Forces on the Osmotic Pressure of Electrolytes. 749 



But by (4) -j~ = -- T ' whence 



dV 



3V 



1RT 

 6 V 



WO, 



which gives the same equation (5) for the osmotic pressure 

 as before. 



Effect on the Freezing- Point. — The thermodynamical relation 

 between the osmotic pressure of a solution and the lowering 

 t of its freezing- point below 0° C, reduces in dilute solutions 

 to 



PV_ t _T 



RT ~ 1-86 C ~~ 1-86' 



where C is the concentration (gm.mols./litre) and r = £/0 the 

 molecular lowering. This relation is practically independent 

 of whether the osmotic pressure obejs the gas law or not* By 

 combining it with (5). we get for the variation of t with the 

 concentration in a completely dissociated electrolyte 



T = l-86{2-iV(/«)} (8) 



The appended table shows values of h and ^hf(Ji) for 

 various concentrations : — 



c. 



h. 



W(h). 



•0001 



•0559 



•0056 



•001 



•120 



•0175 



- -002 



•152 



•0245 ■ 



•005 



•206 



•038 



•01 



•259 



•053 



■02 



•327 



•074 



•05 



•443 



•115 



1 



•559 



'162 



•2 



•704 



•224 



In fig. 2 (p. 750) are plotted the experimental values of t for 

 KC1, NaCl, and NH 4 C1. KC1 and NaCl are probably among 

 all substances those for which the lowerings have been most 

 accurately determined at dilute concentrations. In the 

 figure Loomis' results* are indicated by crosses, the ©'s 

 give all the values of other observers collected in Landolt 



* Loomis, Ann. d. Phys. li. p. 500 (189-1) ; lvii. p. 495 (1896). 



