in the Analogy between Solutions and Gases. 91 



constant pressure is maintained only when the total volume of 

 gas or solution is very great compared with V, or in cases of 

 evaporation, where the vapour-pressure is at its maximum. 



We shall also often have to express in calories the work 

 done during isothermal expansion of the kilogram-molecule of 

 a substance as gas, or in solution. If pressure falls a very 

 small fraction AP, corresponding to a small increase of 

 volume AV, the work done will be APAV, or 2AT. 



VI. First Confirmation of Avogadro's Law in its Application 

 to Solutions. — Direct determination of Osmotic Pressure. 



It is to be expected that Avogadro's law, deduced as a con- 

 sequence of Henry's law for solutions of gases, will not be 

 restricted to solutions of substances which usually exist in a 

 gaseous condition. This expectation has been realized, not 

 merely from a theoretical, but from an experimental standpoint. 

 Pfeffer's determinations of the osmotic pressure of solutions of 

 sugar furnish a remarkable confirmation of this extension of 

 the law. 



Pfeffer's solution consisted of 1 gram of sugar dissolved in 

 100 grams of water ; one gram of the sugar therefore exists 

 in about 100*6 cubic centim. of the solution. Comparing the 

 osmotic pressure of this solution with the pressure of a gas 

 (e. g. hydrogen) containing as many molecules in the volume, 

 there are -gf % gram (C 12 H 22 11 =342) in 1006 cubic centim. 

 Now one litre of hydrogen gas at 0° and 760 millim. pressure 

 weighs 0*08956 gram ; and the above concentration is equi- 

 valent to 0*0581 gram per litre ; the pressure at 0° is 0*649 

 atmosphere, and at t, 0*649(1 + 0*00367*). Placing these 

 results beside Pfeffer's, we obtain the following agreement : — 



Temperature (t). Osmotic pressure. 0-049(1 +0-00367 0- 



6-8 0*664 0*665 



13*7 0*691 0*681 



14*2 0*671 0*682 



15*5 0*684 0*686 



22*0 0*721 0*701 



320 0716 0*725 



36*0 0*746 0*735 



The directly determined osmotic pressure of a solution of 

 sugar is thus seen to be equal to the pressure of a gas at tbe 

 same temperature, containing the same number of molecules 

 in unit volume as the sugar-solution. 



Starting from cane-sugar, this relation can be calculated for 

 other dissolved substances, such as invert sugar, malic acid, 

 tartaric acid, citric acid, magnesium malate and citrate, all of 



