6.1 Masses of Atoms and Molecules
Learning Objectives
 Express the masses of atoms and molecules.
Because matter is defined as anything that has mass and takes up space, it should not be surprising to learn that atoms and molecules have mass.
Individual atoms and molecules, however, are very small, and the masses of individual atoms and molecules are also very small. For macroscopic objects, we use units such as grams and kilograms to state their masses, but these units are much too big to comfortably describe the masses of individual atoms and molecules. Another scale is needed.
The atomic mass unit (u; some texts use amu, but this older style is no longer accepted) is defined as onetwelfth of the mass of a carbon12 atom, an isotope of carbon that has six protons and six neutrons in its nucleus. By this scale, the mass of a proton is 1.00728 u, the mass of a neutron is 1.00866 u, and the mass of an electron is 0.000549 u. There will not be much error if you estimate the mass of an atom by simply counting the total number of protons and neutrons in the nucleus (i.e., identify its mass number) and ignore the electrons. Thus, the mass of carbon12 is about 12 u, the mass of oxygen16 is about 16 u, and the mass of uranium238 is about 238 u. More exact masses are found in scientific references—for example, the exact mass of uranium238 is 238.050788 u, so you can see that we are not far off by using the wholenumber value as the mass of the atom.
What is the mass of an element? This is somewhat more complicated because most elements exist as a mixture of isotopes, each of which has its own mass. Thus, although it is easy to speak of the mass of an atom, when talking about the mass of an element, we must take the isotopic mixture into account.
The atomic massof an element is a weighted average of the masses of the isotopes that compose an element. What do we mean by a weighted average? Well, consider an element that consists of two isotopes, 50.% with mass 10. u and 50.% with mass 11 u. A weighted average is found by multiplying each mass by its fractional occurrence (in decimal form) and then adding all the products. The sum is the weighted average and serves as the formal atomic mass of the element. In this example, we have the following:
[latex]\begin{array}{rrrl} &0.50\times 10.\text{ u}&=&\phantom{1}5.0\text{ u} \\ +&0.50\times 11\text{ u}&=&\phantom{1}5.5\text{ u} \\ \hline &\text{sum}&=&10.5\text{ u}=\text{the atomic mass of our element} \end{array}[/latex]
Note that no atom in our hypothetical element has a mass of 10.5 u; rather, that is the average mass of the atoms, weighted by their percent occurrence.
This example is similar to a real element. Boron exists as about 20.% boron10 (five protons and five neutrons in the nuclei) and about 80.% boron11 (five protons and six neutrons in the nuclei). The atomic mass of boron is calculated similarly to what we did for our hypothetical example, but the percentages are different:
[latex]\begin{array}{rrrl} &0.20\times 10.\text{ u}&=&\phantom{1}2.0\text{ u} \\ +&0.80\times 11\text{ u}&=&\phantom{1}8.8\text{ u} \\ \hline &\text{sum}&=&10.8\text{ u}=\text{the atomic mass of boron} \end{array}[/latex]
Thus, we use 10.8 u for the atomic mass of boron.
Virtually all elements exist as mixtures of isotopes, so atomic masses may vary significantly from whole numbers. Table 6.1 “Selected Atomic Masses of Some Elements” lists the atomic masses of some elements. The atomic masses in Table 6.1 are listed to three decimal places where possible, but in most cases, only one or two decimal places are needed. Note that many of the atomic masses, especially the larger ones, are not very close to whole numbers. This is, in part, the effect of an increasing number of isotopes as the atoms increase in size. (The record number is 10 isotopes for tin.)
Element Name  Atomic Mass (u) 

