44 PHYSICAL PROPERTIES AND COMPOSITION 



then, so that the volume of the solution is calculable from 

 the value for each ion obtained by measurement of a single 

 compound. 



The change of volume on dissociation into ions appears, 

 according to these numbers, to be a diminution. This may 

 be referred to the important fact that the formation of ions, 

 perhaps on account of the attraction of the opposite electric 

 charges, causes a contraction, which may in certain cases 

 be calculated. Thus e. g. if a strong base be neutralized by 

 a strong acid, instead of the contraction that might at first 

 be expected, an expansion takes place, amounting, according 

 to Ostwald, to 20-05 c.c. for one kilogram of each solution, 

 containing a gram-molecule of acid and base respectively. 

 In this case two ions disappear, according to the equation 



~ - (K)(N0 3 ) 



or 



If the acid and base are weak, i. e. not dissociated whilst 

 the salt formed is dissociated, as in the case of butyric acid 

 and ammonia, a contraction of i8'65 c.c. occurs, here new 

 ions are formed : 



C 4 H 8 2 + NH 3 = (C 4 H 7 2 )(NH 4 ). 



Thus the formation or disappearance of two gram-ions 

 in about two litres of water causes a contraction or expan- 

 sion of 20 c.c. on the average, or 10 c.c. for one gram-ion 

 per litre. 



2. PRESSURE RELATIONS. 

 A. Deductions from the Characteristic Equation 1 . 



Starting from the simple form of the characteristic 

 equation 



1 During proof-correction the inaugural dissertation by Reinganum 

 (Gottingen, 1899) on this subject appeared. Dieterici, Wied. Ann. 69. 

 685. 



