has been urged by several writers' and the "Xh" and 

 "specific acidity" methods are the result of carrying such methods to 

 their logical conclusion. The Ph values are subtracted from 7, and 

 the resulting values are called Xh, or chemical potentials. When 

 Xh is negative, Xqh, which is equal to — Xh, may be used instead. 



The number 7 is the exponent of the hydrogen-ion concentration 

 of pure, neutral water, and represents the average of the values of 

 this constant which have been obtained by some 15 different inves- 

 tigators, at 25°. Even though not absolutely exact, it may be con- 

 veniently taken as the standard of reference. 



Correspondingly, to obtain the new concentration values, on the 

 acid side divide the usual hydrogen-ion concentration by 10 ~^ or 

 0.000 000 1 ; and on the alkaline side divide in the reverse direction. 

 The resulting values, since they are referred to water as a standard, 

 may be called, respectively, specific acidities and specific alkalinities. 



In a recent work,^ W. M. Clark has raised certain objections to 

 methods in which computation begins at the neutral point, which 

 may well be answered here. For simplicity, only the respective 

 potential methods, Xh and Ph, will be discussed, although the 

 arguments apply equally well to the concentration methods. 



(j) The Xh method does, while the Ph (or pH) method does not, 

 "involve any assumption regarding the nature of that pure water which 

 is never used, [and] which seldom is considered in calculations " 



(Ans.) The Xh method does not, while the Ph method does, involve 

 assumptions as to the nature and the hydrogen-ion concentration of a 

 hypothetical acid which is completely ionized in normal solution. 

 Such an acid is at least as imaginary as is pure water, and its hydrogen- 

 ion concentration is known with at best no greater certainty. More- 

 over, on the alkaline side, the Ph method does involve the data for 

 pure water; for the dissociation constants of bases are expressed 

 (however measured) in terms of 0H~ concentration, and by definition 

 pure water contains equivalent amounts of H+ and OH"; any dis- 

 crepancy, therefore, between the H+ and 0H~ scales will be halved 

 in the Xh method, whereas the entire error is referred to the range of 

 alkaline solutions by the Ph method. The facts that the hydrogen- 



^ Walker and Kay, Journ. Soc. Chem. Ind. 31: 1013. 1912; Henderson, Science 

 46:73. 1917; Wherry, This Journal 6: 675. 1916; 8: 591. 1918; and 9: 305. 1919; 

 TiLLMANS, Zeitschr. Nahr. Genussm. 38: 1. 1919. 



2 The determination of hydrogen ions, p. 28. Williams and Wilkins Co., Baltimore, 

 1920. 



