276 PEOCEEDINGS OF THE AMERICAN ACADEMY. 



state of infinitely attenuated vapor. We will denote this quantity by 

 Y. It bears the same relation to the value Y of a pure substance as 

 the quantity v does to v. We may call it the partial " ideal heat of 

 evaporation. " 



The above equation then becomes, 



/a In A 

 \dT J 



Y — Pv 



— YTT 



which is a general equation for the influence of temperature upon the 

 activity of one of the constituents of a mixture when the pressure and 

 the composition are constant. ^^ 



Just as equation X was proved we may show that for one mol of the 

 mixture, 



Y = N^, + K,%. XIII 



Hence we obtain an equation analogous to equation XI, namely 



' Nid In ^1 + N,d In L\ Y -Pv 



(■ 



— XIV 



dT )p,N BT^ 



Here as before v is the volume occupied by one mol of the mixture 

 and Y the increase in internal energy when one mol of the mixture is 

 converted into infinitely attenuated vapor, or in other words when it 

 evaporates in a vacuum. ^^ 



^^ The approximate equation for the vapor pressure of oue constituent of a 

 binary mixture obtained from equation XII is, 



'd In /) 



\ dT )p,N~ RT^' 



where Q is the partial heat of vaporization (including tlie external work). This 

 is in a simpler form than tlie equation obtained by Kirchhoff, 



(^^\ (f) 



\ dT Jp,x RT^ 



(see Nernst, Theoretische Chemie, 4 Edit., p. 118). 



^2 Equation XII bears tlie same relation to XIV that the equation of Kirchhoff 

 does to one obtained by Nernst, namely, 



p p_ _ _ Q{^ 



(IT ~ RT^ 



(Nernst Theor. Chem., 4 Edit , p. 117). 



