WEIGHT-NORMAL SYSTEM FOR SOLUTIONS. 99 



Apparently the confusion of mind which prevailed for several years 

 after the publication of van't Hoff's paper — and of which one sees 

 many evidences, even at the present time — was due, in great part, 

 to the persistence of the habit of regarding the simple equations which 

 apply to so-called "ideal" conditions as the embodiments of the general 

 laws for gases and solutions. The really comprehensive equation for 



gases is, of course, that of van der Waals (P+y 2 ) (V — b)=RT; while 



the equation for so-called "ideal" gases, PV = RT, covers only a special, 

 and, in fact, a purely imaginary and impossible case, that, namely, 



in which the y 2 and the b of van der Waal's equation have become zero. 



It is conceivable that in the course of time an approximately com- 

 prehensive equation will be developed for osmotic pressure, but, in the 

 opinion of the writer, it will be the fruit of extensive and painstak- 

 ing experimental research rather than of ingenious speculation. In 

 other words, it will be the embodiment of the general rule which is 

 finally formulated for the purpose of correlating a great variety of 

 authenticated facts concerning osmotic pressure. The equation of 

 van't HofT will, of course, stand in much the same relation to it as 

 does the expression PV = RT to the more general equation of van der 

 Waals. It is doubtful, however, if any proposed general equation for 

 osmotic pressure, although containing suitable terms for all the factors 

 which must be taken into account, would be of any present utility in 

 the case of aqueous solutions, since the value of at least some of these 

 terms — e. g., that covering hydration — must still be experimentally 

 determined for every solute and at every temperature and in each 

 individual concentration of solution. If it is true that the value of an 

 equation is to be measured by its competence to foretell the truth in 

 any case to which it may appropriately be applied, then every general 

 equation for osmotic pressure is bound to disappoint one who attempts 

 to apply it to aqueous solutions. To illustrate : There is no equation 

 conceivable which could foretell, in the case of cane-sugar solutions, 

 that the value of the hydration term is constant for each concentra- 

 tion between 0° and 25°, or that it soon thereafter begins to decline 

 in value to become zero at some definite higher temperature; or 

 further, how what may be called the idiosyncrasies of hydration may 

 be expected to vary from one solute to another. In view of the 

 necessary limitations of its usefulness as a means of discovering truth, 

 the author does not regard a general equation as the ultimum bonum in 

 the field of osmotic pressure or (in the present meager and inexact 

 state of our knowledge of the subject) as even highly desirable. The 

 osmotic pressure of solutions — especially of aqueous solutions — depends 

 upon such a variety of still unmeasured and imperfectly understood 

 conditions that any attempted comprehensive expression for it at the 