Aluminum  26.981 
Argon  39.948 
Arsenic  74.922 
Barium  137.327 
Beryllium  9.012 
Bismuth  208.980 
Boron  10.811 
Bromine  79.904 
Calcium  40.078 
Carbon  12.011 
Chlorine  35.453 
Cobalt  58.933 
Copper  63.546 
Fluorine  18.998 
Gallium  69.723 
Germanium  72.64 
Gold  196.967 
Helium  4.003 
Hydrogen  1.008 
Iodine  126.904 
Iridium  192.217 
Iron  55.845 
Krypton  83.798 
Lead  207.2 
Lithium  6.941 
Magnesium  24.305 
Manganese  54.938 
Mercury  200.59 
Molybdenum  95.94 
Neon  20.180 
Nickel  58.693 
Nitrogen  14.007 
Oxygen  15.999 
Palladium  106.42 
Phosphorus  30.974 
Platinum  195.084 
Potassium  39.098 
Radium  n/a 
Radon  n/a 
Rubidium  85.468 
Scandium  44.956 
Selenium  78.96 
Silicon  28.086 
Silver  107.868 
Sodium  22.990 
Strontium  87.62 
Sulfur  32.065 
Tantalum  180.948 
Tin  118.710 
Titanium  47.867 
Tungsten  183.84 
Uranium  238.029 
Xenon  131.293 
Zinc  65.409 
Zirconium  91.224 
Now that we understand that atoms have mass, it is easy to extend the concept to the mass of molecules. The molecular mass is the sum of the masses of the atoms in a molecule. This may seem like a trivial extension of the concept, but it is important to count the number of each type of atom in the molecular formula. Also, although each atom in a molecule is a particular isotope, we use the weighted average, or atomic mass, for each atom in the molecule.
For example, if we were to determine the molecular mass of dinitrogen trioxide, N_{2}O_{3}, we would need to add the atomic mass of nitrogen two times with the atomic mass of oxygen three times:
[latex]\begin{array}{rrrrrl} &2\text{ N masses}&=&2\times 14.007\text{ u}&=&28.014\text{ u} \\ +&3\text{ O masses}&=&3\times 15.999\text{ u}&=&47.997\text{ u} \\ \hline &&&\text{total}&=&76.011\text{ u}=\text{the molecular mass of N}_2\text{O}_3 \end{array}[/latex]
We would not be far off if we limited our numbers to one or even two decimal places.
Example 6.1
Problems
What is the molecular mass of each substance?
 NBr_{3}
 C_{2}H_{6}
Solutions
 Add one atomic mass of nitrogen and three atomic masses of bromine:
[latex]\begin{array}{rlrrrrrl} &1\ce{N}\text{ mass }&=&1\times 14.007\text{ u}&=&14.007\text{ u}&& \\ +&3\ce{Br}\text{ masses}&=&3\times \phantom{1}79.904\text{ u}&=&239.712\text{ u}&& \\ \hline &&&\text{total}&=&253.719\text{ u}&=&\text{the molecular mass of }\ce{NBr3} \end{array}[/latex]
 Add two atomic masses of carbon and six atomic masses of hydrogen:
[latex]\begin{array}{rlrrrrrl} &2\ce{C}\text{ masses}&=&2\times 12.011\text{ u}&=&24.022\text{ u}&& \\ +&6\ce{H}\text{ masses}&=&6\times \phantom{1}1.008\text{ u}&=&6.048\text{ u}&& \\ \hline &&&\text{total}&=&30.070\text{ u}&=&\text{the molecular mass of }\ce{C2H6} \end{array}[/latex]
The compound C_{2}H_{6} also has a common name—ethane.
Test Yourself
What is the molecular mass of each substance?
 SO_{2}
 PF_{3}
Answers
 64.063 u
 87.968 u
Chemistry Is Everywhere: Sulfur Hexafluoride
On March 20, 1995, the Japanese terrorist group Aum Shinrikyo (Sanskrit for “Supreme Truth”) released some sarin gas in the Tokyo subway system; twelve people were killed, and thousands were injured. Sarin (molecular formula C_{4}H_{10}FPO_{2}) is a nerve toxin that was first synthesized in 1938. It is regarded as one of the most deadly toxins known, estimated to be about 500 times more potent than cyanide. Scientists and engineers who study the spread of chemical weapons such as sarin would like to have a less dangerous chemical, ideally one that is nontoxic, so they are not at risk themselves.
Sulfur hexafluoride is used as a model compound for sarin. SF_{6} has a similar molecular mass (about 146 u) as sarin (about 140 u), so it has similar physical properties in the vapor phase. Sulfur hexafluoride is also very easy to accurately detect, even at low levels, and it is not a normal part of the atmosphere, so there is little potential for contamination from natural sources. Consequently, SF_{6} is also used as an aerial tracer for ventilation systems in buildings. It is nontoxic and very chemically inert, so workers do not have to take special precautions other than watching for asphyxiation.
Sulfur hexafluoride also has another interesting use: a spark suppressant in highvoltage electrical equipment. Highpressure SF_{6} gas is used in place of older oils that may have contaminants that are environmentally unfriendly.
Key Takeaways
 The mass of a molecule is the sum of the masses of all the elements that make it up.
Exercises
Questions
 Define atomic mass unit. What is its abbreviation?
 Define atomic mass. What is its unit?
 Estimate the mass, in whole numbers, of each isotope.
 hydrogen1
 hydrogen3
 iron56
 Estimate the mass, in whole numbers, of each isotope.
 phosphorus31
 carbon14
 americium241
 Determine the atomic mass of each element, given the isotopic composition.
 lithium, which is 92.4% lithium7 (mass 7.016 u) and 7.60% lithium6 (mass 6.015 u)
 oxygen, which is 99.76% oxygen16 (mass 15.995 u), 0.038% oxygen17 (mass 16.999 u), and 0.205% oxygen18 (mass 17.999 u)
 Determine the atomic mass of each element, given the isotopic composition.
 neon, which is 90.48% neon20 (mass 19.992 u), 0.27% neon21 (mass 20.994 u), and 9.25% neon22 (mass 21.991 u)
 uranium, which is 99.27% uranium238 (mass 238.051 u) and 0.720% uranium235 (mass 235.044 u)
 How far off would your answer be from Exercise 5a if you used wholenumber masses for individual isotopes of lithium?
 How far off would your answer be from Exercise 6b if you used wholenumber masses for individual isotopes of uranium?
 Find the atomic or molecular mass of oxygen in each of these forms:
 An oxygen atom
 Oxygen in its elemental form
 Find the atomic or molecular mass of bromine in each of these forms:
 A bromine atom
 Bromine in its elemental form
 Determine the mass of each substance.
 F_{2}
 CO
 CO_{2}
 Determine the mass of each substance.
 Kr
 KrF_{4}
 PF_{5}
 Determine the mass of each substance.
 Na
 B_{2}O_{3}
 S_{2}Cl_{2}
 Determine the mass of each substance.
 IBr_{3}
 N_{2}O_{5}
 CCl_{4}
 Determine the mass of each substance.
 GeO_{2}
 IF_{3}
 XeF_{6}
 Determine the mass of each substance.
 NO
 N_{2}O_{4}
 Ca
Answers
 The atomic mass unit is defined as onetwelfth of the mass of a carbon12 atom. Its abbreviation is u.

