942 T hermodynamical Theory of Solutions. 



The Comparison and Tabulation of Experimental 

 Results. 



Vapour-pressure and osmotic pressure measurements form 

 two independent methods of investigating the thermo- 

 dynamical properties of solutions. The simplest method of 

 comparing and tabulating such results is to calculate from 

 the experimental data the lowering of the chemical potential 

 of the solute at some standard pressure (atmospheric or the 

 pure solvent vapour-pressure) *. These calculations may be 

 performed by means of equations (5) and (8). In the case 

 ot concentrated solutions it is impossible to measure the 

 ordinary osmotic pressure. A possible way of carrying out 

 the osmotic investigation of such solutions is to measure the 

 equilibrium pressures of successive pairs of a series of 

 solutions of gradually increasing concentration (starting 



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from the pure solvent). If for example in each measurement 

 the weaker solution was under atmospheric pressure, we 

 should have 



/ (0, w, 0)-/o(si, *r, 0)=n l P o (s li ot-*ot+0 15 6), 



/oOl, ™> 0)— /o(*2l ^ 0)=n 2 F {s 2 , <S7-><5T + n 2 , 0), 



/ (^_ b ot, 6)-f (s n , ot, 6)=n n 'p (s n , ot-^ot+h,„ 0), 



where s l5 s 2 , s n are the successive values of the con- 

 centration and XI], D 2 , fl n are the successive osmotic 



differences of pressure. The value of/ (0, ot, 0)—f (s n , ot, 6) 

 may thus be found by adding the quantities on the right- 

 hand sides of the above equations. It is perhaps hardly 

 necessary to remark that the osmotic pressure of the strongest 

 solution is not equal to the sum of the successive osmotic 

 differences of pressure. 



The University, Leeds, 

 June 80th,' 1911. 



* The fact that the thermodynamic potential is a more suitable mag- 

 nitude to deal with than the osmotic pressure in the case of concentrated 

 solutions, Avas pointed out by Duhem several years ago {La Mecunique 

 Chimique, vol. iii. p. 70). 



