172 Prof. W. Ramsay. The Complexity and the [June 14,. 



Now van der Waals has shown that the relations between critical 

 temperature, pressure, and volume are given by the equation 



The denominator on the right-hand side of the equation is nearly 

 equal to unity. Assuming this to be the case, and introducing the 



value of a = 



where k is the "critical coefficient," or the critical temperature 

 divided by the critical pressure. 



Now the value of is related to b by the equation 



= 3&, 

 and b being proportional to the molecular refraction, the relation 



7 273 + 6* 1 2 -l M ! 



* = - = -3 -TT- ' T = 7 

 TT / n* + 2 d f 



should hold. That is, fc, the quotient obtained on dividing the abso- 

 lute critical temperature by the critical pressure, should, when 

 multiplied by a constant, be equal to the molecular refraction. 



While the majority of substances examined by Guye appear to 

 consist of simple molecular groups at their critical points, water, 

 methyl alcohol, and acetic acid yield numbers which point to associa- 

 tion, inasmuch as the constant /, instead of having its usual value 1'8, 

 has decreased to about I'l. 



b. The densities of most liquids at their critical points may be 

 found by multiplying their theoretical densities by a number approxi- 

 mately equal to 3'85 (Young and Thomas, ' Trans. Chem. Soc.,'1893, 

 p. 1251 ; also ' Phil. Mag.,' 1892, p. 507). But for a few substances, 

 the following values were found : 



Methyl alcohol .......... 4'52 



Ethyl alcohol ........... 4'02 



Propyl alcohol .......... 4'02 



Acetic acid ............. 5'00 



The factor should be greater, if association occurs, because the 

 theoretical density calculated by Boyle's and Gay-Lussac's laws 

 would then be greater than if it were supposed that the molecules of 

 methyl alcohol, for example, were represented by the simple formula 

 CH 4 O. Here, again, the evidence points to complex molecules at the 

 critical temperature. 



