# Conversion factor for chemical to physical scale of atomic masses

Before the 1960s chemists and physicists used to have different atomic mass tables. The main difference was that the physicists assigned the $$^{16}$$O as the O=16 from mass spectrometry. Chemists on the other hand were using the ordinary oxygen which is a mixture of $$^{16}$$O, $$^{17}$$O and $$^{18}$$O as O=16. Of course, this confused everyone before carbon-12 was suggested as a compromise as both parties were not willing to budge. The % abundance of $$^{16}$$O is 99.76, $$^{17}$$O is 0.04, $$^{18}$$O is 0.2.

People were able to develop a conversion factor between a chemist's atomic mass and a physicist's atomic mass tables. A book by Guggenheim "Physicochemical Calculations" shows the example how the conversion factor was obtained. He doesn't explain anything clearly.

Could anyone shed some light, how the author is calculating this factor? I assume by $$\frac{O}{^{16}O}$$ the author mean how heavy is ordinary oxygen with respect to true $$^{16}$$O . I don't know where 1 is coming from and why there is a 2 besides O-18 isotope.

$$\frac{\ce{O}}{\ce{^16O}}=\frac{(.9976\times\ce{^16O})+(.0004\times\ce{^17O})+(.002\times\ce{^18O})}{\ce{^16O}}$$ $$=\frac{(.9976\times\ce{^16O})+(.0004\times(\ce{^16O}+1))+(.002\times(\ce{^16O}+2))}{\ce{^16O}}$$ $$=\frac{(\ce{^16O})+(.0004\times1)+(.002\times2)}{\ce{^16O}}$$
Essentially, it comes from collecting factors of $$\ce{^16O}$$.
• Thanks for solving this mystery. One part which is still troublesome is that O-16 is $exactly$ 16 by definition (let us assume we are in 1960s). However, O-17 is not 17.0000000 and O-18 is not 18.000000. The conversion factor value is correct, but this assumption that O-17 = 16+1, is not correct even by 1960s, because mass spectrometers could tell us the exact mass of O-17, if we set O-16 as exactly 16. So why do you think Guggenheim and the rest calculated would have calculated it that way. Am I missing something? Apr 12 '20 at 0:43
• I guess the mix between the low abundance and how close they are ($\ce{^17O}=16.99913$ and $\ce{^18O}=17.99913$ from Wikipedia) made the difference small enough for whatever they were applying it to just call them 17 and 18 Apr 12 '20 at 1:01