32 THE TRUE VALUE OF a OF VAN DER WAALS' 



has a density of 0.077 (Dewar). d, at 14.83° is 0.07631. 

 M = 2.014. 'n 113 = 8.463 X 10 7 . T c = 31.95. T e —T= 17.12° 

 a = 0.254X10 12 In this calculation the density of the vapor, D, 

 at 14.83° Avas neglected. If it has any appreciable effect on the 

 calculation neglecting D will make a smaller than it really is. 

 Moreover the surface tension was measured by the capillary rise 

 method and this gives generally a value lower, rather than higher, 

 than it ought to be. Hence 0.254 is to be regarded as a minimum 

 value for a. The true value is certainly not lower than this and 

 it probably is higher, but we cannot say how much higher. 



Conclusion: From the surface tension we have a equal to 0.254; 

 and from the pressure-volume formula, 0.270 or 0.319, more 

 probably the latter. The true value for a certainly lies between 

 0.254 and 0.319 X 10 12 , but it cannot yet be said just what the 

 value is. From the gravitation and valences by my formula, a 

 is computed as 0.298 X10' 2 , which would appear to be certainly 

 not very far from its real value. In this calculation 2 valences 

 were assumed to be present in the molecule; the formula used 

 was a = N\vrk X Val\Mf' ? \ The value for a computed by van 

 Laar and used in his calculations was 0.120 X 10 12 . This value 

 is certainly 100 °/ o below the true value for a. It is probably 

 still more in error than this. Furthermore the value he adopts 

 for a gives for b r the figure /'./2.50. This as I shall point 

 out presently is impossible, for the reason that the molecules of 

 hydrogen are more compressible than those of pentane, not less. 

 On the other hand the value for a computed by my rule from 

 the gravitation and valences appears to be very close to the true 

 value. The correction which van Laar has made, the factor y, to 

 the computation of a by the ordinary aan der Waals method, 

 is clearly shown , I believe , to be a correction which is directly 

 contradicted by the facts , since the calculation of a by the usual 

 A'AN der Waals' formula without this correction gives a value not 

 so far from the truth as that of aan Laar's method. 



To save repetition it miay be stated here that in all the calcu- 

 lations Avhich follow the number of molecules in a gram mol has 

 been taken to be that found by Millikan of 6.062 X 10 23 so that 

 the value of 7V ,/f is 8.463 X 1 7 . • The computation for a by 

 the valences and molecular weight has been made by the formula: 

 a = 1.1763 X 10 U (MX Vàlf*. This is identical with the for- 

 mula a = N\m 2 k X ValjMf* the factor 1.1768 X 10" bein g 

 equal to N 2 multiplied by the factor {m\k) 2iz where nu is the mass 

 of a molecule of unity molecular weight and unity valence. 



