Properties of Aqueous Solutions to their State of Ionization. 101 



each series are found to run very close together, so close that 

 it is impossible to determine exactly at what points they touch 

 or cross ; and when the observational errors admitted by the 

 authors are taken into account, they must be considered to be 

 within touching or crossing distance at considerable distances 

 on each side of the points at which Bender and Bruckner 

 assumed them to be in contact or to intersect. It is probably 

 needless to give details ; but I may say that I have plotted a 

 number of these curves so as to indicate accurately all signi- 

 ficant figures, and have found, on taking possible errors of 

 observation into account, that in no case can a more definite 

 conclusion be drawn than that " corresponding " solutions 

 have pretty nearly the simple relations as to concentration 

 claimed by the authors. I have found also that in most cases 

 the limits of the concentration of the second salt within which 

 the curves must be considered to be possibly in contact, 

 include the isohydric concentration. It would thus appear 

 that both Bender and Bruckner drew too definite conclusions 

 from their observations, and that the observations themselves 

 are not inconsistent with the applicability of expression (1) 

 to the physical property of solutions. 



Applications of the Assumed Law of Ionization- Constants. — 

 Variation of Temperature and other Coefficients ivith Con- 

 centration. 



If the expression under consideration is applicable to solu- 

 tions of moderate dilution it should give by deduction the 

 laws which have been found to hold for particular properties 

 of such solutions, and might be expected to be of use in show- 

 ing their relation to one another. I need not refer here to 

 the more obvious of such deductions, as, for example, the 

 properties of non-electrolytes, or of electrolytes at extreme 

 dilution, but may restrict myself to cases in which both con- 

 stants k and I play a part. 



The temperature-coefficient for any property of a solution 

 of given concentration will be 



dP«; ,B* ,/"dl "dk\ -da 



iwjw + ^ n+ {wt-wtr n - h(l ~ k) wt n m 



I' 'dt ¥ w + kn + (l-k)om ' ' [i) 



The pressure-coefficient will have the same form, p being- 

 written for t. The concentration-coefficient will be 



iaP_ *+(*-*)(«+g ") 



P dn ~ " P,„ + kn + {l— k)an ' 



(8) 



