Question

# The mass spectrum of an organic compound shows the relative abundances of M to be 44.02%...

The mass spectrum of an organic compound shows the relative abundances of M to be 44.02% and M 1 to be 3.333%. Assuming the peaks are caused by 12C and 13C isotopes, determine the number of carbon atoms in the compound. Natural abundances: 12C is 98.93% and 13C is 1.07%

The relative abundance of M and M+1 peaks are 44.02% and 3.333%. We need to convert the relative abundance of M to 100% to proceed with the problem. This can be simply done as 100%/44.02% = 2.272, a simple multiplication of the relative abundance to scale it to 100%.

The relative abundance of M+1, scaled to 100 is (3.333% * 2.272) = 7.572%. To calculate the number of carbon atoms, we simply divide the relative abundance of M+1 peak by the natural abundance on 13C. This gives the number of carbon atoms as 7.572/1.07 = 7.07 ̴ 7.

To be on the safe side, we take extreme values and say that the number of carbon atoms is either 7 or 8.

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