A METHOD OF DETERMINING "a" OF VAN DER 

 WAALvS' EQUATION FROM THE SUR- 

 FACE TENSION 



BY ALBERT P. MATHEWS. 



Uncertainty still exists as to the correct value of van der 

 Waals' constant "a, " which expresses the cohesive pressure of 

 a fluid. 



It is well known that if "a" and "6" are both supposed 

 to be constant, the equation of state may be solved and the 

 relationships obtained: a = 3P C V C 2 ; V c --= 36; P c == a/2~b 2 ; and 

 T, = 8a/2jbR. As this solution depends on the er- 

 roneous assumption of the constancy of ''6," there is no 

 certainty that any of these expressions is correct; and as a 

 matter of fact, only one of them, i. e.,P c = a/2jb 2 , happens 

 to approximate very closely to a correct value. Were these 

 relationships true, the calculation of "a" and "6" from the 

 critical data would be very simple; but as they are not true, 

 except for. unknown values of "6," ii: is necessary to find 

 some other means of computing "a," which does not require 

 a knowledge of the real molecular volume, or " b. " 



While the formula usually employed for the calculation 

 of "a, ' ;. r., a = 271^/64 X 273" X P c , gives a value at least 

 approximately correct for non-associating substances of me- 

 dium molecular complexity, it is still uncertain whether the 

 value thus obtained is correct for very simple substances 

 such as hydrogen, or for very complex substances such as 

 diphenyl methane. The ratio 27/64 can only be justified 

 theoretically if "6" were constant and it is probable that 

 this ratio, 27/64, is not constant, but diminishes as molecular 

 compressibility increases. "6 C " may not always be the 

 same fraction of V c , for it is possible that this fraction also 

 varies with the compressibility of the molecule. All other 

 formulas for "a" are also more or less unsatisfactory. Thus 

 in the formula a --= 6.28V C 2 P C , the coefficient is not the same 

 for all substances. In the formula a --= 2jb c 2 P c a knowledge 



