﻿Molecular Thermodynamics. G1D 



or if we write 



y-[M,i =d\og{l + mC)-~G x "\ . (45) 

 then 



|(l-* s ) = *.u-*.) («) 



If now we write ,r s as a series of ascending integral 

 powers of y, we can show that a few terms only need be 

 taken for our practical purposes *, so long as y is little 

 greater than unity — that is, we obtain a practical expression 

 for x s which will serve up to very high concentrations. 



Putting then 



<r s = •?>, + % + % 2 + % 3 + • • • +b„y n . . . 

 by straightforward substitution in (45) (and equating co- 

 efficients) we obtain b l9 b 2 , in terms of x Sq . 



A simple relation between these coefficients enables them 

 to be written down very easily, viz. : 



n b n== l 1 - — h n _j, 



the first coefficient b Y being #*<,(#«„ — 1), and being a factor of 

 all the others. The alternate coefficients are also divisible 



Tlie numerical values of the coefficients depend, of course, 

 on that of x So which may be any proper fraction (positive). 

 Their maximal (absolute) values can be obtained and shown 

 to decrease rather rapidly. The higher members of the 

 series have, of course, several maxima, but the greatest 

 maximal (absolute) values diminish by alternate long and 

 short steps, the. following round values being sufficient for 

 present consideration : 



b x . b 2 . b 3 . & 4 . b b . b 6 . b 7 . 



1 I J_ J_ A — __L 



4 22 48 300 480 4400- 



Taking I per cent, as our standard of experimental accuracy r 

 we see that the series as far as y z , 



ff, = tf +% + % 2 + % 3 5 (47) 



will suffice until y closely approaches unity, when the y 4 term 

 will be just appreciable. 



* That is, the remainder after a few terms is negligible experimentally 

 up to high concentrations. We may conveniently call this " converging 

 practically up to high concentrations." 



