320 



HEAT. 



Solutions. 

 Vapour-Pressure of a Solution always Less than that of the 



Solvent. It has long been known that when a stilt is dissolved in a 

 liquid the vapour-pressure of the solution is less than that of the pure 

 solvent, the reduction of pressure increasing with the proportion of salt 

 dissolved. 



It follows that if we have two vessels in an enclosure, as in Fig. 182, 

 one containing pure solvent and the other containing a solution, the rest 

 of the space being filled with vapour of the solvent the salt being 

 supposed to have no appreciable vapour then the solvent will distil 

 over into the solution, and the level of the latter will tend to rise till its 

 surface is so high that the pressure of the 

 vapour actually present at the new level is 

 equal to the vapour-pressure of the solution. 



Let h be the difference in levels of the 

 surfaces when equilibrium is attained, let o> 

 be the vapour-pressure of the pure solvent, 

 o>' that of the solution, and cr the density of 

 the vapour. We suppose that the solution is 

 very dilute so that h will not be too great to 

 suppose a- uniform in the column intervening 

 between the levels of the two surfaces. Then 

 we have 



lutio i 



vapour 



I 7 



= o> + gph 



where p is the density of the solution, and if 

 FIG. 182. this is very dilute it is equal practically to that 



of the solvent. Let us put P = ypli, then P is 



the excess of hydrostatic pressure in the solution over that in the solvent 

 at the level of the surface of the latter. 



Then 



Po- 



(1) 



But (p. 315) if we put pressure P on to the solution its vapour- pressure 



j u Po- 



is increased by , or since 



P 



, Po- 

 tt) = CO -\ , 



p 



it is increased to the vapour-pressure of the solvent. Hence the solution 

 will be in equilibrium with the vapour at such a height above the surface 

 of the solvent that the hydrostatic pressure due to that height of liquid 

 will make the vapour-pressure of the solution equal to that of the pure 

 solvent. 



We can see this also by imagining a capillary tube, which the 

 solution does not wet, to be fixed in the side of the solution vessel, as in 

 Fig. 182, and of such narrow bore that the solution is depressed in it to 

 the level of the surface of the solvent. Evidently the vapour-pressure 



