# Why is the Molar mass of CO2 different than the weight of the sum of its particles?

The Molar mass of CO2 is stated to be 44.009 grams per mol

But in a calculation of the weight of each atom's particles((Electrons,Protons,Neutrons) times Avogadro's constant I get 44.36 grams per mol

The same happens with every other molecule.

What is the reason for this difference in values?

• First If this is a Chemical MW then you must use the natural abundance If you used C-12(O-16)2 ..... Each nucleus has its distinct mass. it is the mass of the protons + neutrons less the binding energy released by the strong nuclear force. This means that the mass of the nucleons differs for every nuclide. If you actually did the math and arithmetic correctly you have discovered What holds the nucleus together and why there are different isotopes and elements. Commented Jul 15 at 7:14
• You need not have done it for all the molecules, just the atoms would have sufficed because the molecular bonding energy mass change is too small to be measured with current instruments. Yes, the mass of a molecule is less than the mass of its component atoms. This really is important in studying nuclear chemistry and physics so think harder and deeper about it. Commented Jul 15 at 7:21
• By starting with isolated proton and neutrons you will miss the binding energy of the nuclei, and energy is mass. Commented Jul 15 at 12:34
• @jimchmst I didn't ask the question... Still not sure why you find this question so outrageous or offensive, but you should probably take control of your temper before you make any more mistakes which make your attention to detail appear questionable. Commented Jul 16 at 10:42
• @isolatedmatrix I already flagged his comment as I felt that kind of attitude could discourage users from asking questions And asking questions is what this website is all about. Commented Jul 16 at 12:00

## 1 Answer

This is a really interesting question actually! I'm new to answering questions on this site but I'll explain as best I can.

As others have said, the difference in this particular calculation comes down to nuclear binding energy. As jimchmst pointed out, you can just look at the weights of the atoms to see this difference.

If you add up the mass of 6 protons and 6 neutrons, and then divide by the conversion factor from kg to amu, you get something around 12.096, but the actual measured mass of carbon-12 is exactly 12 amu.

This difference turns out to hold true for all nuclei; their mass is a little less than the sum of their parts. The reason for this is conservation of energy and the mass-energy equivalency. Nuclei are more stable together than apart (generally) - that is why atoms exist all over the place! This means there must be an energy difference between the protons and neutrons apart and the protons and neutrons together. But that energy that had to have gone somewhere - it was carried away as a high energy photon when the nucleus was made. Since mass and energy are equivalent, this means that some mass was also lost in the formation of the nucleus - the mass defect.

If you look up the masses of carbon-12 and oxygen-16, and add them up stoichiometrically for CO2, you get about 43.99 - very close to the true molar mass of CO2! The remaining difference comes from isotopic abundance - that is, not all carbons have 6 neutrons, and not all oxygens have 8.

For CO2, it works out that the isotopic abundance makes little difference, but for some other molecules this is not always the case. Take for example, HBr. Bromine has two main isotopes which are roughly equally abundant. Attempting to calculate the molar mass of HBr using either one of the isotopes' mass results in a molar mass off by almost 1 whole amu! The true molar mass is a weighted average of all the possible masses of each combination of isotopes. When calculating the molar mass of a compound, we generally start from the masses given on the periodic table because these already account for both mass defect and isotopic abundance.

Hope that helps!

• If you like the question, you can vote for it (maybe you did, voting is anonymous).
– Karsten
Commented Jul 17 at 22:55
• I did! I thought it was a good question :)
– cp95
Commented Jul 18 at 21:02
• Yes it did help, thank you, I know we are supposed to refrain from "Thank you" comments, but still :) Commented Jul 20 at 11:00