# Where does the molar mass difference between N₂ and CO come from?

The molar masses of $\ce{N2}$ is 28.0134 g/mol, for $\ce{CO}$ it's 28.0101 g/mol (WolframAlpha computation).

Of course, they do have the same mass in atomic units (28). My question is, where does this small discrepancy come from? Different binding energies in the respective nuclei? I know that oxygen is a "double-magic" nucleus from an atomic physics POV, that is, it's binding energy per nucleon is higher than what would be expected. But since normally, you equate mass with energy, shouldn't $\ce{CO}$ be heavier then?

The differences in molecular mass stem from two sources:

Nuclear binding energy

The definition of the atomic mass unit and Avogadro's number (and thus the g/mol), is the mass of one atom of the carbon-12 isotope $\ce{^{12}_6 C}$. 1 amu = $\frac{1}{12}$ the mass of one atom of $\ce{^{12}_6 C}$ and the g/mol unit is based on the definition of Avogadro's Number, which is the number of $\ce{^{12}_6 C}$ atoms in 12 grams of $\ce{^{12}_6 C}$.

Because of the differences in binding energies in the various nuclei, the monoisotopic mass of individual isotopes are not integers. For example, the mass of $\ce{^{16}_8 O}$ is 15.99491463 amu (and not 16). The monoisotopic masses of the most common isotopes of oxygen, nitrogen, and carbon is shown below:

           mass number   % absundance    isotope mass
Carbon     12            98.930          12 (defined)
Nitrogen   14            99.632          14.003074
Oxygen     16            99.757          15.99491463


Isotopes

Generally, molecular masses (unless otherwise specified) are average molecular masses composed of average molecular masses of the elements based on their isotopes. For example, even though the most common isotope of carbon has a mass defined as 12 amu, there is another naturally occurring isotope $\ce{^{13}_6 C}$ with 1.07% natural abundance, leading to carbon having a non-integer average atomic mass of 12.01 (to 4 significant figures). There are two isotopes of nitrogen, and three isotopes of oxygen.

            Average atomic mass
Carbon      12.011
Nitrogen    14.007
Oxygen      15.999


Thus, $\ce{CO}$ has a molecular mass of $12.011 + 15.999 = 28.010$ and $\ce{N2}$ has a molecular mass of $14.007+14.007=28.014$. Even their monoisotopic masses are different:

                    average molecular mass       monoisotopic mass
dinitrogen          28.014                       28.006148
carbon monoxide     28.010                       27.99491463

• Just a little nitpick: You are using the abbreviation for atomic mass unit, which was originally defined through $$\mathrm{amu}=\frac{1}{16}m(\ce{{}^{16}_8O}).$$ It has been replaced with the unified atomic mass unit, which is based on the definition you used, hence $$\mathrm{u}=\frac{1}{12}m(\ce{{}^{12}_6C}).$$ While this usually does not make a big difference, the latter should be used exclusively. Se also wikipedia for a short historical summary. – Martin - マーチン Dec 5 '14 at 2:20
• So you are arguing that over all the $\mathrm{CO}$ and $\mathrm{N}_2$ molecules there are in a mol, the mass difference comes from the isotope mixing? What would happen if I looked at two specifically picked $\mathrm{CO}$ and $\mathrm{N}_2$ molecules where I know that I have nitrogen-14 and carbon-12 with oxygen-16? Which one would be heavier then? – John W. Dec 5 '14 at 23:14
• @PMPJohn - I calculated the monoisotopic mass in my post already. Due to the nuclear binding energy, $\ce{N2}$ would still be heavier (and in fact the mass difference for the monoistopic version [0.011] is larger than the average atomic mass version [0.004]). – Ben Norris Dec 6 '14 at 1:43

There are three factors to consider:

1. The natural abundance isotope composition of each element.

Carbon isn't all carbon 12, there is 1.1% Carbon 13.

Oxygen isn't all oxygen 16, etc.

1. The neutron-proton ratio of each isotope. The mass of a neutron is greater than the mass of a proton plus electron. Isotopes having a higher neutron-proton ratio relative to carbon 12 (which is 1:1) will be relatively heavier per nucleon.

2. The binding energy of each isotope.

• And binding energy is the winner! I would also add that N-14 does not have a mass of 14.000000 amu (well, because of the binding energy of the nucleus being different per nucleon than for C-12). So N-14 has an official mass of 14003074.00443 micro-amu per the 2012 atomic mass evaluation (AME2012). O-16 is 15994914.61957 micro-amu (so more tightly bound than C-12). C-12, of course, has a mass defined as 12000000.0 micro-amu. You can look these up through the National Nuclear Data Center based at nndc.bnl.gov (Brookhaven national Laboratory). – Jon Custer Dec 4 '14 at 20:54