272 The Earl of Berkeley : Notes 



Theory and experiment give some information as to parts 

 of these curves. P a leaves as a straight line ; this is the 

 part of the curve where for undissociated substances Boyle's 

 law is followed ; even if Boyle's law is not followed, we 

 know from general principles that (where no chemical 

 reaction takes place) the properties of very dilute solutions 

 are additive, hence the straight line. Experiments hitherto 

 have shown that for undissociated substances the curve then 

 becomes convex to the ordinate through D. Similarly for 

 the curve of P^ starting at D. 



In " Theory," p. 604, equation (18) (but using another 

 notation), it has been shown that for any given solution with 

 the same pressure on it when measuring the two osmotic 

 pressures, the relation 



™j$?m P =b Sb (b? b fa) n * .... (7) 



holds between the differentials. 



It has already been stated that the effect on (say) P a of a 

 change of pressure on the solution is but small ; we may 

 therefore consider equation (7) as applicable over a finite 

 range of pressure, and if we assume that we are dealing with 

 ideal liquid mixtures where s a and s b are independent of 

 concentration, we can then get an idea as to what takes 

 place in the upper part of the two curves. 



Near D, dP^/da is constant, hence (d¥ b /'dii)p b = kasjb* b , 

 but it seems reasonable to suppose that while s a and s b 

 diminish with increasing pressure, they tend to a finite 

 although small limit when p is very great, and neither 

 vanish nor become infinite when a=l. Hence we have 

 (dT b /'da)p b =7c f a/b = k , a/(l — a). This on integrating within 

 the range for which these assumptions are valid gives 

 P =C — £'[a-f log(l-a)], where C is a finite constant. 

 Hence P 6 becomes indefinitely great along with — log (1 — a) 

 as a approaches unity. 



Similarly for P a . 



Consider now the system shown in fig. 4, where we have 

 the pure gas B (in compartment (1)) in osmotic equi- 

 librium through a membrane permeable to B only, with 

 a solution of gas B dissolved in A (in compartment (2)). 



Performing the standard cycle (as already detailed) between 

 compartments (1) and (2), the pressure limits being p and 



* This relation is exact, and can be derived from equation (31) of 

 "Theory," p. 617. 



