DETERMINATION OF ATOMIC WEIGHTS 521 



Let us consider how Guye modifies his equation in order to 

 deduce the molecular weights of readily liqucfiablc gases. In 

 common with van der Waals, van Laar and others, he sup- 

 poses that the original van der Waals' equation can be made 

 to represent accurately the behaviour of a gas if the values of 

 a and b are assumed to vary with temperature and pressure. 

 Therefore, he regards the values of a and b calculated from 

 critical data as being valid at the critical temperature and pro- 

 poses two empirical equations from which to determine a PiT and 

 b PjT , the values of a and b at p, T. These equations are : 



ap.x = a(^-) 5 , b p , T = b (1 + ~^)(i - f) (18) 



/3 being a constant common to all the gases. The values a and 

 b assumed by a and b at N. T. P. are therefore 



— • ds)'. b „ = b ( 1+ I^Z3)( I _3 Pc ) (I9) 



Using these values, Guye calculates the molecular weights from 

 the equation 



., 22*412 L z x 



M = 7 ^7 r-r (20) 



(i+a )(i-b ) v 



The empirical character of equations (18) is sufficient to 

 nullify the theoretical value of Guye's method. Moreover, the 

 demonstration that, at N.T. P., the relative volumes of different 

 gases that contain equal numbers of molecules are proportional 

 to expressions of the type 1/(1 + a)(i - b) is based upon the 

 assumption that b is independent of the pressure ; therefore 

 as soon as equation (18) for b P>T is accepted, the proof of formula 

 (15) becomes invalid. 



The expression for b is easily seen to be, at the best, of 

 limited application. In the cases of hydrogen, nitrogen and 

 carbon monoxide it gives negative values, an absurd result when 

 the theoretical meaning of b is considered. Moreover, according 

 to formula (18) b PiT approaches ± co as the pressure approaches 

 zero. 



As has been already mentioned, Guye only applies the 

 preceding calculations to the readily liquefiable gases. In order 

 to determine the numerical value of /3, he adopts carbon 

 dioxide as the standard gas and takes as the atomic weight of 

 carbon the value 12*002 deduced from gravimetric measurements 

 of the ratios C ; CO2 and CO : C0 2 . Hence M = 44/002 and 



