Atomic mass units(old and new)

[Visceral]

Homework Statement

Prior to 1961, the physical standard for atomic masses was 1/16 the mass of the oxygen atom. The new standard is 1/12 the mass of the carbon atom. Determine the conversion factor needed to convert from old to new atomic mass units. How did this change affect the value of the avagadro constant?

Homework Equations

The Attempt at a Solution

I must really be derping here. 1/16th the mass of an oxygen atom is the same as 1/12 the mass of the carbon atom. I haven't taken chemistry in awhile so maybe I am missing something really basic here.

 

[DaveC426913]

I must really be derping here. 1/16th the mass of an oxygen atom is the same as 1/12 the mass of the carbon atom.

Really? You know that mass does not vary exactly with atomic number, yes?

 

[Visceral]

You mean that the atomic mass is not exactly equal to the atomic number? Isn't the atomic mass really an average over all the different isotopes of a certain element?

 

[DaveC426913]

Well, if I simply check Wiki or some more reliable source, and read off the mass of carbon and oxygen, I don't see integer values for either.

Whether that's an average or a specific value of a specific isotope seems to be largely beside the point.

 

[Ygggdrasil]

You mean that the atomic mass is not exactly equal to the atomic number? Isn't the atomic mass really an average over all the different isotopes of a certain element?

The atomic mass of a specific isotope is approximately equal to the sum of the number of protons and neutrons in the nucleus of that atom. However, the atomic mass is actually less than the sum of the masses of the protons and neutrons that make up that atom. How can that be? Where did the extra mass go?

The "missing mass" (formally referred to as the mass deficit) represents the amount energy that holds the nucleus together (formally called the nuclear binding energy). Remember from Einstein that mass and energy are equivalent; if you know the amount of mass deficit for an atom, you can calculate the nuclear binding energy from E = mc².

The phenomenon of mass deficit helps explain why the mass of an oxygen-16 atom is not exactly 16.

Note: when looking up the masses carbon-12 and oxygen-16 to solve this problem, you'll have to remember that the value reported on the periodic table is the atomic weight -- an average over all the different isotopes of the element. You'll need to look for another source to get the masses of the specific isotopes you're interested in.

 

[Visceral]

Thank you all for the help. I looked up the atomic weight of the individual isotopes and found that O-16 is 15.994914.6 g/mol and C-12 is of course 12 g/mol. I calculated using avagadros constant that 1/16th the mass of an O-16 atom is 1.03272*10^-24 g/atom, and the mass of a C-12 atom is 1.66058x10^-24 g/atom. To convert from "old" to "new" amu's we just multiply the first value times 1.6 to get the second value. So 1.6 is the conversion factor(I think).

Now, the second part of the problem asks how this change affected the value of the avagadro constant. Still a little confused, because I had to use this value to get the masses of the atoms in the first place. The constant is defined to be the number of atoms in 12 g of C-12. So, to be consistent, I guess the "old" value of the avagadro constant would have to have been the number of atoms in 16 g of O-16. If I use the formula m(g)= A/N_a, where m(g) is mass per atom, A is the atomic weight, and N_a is avagadros constant, then I could solve for N_a by doing 16/m(g) and I get 1.549*10^25 atoms(noting that the atomic weight of O-16 is 16 by the "old" standards). This makes sense I suppose...but I am still not sure.

 

[Ygggdrasil]

I calculated using avagadros constant that 1/16th the mass of an O-16 atom is 1.03272*10^-24 g/atom

This calculation is wrong. The conversion factor you calculate should be very close to one.

Now, the second part of the problem asks how this change affected the value of the avagadro constant. Still a little confused, because I had to use this value to get the masses of the atoms in the first place. The constant is defined to be the number of atoms in 12 g of C-12. So, to be consistent, I guess the "old" value of the avagadro constant would have to have been the number of atoms in 16 g of O-16. If I use the formula m(g)= A/N_a, where m(g) is mass per atom, A is the atomic weight, and N_a is avagadros constant, then I could solve for N_a by doing 16/m(g) and I get 1.549*10^25 atoms(noting that the atomic weight of O-16 is 16 by the "old" standards). This makes sense I suppose...but I am still not sure.

I always think of Avogadro's constant as the conversion factor between amu and grams. Given the definition of amu, these definitions are equivalent.

 

[Visceral]

This calculation is wrong. The conversion factor you calculate should be very close to one.



I always think of Avogadro's constant as the conversion factor between amu and grams. Given the definition of amu, these definitions are equivalent.

Oops! Yes that is definitely wrong. I recalculated and found the mass of a O-16 atom to be 1.66005*10^-24 g, and this would give a conversion factor of 1.00032. Hopefully this is correct.

Also, were you implying that my method for attaining the last part of the problem was wrong? I recalculated using the correct mass of an O-16 atom and found the (old) avagadro constant to be 9.638*10^24

 

[Ygggdrasil]

Also, were you implying that my method for attaining the last part of the problem was wrong? I recalculated using the correct mass of an O-16 atom and found the (old) avagadro constant to be 9.638*10^24

If you're calculating the number of oxygen atoms in 16g of oxygen-16, this number is incorrect. Remember that the 1.66005*10^-24 g you calculated above is 1/16th the mass of an oxygen-16 atom. Again, the value you get here should be very close to the ¹²C-based value of Avogadro's number.

I will also mention that performing calculations with the proper numbers of significant figures here is very important. Be sure to use a very precise value for Avogadro's constant for all of your calculations (the number you use should have at least five or six significant figures).

 

[Visceral]

If you're calculating the number of oxygen atoms in 16g of oxygen-16, this number is incorrect. Remember that the 1.66005*10^-24 g you calculated above is 1/16th the mass of an oxygen-16 atom. Again, the value you get here should be very close to the ¹²C-based value of Avogadro's number.

I will also mention that performing calculations with the proper numbers of significant figures here is very important. Be sure to use a very precise value for Avogadro's constant for all of your calculations (the number you use should have at least five or six significant figures).

Thank you for your advice. I calculated that 1/16th the mass of an oxygen-16 atom as 1.66001*10^-24 g/atom, and 1/12th the mass of a carbon-12 atom to be 1.66054*10^-24 g/atom. So to get from the the first value to the second(old amu to new), we multiply the first value by 1.00032 and get the answer. This conversion factor is correct right?

Since I calculated an oxygen-16 atom to be 2.65602*10^-23 g, and noting that the atomic weight would be 16(for old amu's), then I can calculate the Avogadro constant by dividing the "old" amu value for oxygen-16(which is simply 16) and diving that by the mass of 1 oxygen-16 atom. This yields a value of 6.02406*10^23, which is very close to the current Avogadro constant of 6.02214*10^23. In fact, the ratio between old and new gives the same conversion factor of 1.00032, so this must be right.

 

[Ygggdrasil]

Yes, those numbers look correct to me. Good work.

 

[Visceral]

thank you once again for your assistance.