 1
 3
 56

 6.940 u
 16.000 u
 We would get 6.924 u.

 15.999 u
 31.998 u

 37.996 u
 28.010 u
 44.009 u

 22.990 u
 69.619 u
 135.036 u

 104.64 u
 183.898 u
 245.281 u
Key Takeaways
 The atomic mass unit (u) is a unit that describes the masses of individual atoms and molecules.
 The atomic mass is the weighted average of the masses of all isotopes of an element.
Exercises
Questions
 Define atomic mass unit. What is its abbreviation?
 Define atomic mass. What is its unit?
 Estimate the mass, in whole numbers, of each isotope.
 hydrogen1
 hydrogen3
 iron56
 Estimate the mass, in whole numbers, of each isotope.
 phosphorus31
 carbon14
 americium241
 Determine the atomic mass of each element, given the isotopic composition.
 lithium, which is 92.4% lithium7 (mass 7.016 u) and 7.60% lithium6 (mass 6.015 u)
 oxygen, which is 99.76% oxygen16 (mass 15.995 u), 0.038% oxygen17 (mass 16.999 u), and 0.205% oxygen18 (mass 17.999 u)
 Determine the atomic mass of each element, given the isotopic composition.
 neon, which is 90.48% neon20 (mass 19.992 u), 0.27% neon21 (mass 20.994 u), and 9.25% neon22 (mass 21.991 u)
 uranium, which is 99.27% uranium238 (mass 238.051 u) and 0.720% uranium235 (mass 235.044 u)
 How far off would your answer be from Exercise 5a if you used wholenumber masses for individual isotopes of lithium?
 How far off would your answer be from Exercise 6b if you used wholenumber masses for individual isotopes of uranium?
Answers
1. The atomic mass unit is defined as onetwelfth of the mass of a carbon12 atom. Its abbreviation is u.
3 a. 1
3 b.3
3 c. 56
5 a. 6.940 u
5 b. 16.000 u
7. We would get 6.924 u.