THERMODYNAMICS OF CHANGE OF STATE, ETC. 32J 



at this surface must be equal to that of the solvent, otherwise a one- 

 temperature reversible cycle giving work could be arranged. Or, 

 again, the vapour-pressure of the solution is made equal to that of 

 the solvent by putting pressure on it, ~P = yph, where h is the height 

 at which the solution is in equilibrium with the vapour above the 

 solvent. 



The pressure P which must be put on to the solution to equalise the 

 vapour-pressures is, for a reason to be given later, called the OSHLOtic 



pressure. 



If the difference of vapour-pressures is too large to allow us to assume 

 the vapour-density constant, we must use the logarithmic formula, whence 



to Po- 

 log e , = 

 to top 



or 



This may be obtained, of course, exactly as on p. 316. 



Raising Of the Boiling-Point. One effect of the lowering of the 

 vapour-pressure by solution is a rise in 

 the boiling-point. For, if the solvent 

 vapour has a pressure of 1 atmo. at a 

 given temperature, the solution has a 

 pressure less than 1 atmo. at that tem- 

 perature, and it must therefore be raised 

 to a higher temperature before it will 

 boil. 



We can easily calculate the rise of 

 boiling-point in terms of the osmotic 

 pressure. 



For if AO, BO, Fig. 183, represent the j> 

 pressures of solvent and solution vapours |_ 

 at the normal boiling-point of the solvent, 

 and AD, B(J, the vapour-pressure lines as 

 the temperature rises, if we draw AC 

 parallel to the temperature axis to meet 

 BC in C, AO is the rise in boiling-point, 

 say dO. As we suppose the solution to be dilute, AD and BC will be near 

 together and may be regarded as parallel straight lines. This follows 

 also from Raoult's researches (see below) confirming earlier work, which 



~Df) 



showed that for a given solution - is independent of the temperature. 



AO 



AB 



Then AD is practically parallel to BC if ^ is very small. 



o 



Temperature 



FIG. 183. 



Then 



CD CD 

 AC 



