Sec. 8.2] INDIRECT METHODS FOR MEASURING DEUTERIUM 265 



fraction, but the molecular volume is). Other evidence shows the solutions 

 to be ideal in the very low (tap-water) deuterium oxide concentration 

 range, [35] quoted in [31]. At 25°C the equation [31] 



9.257A5 



Nd,o = 



1 - 0.033AS 



where iV D2 o = mole fraction of deuterium oxide and AS = d\\ — ■ 1 relative 

 to deuterium-free water, may be used to calculate the mole fraction of deu- 

 terium in a sample from the density of the sample. This equation in the 

 form 



Nv„o 



d = 1 + 



9.257 + 0.033,V D , o 



was used to calculate Table 30. 



The abundance of deuterium oxide in nature has been the object of exten- 

 sive research [10,22,36]. Long before the discovery of isotopes a variation of 

 8 parts in 10 7 was found in the densities of various samples of water that were 

 expected to be identical. The average ratio of D2 to H2 is about 1:6,500 

 [51,52]. The issue is confused by variations in the abundance of O 18 which 

 produces similar variations in density [29,38-43]. The accepted ratio for the 

 relative abundance of the oxygen isotopes in 1941 was 



O 16 :O 18 :O 17 ::(506 + 10) :1: (0.204 ± 0.008) [54] 



Commercial oxygen obtained from liquid air was found to have an atomic 

 weight 2.2 X 10~ 6 unit heavier than atmospheric oxygen. That obtained 

 by electrolysis is lighter, the fractionating factor being 1.008 [40]. The 

 atomic weight of atmospheric oxygen is 11.9 X 10 -6 unit greater than that 

 in water, and the average density for water made from air is 6.4 X 10 -6 gm 

 per ml heavier than ordinary water [41]. Lewis and Luten [18] show that 

 from determination of both the refractive index and the density of a water 

 sample the concentrations of both O 18 and deuterium may be found by solving 

 two simultaneous equations relating the effects. 



Tables of the density of water to seven decimal places at temperatures 

 from to 40°C by 0.1°C intervals are available, but Dorsey [37] questions 

 the accuracy of such tables because variations in deuterium oxide content 

 exceed the precision indicated. 



At room temperature the density of water decreases by about 0.03 per cent 

 per degree centigrade rise in temperature. Table 31 lists the densities d\ of 

 natural water and of deuterium oxide. The values up to 42°C in the column 

 for water were obtained by rounding off to six places the values from Dorsey 

 [37]. Comparison with the last two columns [30,44] shows that deuterium 

 oxide does not expand with temperature at quite the same rate as does water. 



