Do Molecules Attract, Etc. 



527 



apparent decrease in b v , it is practically certain that the 

 differences between b^ and b v are actually larger than those 

 indicated. The main fact is then established that b v is actually 

 larger than b l for some degrees below the critical point in spite of 

 the association which tends to mask the actual molecular ex- 

 pansion and which, at lower temperatures, conceals it en- 

 tirely. 



It will be seen, also, that, as one would expect, b v actually 

 decreases close to the critical temperature, owing to the com- 

 pression of the molecules due to the great increase in internal 

 and external pressure. This increase of pressure (P + a/V 2 ) 

 is indicated in Table 2 in the case of pentane, the pressures 

 being given in atmospheres per sq. cm. 



It is of interest, in this connection, to compute what is 

 possibly the real value of b v , making van der Waals' assumption 

 that in the vapor, at low temperatures, b v is equal to 2& r 

 Supposing that this is the case at absolute zero we may write 

 the rectilinear diameter formula : 6 t + b^ = b c ((3T C + T)/2T C ). 

 This assumes that at absolute zero the molecules are so com- 

 pressed that in the solid their volume is one-half of what it 

 would be in the vapor at the same temperature, and that the 

 volume of the vapor molecules at absolute zero is that of b c . 



+ T)/ 2 T C ))-& 1 . 



b c is very nearly V c /2 . Table 3 b v 



TABLE 3 

 Pentane 



The parabola represented by these figures is given in 

 Fig. i. If there is any association in the liquid the effect 



