8.1.2 Definition of the Atomic Mass Scale and Average Masses

The of the $^{\textrm{12}}$C atom is defined to be exactly 12 amu. This means there are an infinite number of significant figures in the mass of carbon-12. The mass of C is 12.011 amu. What? Is it 12.(infinite 0's) amu or is it 12.011 amu?

• The atomic mass scale is defined by the mass of the $^{\textrm{12}}$C atom. Note that this is a specific isotope of carbon. All other atomic masses are relative to the mass of this atom. In addition, the mole is a number unit defined from the atomic mass scale as the number of particles in exactly 12 g of carbon-12. The molar mass of carbon-12 is defined to be exactly 12 g/mol.
• What does the symbol C represent? Recall that there are three 'common' isotopes of carbon: $^{\textrm{12}}$C, $^{\textrm{13}}$C and $^{\textrm{14}}$C. The symbol C represent 'natural carbon,' which means a sample of carbon that contains all three isotopes distributed in their natural relative abundances.
  • The molar mass of natural carbon is the mass of one mole of natural carbon. Taken relative to one mole of carbon-12, the molar mass of natural carbon is experimentally found to be 12.011 g/mol. Further, this mass is the average mass as calculated from
    
    $$Average\: Mass=\sum_{i}\left(Probability\: Isotope_{i}\right)\left(Mass\: Isotope_{i}\right)$$
    
    
    Using 98.9% for the natural abundance (probability) of carbon-12 and 1.1% for the probability of carbon-13, the average carbon mass is calculated to be 12.011 amu.
  • This applies to other elements as well.

Exercise: Consult a CRC Handbook of Chemistry and Physics or a General Chemistry Text for the mass of carbon-13 and confirm the calculation of average mass of carbon (Hint: the mass of carbon-13 is not exactly 13 amu).