Dr. F. Tinker on Osmotic Pressure, 447 



But at osmotic equilibrium, 



El— *~st _ i 9_ 



ir{~* ~ L RT 

 (see p. 443). 



Hence, if e (P) is the total expansion per solute molecule 

 when the solution is under the hydrostatic pressure P * (i. e. 

 the osmotic pressure), we have 



N + 7i n / V 2 -^2 + € (P) \ _ _ Q^ 



N ~K\ L Vx-ftj / RT' 



whence 



ne (P) = -n(V 2 -6 3 ) RT ; . . . . [23] 



Now the contraction due to applying the osmotic pressure 

 to the solution is we, a) — ne, P) ; and if /8 is the average co- 

 efficient of compressibility of the solution! between zero 

 pressure and the osmotic pressure, it is also equal to 

 PflCNV + nV,'). 



Hence 



PjSCNVt'+nV, 1 ) = « w -*ta, • • • [24] 



where e (o) and e (P) have the values given to them by 

 equations [7] and [23] respectively. 



For dilute solutions with no heat of dilution, we can 

 neglect nY 2 ' ; and substituting the values of e, * and e (P v 

 for such solutions, the equation becomes 



P,SNV! = 



.. n{ (V 1 -b 1 )-(V 2 -b,)}-{-n(V ^ - 



-h)} 





■. n(V 1 -b 1 ). 





Putting 



FV.-REj, 





this becomes 



BT^.N/8 = n(V 1 -6 1 ); 





whence 



p RT 

 and ¥,-*! = /8RT{, . . . 





[25] 



* Supra, p. 432. The value of e varies with the hydrostatic pressure 

 placed on the solution, diminishing with increase of the latter and tending 

 to become more and more negative with high pressures. 



t Defined as the shrinkage of 1 c.c. per atmosphere applied. 



t It is to be remembered that, since P is measured in atmospheres 

 and V in c.c, the constant R is measured in c.c. atmospheres and is 

 equal to 82-07. 



