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Calculating Atomic Mass

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Calculating Atomic Mass

<!-- @@image_id="C-IntCh-02-01-20-Rocks" --> Pile of rocks and boulders

Have you ever tried to move a boulder?

You have a pile of rocks to move and need to decide what equipment you want to rent to move them.  If the rocks are fairly small, you can get a shovel to pick them up.  Larger rocks could be moved by hand, but big boulders will need some sort of mechanical scoop.  The amount of each kind of rock will also determine how much time you will need to get the job done.  Knowing the relative amounts of large, medium, and small rocks can be very useful in deciding how to approach the job.

Most elements occur naturally as a mixture of two or more isotopes. Table below shows the natural isotopes of several elements, along with the percent natural abundance of each.

Atomic Masses and Percent Abundances of Some Natural Isotopes
Element

Isotope

(symbol)

Percent natural

abundance

Atomic

mass (amu)

Average

atomic mass (amu)

Hydrogen

^{1}_{1}\text{H}

^{2}_{1}\text{H}

^{3}_{1}\text{H}

99.985

0.015

negligible

1.0078

2.0141

3.0160

1.0079
Carbon

^{12}_{6}\text{C}

^{13}_{6}\text{C}

^{14}_{6}\text{C}

98.89

1.11

trace

12.000

13.003

14.003

12.011
Oxygen

^{16}_{8}\text{O}

^{17}_{8}\text{O}

^{18}_{8}\text{O}

99.759

0.037

0.204

15.995

16.995

17.999

15.999
Chlorine

^{35}_{17}\text{Cl}

^{37}_{17}\text{Cl}

75.77

24.23

34.969

36.966

35.453
Copper

^{63}_{29}\text{Cu}

^{65}_{29}\text{Cu}

69.17

30.83

62.930

64.928

63.546

For some elements, one particular isotope predominates greatly over the other isotopes. Naturally occurring hydrogen is nearly all hydrogen-1 and naturally occurring oxygen is nearly all oxygen-16. For many other elements, however, more than one isotope may exist in more substantial quantities. Chlorine (atomic number 17) is a yellowish-green toxic gas. About three quarters of all chlorine atoms have 18 neutrons, giving those atoms a mass number of 35. About one quarter of all chlorine atoms have 20 neutrons, giving those atoms a mass number of 37. Were you to simply calculate the arithmetic average of the precise atomic masses , you would get 36.

\frac{(34.969+36.966)}{2}=35.968 \ \text{amu}

Clearly the actual average atomic mass from the last column of the table is significantly lower. Why? We need to take into account the percent natural abundances of each isotope in order to calculate what is called the weighted average. The atomic mass of an element is the weighted average of the atomic masses of the naturally occurring isotopes of that element. The sample problem below demonstrates how to calculate the atomic mass of chlorine.

Sample Problem: Calculating Atomic Mass

Use the atomic masses of each of the two isotopes of chlorine along with their percent abundances to calculate the average atomic mass of chlorine.

Step 1: List the known and unknown quantities and plan the problem.

Known

  • chlorine-35: atomic mass = 34.969 amu and % abundance = 75.77%
  • chlorine-37: atomic mass = 36.966 amu and % abundance = 24.23%

Unknown

  • Average atomic mass of chlorine

Change each percent abundance into decimal form by dividing by 100. Multiply this value by the atomic mass of that isotope. Add together for each isotope to get the average atomic mass.

Step 2: Calculate

& \text{chlorine-35} && 0.7577 \times 34.969=26.50 \ \text{amu}\\& \text{chlorine-37} && 0.2423 \times 36.966=8.957 \ \text{amu}\\& \text{average atomic mass} && 26.50 + 8.957=35.45 \ \text{amu}

Note: Applying significant figure rules results in the 35.45 amu result without excessive rounding error. In one step:

(0.7577 \times 34.969)+(0.2423 \times 36.966)=35.45 \ \text{amu}

Step 3: Think about your result.

The calculated average atomic mass is closer to 35 than to 37 because a greater percentage of naturally occurring chlorine atoms have the mass number of 35. It agrees with the value from the Table above .

Watch these videos to learn more about these calculations:

http://www.kentchemistry.com/links/AtomicStructure/atomicmasscalc.htm

Summary

  • The atomic mass of an element is the weighted average of the atomic masses of the naturally occurring isotopes of that element.
  • Calculations of atomic mass use the percent abundance of each isotope.

Practice

Click on the link below to get some experience in atomic mass determinations:

http://www.collegeadjuncts.org/javascripts/AtomicMass.html  

Review 

Questions

  1. Define atomic mass.
  2. What information do you need to calculate atomic mass for an element?
  3. Calculate the atomic mass for carbon using the data provided in Table below .

mass number

exact weight

percent abundance

12

12.000000

98.90

13

13.003355

1.10

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