_ 2 OF THE AMERICAS ACADEMY. 



the activity of the water is lowered by the same per cent as when 

 1 grain of sugar 18 added to L000 grains of pure water. 



An interesting system is one composed of two phases, both of which 

 are mixtures of the same composition. An important example of a 

 a system is a constant boiling mixture and its saturated vapor. 1! 



A'. ; , etc., which are the molecular fractions in the one phase, are 

 equal respectively to A'' L ., X' 3 , etc., in the other phase. If the condi- 

 tions are changed by changing the temperature or pressure or by adding 

 a third substance Xi to one or both of the phases, then equilibrium can 

 only he maintained by keeping the activity of each component the same 

 in both phases; thus we may write as usual, 



d In & = d In K, d\n£ 3 = d In & , 



etc. ; but since 2VJ = X' 2) etc., we may write 



ZWln& + 2V~ 8 <*ln& + • • • = X',d\n$', + 2Wln& + « ■ • 



Now the first member of this equation represents a change which may 

 be the resultant of the changes produced by change of temperature, 

 change of pressure, and the addition of dXi mols of the solute X,. 

 E ili of these changes is represented alone by equations XVI, XVII. 01 



XX. Therefore, 



NJ\n£ a + 2v* i 81n&+. \ * JT Y - /V 



<// = dT t 



< r rv /;/ 



( 



/ A'..? In $ 2 + X,,? In £, + • • • \ .„ v ln 



\ W )r., d/ = A'/" 7 ' 



/ A'./ I n f 8 -f iN^lng 8 + - • • \ 



V 9N t Jr. 



,/A', = - dN v 



"We may therefore write the sum of these as follows : 



2vV*ln6 + Win I, + • • • = Y »Jm° JT+ fif dP ~ dN *' 



Likewise we find 



-V,/hu" a + AVlnf',+- • • =—~'* r '</T+ ^dP-dN 1 !, 



where dN*\ is the number of mols of the solute in one mol of the second 

 phase. Equating the second members of these two equations we have, 



