528 



Albert P. Mathews 



of. correcting for it would be to reduce the value of b v and 

 increase b l and so to make the parabola flatter. I have 

 computed b l assuming that there is no association in the 

 liquid. The increase of b v with the temperature is seen to be 

 very slight. From absolute zero to the maximum value at 

 100 the increase is at the rate of 0.074 cc per degree for gram 

 mol quantities. On the other hand "6" changes markedly 

 with the pressure. 



There are several reasons for believing that "b" is the 

 real volume of the molecules and not four times the volume 

 as was originally suggested. One is that "b" at the critical 



Fig. i Volumes of molecules (b for gram mol quantities in cc.) for pentane. 

 b l calculated from formula b 1 = V 1 RT/(P + a/Vf ) assuming no asso- 

 ciation; b v calculated by formula: b v = b c ((sT c + T)/2T C )) b^, b v f apparent 

 volume of b v by formula: &' = V v RT/(P + a/Vj) assuming no association. 



temperature is very nearly V c /2 and this is just twice the 

 volume at absolute zero. It is unlikely that the molecules 

 do not expand in passing from absolute zero to the critical 

 temperature, since at the former temperature they are under 

 a pressure of 3572 atmospheres in pentane, whereas at the 

 critical temperature the pressure is only 240 atmospheres. 

 It would take very little separation of the atoms to double 

 the volume. 



The latent heat shows, also, that heat is absorbed by the 

 molecule roughly proportional to the number of atoms in 

 the molecule. This would mean that the atoms vibrated 

 (or expanded) and they must hence take up more space as the 

 vigor of vibration increases. This would seem to be sufficient 



