86 



PHENOMENA, ATOMS, AND MOLECULES 



We then find that A = o or Ai=. A^ at a critical temperature Tc 

 given by 



T.= 



5'(p 



2K 



(29) 



Above this temperature the hquids are miscible in all proportions, so 

 that there is only one phase, while at lower temperatures two phases exist. 



The values of qp calculated from these equations come out usually some- 

 what lower (10 to 30%) than those from vapor pressures and are probably 

 less accurate. Undoubtedly, in mutually saturated liquids, especially near 

 the critical temperature, the conditions are favorable for orientation and 

 segregation of the molecules in the liquids, so that we should not expect 

 our equations for solubilities to hold as well as those for the vapor pressures 

 of mixtures of liquids which mix in all proportions. 



Nevertheless, the general agreement between the theory and the ex- 

 perimental data seems very sati factory, especially if we are willing to 

 consider mainly relative rather than the absolute values of (p. 



The effects of the relative surface areas of the molecules indicated by 

 Equations (27) seem to be well verified by the experimental data. Thus, 

 in general, for two substances only slightly soluble in one another, the 

 substance having the molecules of the larger surface shows the lower 

 solubility in the other. 



TABLE VI 



Solubilities of Fatty Acids in Water 



Acid 



4 Butyric 



5 jValeric , 

 9 iNonylic 



14 IMyristic 



Temp. 



— 2° 

 16° 

 25° 

 20° 



Observed 

 Solubility 



Mol 

 Fraction 



0.052 



0.0062 



1.4 X 10" 



ca. 10-* 



0.402 

 0.357 

 0.272 

 0.198 



(pob.i 



10.5 

 15.0 

 26.0 

 33.0 



Cpo 



13.3 

 17.3 

 25.0 

 31.9 



Even when solubilities are large, nearly to the point of complete mixing, 

 the same rule applies. For example, the critical temperature of butyric 

 acid-water mixtures is — 2.5° C. At — 6° C. there are two phases. The 

 water phase contains 0.053 mol fraction of butyric acid, but the acid phase 

 contains 0.76 mol fractions of water. The much greater solubility of the 

 water as compared to the acid corresponds to the smaller surface area of 

 the water {Sb = 37.8A2) ^g compared to that of the acid {S = 115A-). 

 In fact the difiference in solubility is almost exactly what the theory in- 

 dicates, for the value of (p calculated by Equations (26) from Ax/A^, 



