134 THE STRUCTURE OF THE NDCLEDS. 



since the ju'essiire, tension, size, and density of the droplet of solution have all 

 changed \>y the partial evajwi-atiou of the drop. But as the more concentrated 

 drojt (»f radius /•' now persists,/*' ,, = p^,, the vapor pressure at the flat surface of the 

 oritriiial solution. Hence 



s 



For the case in which a solid is dissolved, its mass remains fixed within each 

 suspended drop of water. The case of a gas may be supposed to a])proximate to 

 these conditions. Hence p' may be expressed in terms of p, or 



/y = 1 + (p - \)0-3/r'^), 

 whence finally, 



p'^=p^-'^^,./^';:,^,.- (4) 



For dilute solutions, p= 1, nearly, or^'^ =jP» — 2(jl'/r'. If r' = cc,p'^ =/'x> 

 the vapor pressure at the fiat surface. 



It will l)e seen that in^' and T' the original radius of the droplet is implicitly 

 involved. If Sp=Pa>—p<i>, and c=r^/r'^, equation (4) may be written: 

 /•■ = 2gT'/((1 + (p — l)':')(5/->). If Sp be expressed in terms of Raoult's law, u/JV 

 and n/N' being the original and final latios of the number of molecules in solute 

 and solvent and /)o„ =/>, 



sp = p{7i/N' - /i/l\)/{l + n/N'). 



Finally, in a law (7'= 83 + 187/i/iV) discovered empirically by Quincke' 

 T' = T+ 187 {)i/N' - >i/N), where 7' is the initial and T the final surface ten- 

 sion in dynes. Thus if (ii/N'— it-fN^ =^ it, 



,.' = ^_" .^+J»7^ (1 +n/N'). 



'i'his e.\pre.><ses the radius of the dro[)let in terms of the orii^inal and final ratios 

 of the niiml)er of molecules of .solute and solvent in solution. It does not, however, 

 admit of any simple interpretation, and is, as a rule, liable to considerable or even 

 fatal error, because the nuclear conditions are probal)ly not leached until the solu- 

 tion is too concentrated. In this case the usual laws of [)liysical chemistrj' lo.se 

 their meaning. Of'. § 48. 



40. Eqaatioiu for concentrated solution.'i. — A statement of the case is better 

 made as follow.s, supposing the effect of solution in diminishing vapor pressure to 

 be known, particularly in the region of concentrated solutions. Let Sp = /(c), 

 where Sp is the decrement of vapor pressure at the high concentration r, of the 

 solution. Hence 



nearly. This condition holds when evaporation ceases with the occuri-ence of a 

 stable nucleus. 7'and p refer to pure watei-. 



If ^' and Cj l)e the original concentrations of two given dilute .solutions; if c' 

 and c', lie the concentrations after evaporation to the nuclear stage, .uid if tlie cor- 



' C/. Winkelmann's Handbuch. 



