DETERMINATION OF ATOMIC WEIGHTS 505 



relationship would cease to be true. As a matter of fact, the 

 gramme-molecular volumes of gases, measured at the same 

 temperature and pressure, are only nearly very equal. It is 

 necessary to know the relative values of these magnitudes to 

 within at least 1 part in 10,000 if the results of density 

 measurements are to be utilised with advantage in the determina- 

 tion of molecular weights. 



The problem may be stated algebraically in the following 

 manner. Let the weight of a normal litre of a gas — i.e. the weight 

 of the gas which occupies a volume of one litre at o° C. and 

 under a pressure of 760 mm. of mercury at sea-level in lat. 45 — 

 be L grammes. If the gramme-molecular volume, at normal 

 temperature and pressure, of a perfect gas be R litres, then the 

 molecular weight M of the gas in question is not equal to RL 

 but is given by the equation 



M - TTx W 



where X is a small fraction to be determined. For each gas, 

 there is a definite value of X ; and it is necessary to determine 

 the value of (1 + X) with an accuracy of 1 in 10,000. Of the 

 various methods that have been proposed for the determination 

 of \, the three best known are (i) D. Berthelot's Limiting Density 

 Method, (ii) P. Guye's Reduction of Critical Constants Method and 

 (iii) A. Leduc's Molecular Volume Method. 



The Limiting Density Method 



Boyle's Law does not accurately express the behaviour of 

 any known gas at ordinary temperatures and under pressures 

 of one or two atmospheres. If v b denote the volume, under 

 the pressure p b , of a definite mass of a gas and v a its volume at 

 the same temperature as before and under another pressure p a , 

 we may write 



PbVb A Pb, . . . 



1 " i^ = P (Pb " Pa) (2) 



The coefficient A^ is a measure of the average error per 

 atmosphere, over the range p a to p b , that is incurred by 

 assuming the validity of Boyle's Law for the gas (it is under- 



