90 J. van't Hoff on the Function of Osmotic Pressure 



V. General Expression for Boyle's, Gay-Lussac's, and 

 Avogadro's Laws for Solutions and Gases. 



The well-known formula expressing both Boyle's and Gay- 

 Lussac's laws for gases, 



PV=RT, 



are, in so far as these laws are applicable to liquids, also appli- 

 cable as regards osmotic pressure ; with the reservation, also 

 made in the case of gases, that the space occupied by the 

 molecules must be so great that the actual volume of the 

 molecules becomes negligible. 



To include Avogadro's law in the above expression, Horst- 

 mann's suggestion (Berl. Ber. xiv. p. 1243) may be adopted, 

 to express the molecular weight of the substance in kilograms ; 

 taking 2 kilos, of hydrogen, 44 kilos, of carbon dioxide, and 

 so on. Then R in the above equation has always the same 

 value; for, under equal conditions of temperature and pres- 

 sure, these weights occupy the same volume. Calculating 

 this value, and expressing the volume in cubic metres, and the 

 pressure in kilograms per square metre, and choosing hydrogen 

 gas at 0° and 760 millim. pressure as starting-point, then 



P= 10333; V= , ^ 956 ; T = 273; R= 845*05. 



Hence the combined expression for Boyle's, Gay-Lussac's, 

 and Avogadro's laws becomes 



PV = 845T; 



and this expression is applicable to solutions, substituting 

 osmotic pressure for gaseous pressure. 



We may give this equation even a simpler form, inasmuch 

 as the number of calories equivalent to a kilogrammetre of 



work (A= -j =4^5) stands in a very simple relation to R, 



viz. AR = 2 (in reality about one thousandth less). Hence 

 we may choose the form 



APV = 2T; 



and this form has the great practical advantage that work, 

 which will often be discussed in the following pages, receives 

 a very simple expression, if calculated back to heat, measured 

 in calories. 



Let us next calculate the work, expressed in calories, when 

 a gas or a solution, under constant pressure and temperature, 

 expands V volumes ; V volumes containing a kilogram- 

 molecule. This is evidently 2T. It must be added that this 



