88 



J. van't HofF on the Function of Osmotic Pressure 



should not be attached to them, owing to the difficulties of 

 experiment. 



IV. Avogadro's Law applied to Dilute Solutions. 



We have considered the changes produced in the osmotic 

 pressure of solutions by alteration of temperature and con- 

 centration, and attempted to exhibit the analogy between 

 dilute solutions and gases, in relation to these two quantities 

 It now remains to compare directly the two analogous quan- 

 tities, gaseous pressure and osmotic pressure, in one and the 

 same body. It is obvious that this analogy should hold with 

 gases in solution ; and in actual fact it will be shown that, if 

 Henry's law be taken into consideration, the osmotic pressure 

 in solution is absolutely equal to the gaseous pressure, under 

 similar conditions of temperature and concentration. 



To prove this statement, we shall picture a reversible pro- 

 cess by aid of semipermeable diaphragms, temperature being 

 maintained constant ; and we shall again make use of the 

 second law of thermodynamics, which in this case leads to the 

 simple result that no work is transformed into heat, nor heat 

 into work ; and hence the sum of all work done at different 

 stages of the process is zero. 



This reversible process may be conceived by means of two 

 similar cylinders and pistons, like those already described. 

 One contains a gas (A), say oxygen, and in contact with it a 

 saturated aqueous solution of oxygen (B) (fig. 4) . The wall b c 

 allows only oxygen to pass, but 

 no water; the wall a 6, on the 

 other hand, water, but not oxygen; 

 and it is in contact with water, E. 

 A reversible process may be car- 

 ried out by such an arrangement 

 as follows : — By raising the two 

 pistons (1) and (2), oxygen is 

 evolved from its aqueous solution as gas, while the water 

 passes through ab; this change can proceed without altering 

 the concentration of the solution. The only difference between 

 the two cylinders is in the state of concentration of the solu- 

 tions which they contain ; we may explain the action thus : — 

 The unit of weight of the substance in question occupies in 

 the left-hand cylinder a volume v and V, and in the right-hand 

 cylinder, v + dv and Y + dY ; hence, in order that Henry's 

 law may hold, 



v :Y= (v+dv) : (V + dV); hence v : Y = dv : dY. 



If, now, the pressure, or osmotic pressure, as the case may be 



