Atomic Mass

Atomic mass is based on a relative scale and the mass of ¹²C (carbon twelve) is defined as 12 amu.

Why do we specify ¹²C? We do not simply state the the mass of a C atom is 12 amu because elements exist as a variety of isotopes.

Carbon exists as two major isotopes, ¹²C, and ¹³C (¹⁴C exists and has a half life of 5730 y, ¹⁰C and ¹¹C also exist; their half lives are 19.45 min and 20.3 days respectively). Each carbon atom has the same number of protons and electrons, 6. ¹²C has 6 neutrons, ¹³C has 7 neutrons, and ¹⁴C has 8 neutrons and so on. Since there are a variety of carbon isotopes we must specify which C atom defines the scale.

All the masses of the elements are determined relative to ¹²C.

By the way, the mass of an element is not equal to the sum of the masses of the subatomic particles of which the element is made!

Average Atomic Mass

Since many elements have a number of isotopes, and since chemists rarely work with one atom at a time, chemists use average atomic mass.

On the periodic table the mass of carbon is reported as 12.01 amu. This is the average atomic mass of carbon. No single carbon atom has a mass of 12.01 amu, but in a handful of C atoms the average mass of the carbon atoms is 12.01 amu.

Why 12.01 amu?

If a sample of carbon was placed in a mass spectrometer the spectrometer would detect two different C atoms, ¹²C and ¹³C.

The natural abundances of ¹⁴C, ¹⁰C and ¹¹C are so low that most mass spectrometers cannot detect the effect these isotopes have on the average mass. ¹⁴C dating is accomplished by measuring the radioactivity of a sample, not by actually counting the number of ¹⁴C atoms.

The average mass of a carbon is calculated from the information the mass spectrometer collects.

The mass spectrometer reports that there are two isotopes of carbon,

98.99% of the sample has a mass of 12 amu (not a surprise since this is the atom on which the scale is based).

1.11% of the sample has a mass of 13.003355 amu (this isotope is 1.0836129 times as massive as ¹²C)

The average mass is simply a weighted average.

ave. mass = 12.01 amu

(Yes, the number 12.01 has the right number of significant figures, even though 1.11% only has 3 significant figures.)

If we know the natural abundance (the natural abundance of an isotope of an element is the percent of that isotope as it occurs in a sample on earth) of all the isotopes and the mass of all the isotopes we can find the average atomic mass. The average atomic mass is simply a weighted average of the masses of all the isotopes.

(Yes, the sig figs are correct.)

Another kind of question could be asked...

Copper has two isotopes ⁶³Cu and ⁶⁵Cu. The atomic mass of copper is 63.54. The atomic masses of ⁶³Cu and ⁶⁵Cu are 62.9296 and 64.9278 amu respectively; what is the natural abundance of each isotope?

substituting gives

(eq. A)

One equation and two unknowns...is there another equation? If there is another equation we would have two equations and two unknowns, and a system of two equations and two unknowns is solvable.

Since there are only two major isotopes of Cu we know that

or

(eq. B)

Use eq. B to substitute for %⁶³Cu in eq. A.

To the correct number of significant figures

Of course, a question like the one above could be turned around another way.

Gallium, atomic mass 69.72 amu, has two major isotopes, ⁶⁹Ga, atomic mass 68.9257 amu, and ⁷¹Ga. If the natural abundance of each isotope is 60.00 and 40.00 % respectively what is the mass (in amu) of ⁷¹Ga.

The mole

What is the relative mass of 1 C atom as compared to 1 H atom?

What is the relative mass of 100 C atoms as compared to 100 H atoms?

What is the relative mass of 1 W atom as compared to 1 H atom?

What is the relative mass of 100 W atoms as compared to 100 H atoms?

The point here? As long as the number of atoms remains the same the relative mass does not change.

Atoms are small, and it is possible to place 1.0079 g of H on a balance (possible but not easy in the case of hydrogen).

It is also possible to place 183.9 g W, or 12.01 g of C on a balance.

Now, I state with absolute certainty that I have placed the same number of atoms on each balance! How do I know? I know because the relative masses of the samples on the balance, are the same as the relative masses of the individual atoms.

The number of atoms I placed on the balance is know as a mole.

For many years the number of atoms in a mole remained unknown; however, now it is know that a mole of atoms contains 6.02214 x 10²³ atoms.

So, the periodic table provides us with a great deal of information.

The periodic table lists

 

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