,
(6)
where 6 refers to the six isotopic isomers for this isotopologue
(12CHDHD, 12CHHDD,12CDHDH, etc.). In this example, the stochastic value
for x12CH2D2 is
1.16547×10-7 and the stochastic value forx 12CH4 =x H4 x 12C is 0.9884432.
With a measured12CH2D2/12CH4ratio of 1.16000×10-7, we have:
\(CH_{2}D_{2}=10^{3}\left(\frac{\frac{(^{12}CH_{2}D_{2})}{(12\text{CH}_{4})_{\text{measured}}}}{\frac{(^{12}CH_{2}D_{2})}{12\text{CH}_{4})_{\text{stochastic}}}}-1\right)=-16.2\)‰ (7)
Now let us consider the possibility that in the same gas, the methane
molecules were in fact constructed from two pools of hydrogen with
distinct D/H ratios, with the average D/H being the measured bulk value
in our methane, i.e., δD = –100 ‰. If α is the fractionation
factor relating the D/H ratios for the two pools, then: