UNPUBLISHED FRAGMENTS. 419 



On the Values of Potentials in Liquids for Substances which 

 form but a Small Part of the whole Mass.* 



The value of a potential! for a volatile substance in a liquid may 

 be measured in a coexistent gaseous phase, J and so far as the latter 

 may be treated as an ideal gas or gas-mixture, the value of the 

 potential will be given by the equation (276), [" Equilib. Het. Subs."] 

 which may be briefly written 



/z = func(0+ctflogy ga8 , [1] 



where JUL is the potential of the volatile substance considered, either in 

 the liquid or in the gas, t the absolute temperature, y^ the density 

 of the volatile substance in the gas and a the constant of the law of 

 Boyle and Charles. Since this last quantity is inversely proportional 

 to the molecular weight we may set 



_A - 

 ~M> 



where M denotes the molecular weight, and A an absolute constant 

 (the constant of the law of Boyle, Charles, and Avogadro), || and write 

 the equation in the form 



At 



s , [2] 



in which the value of the potential depends explicitly on the mole- 

 cular weight. 



The validity of this equation, it is to be observed, is only limited 

 by the applicability of the laws of ideal gases to the gaseous phase ; 

 there is no limitation in regard to the proportion of the substance in 

 question to the whole liquid mass. Thus at 20 Cent, the equation 

 may be determined by the potential for water or for alcohol in a 

 mixture of the two substances in any proportions, since the vapor 

 of the mixture may be regarded as an ideal gas-mixture. But at 

 a temperature at which we approach the critical state, the same is 

 not true without limitation, since the coexistent gaseous phase cannot 

 be treated as an ideal gas-mixture. At the same temperature how- 

 ever, if we limit ourselves to cases in which the proportion of water 

 does not exceed ^ of one per cent., and suppose the density of the 



*The object of this chapter is to show the relation of the doctrine of potentials to van't 

 Hoff ' s Law (what form van't Hoff s Law takes from the standpoint of the potentials) ; 

 and to the modern theory of dilute solutions as developed by van't Hoff and Arrhenius. 

 " Equilib. Het. Subs." [this volume], pp. 135-138, 138-144, 164-165, 168-172, 172-184. 



t For the definition of this term see p. 93, also pp. 92-96. 



Jin some cases a semi-permeable membrane may be necessary. (Enlarge.) (Is the 

 term coexistent right in this case ?) 



Definition. (Enlarge. ) 



7077 A^/ I YYL 



II = A, pv=-:rjAt. Is absolute used correctly ? 



