ASP - Isotopes and Average Atomic Mass (Lesson)
Isotopes of Elements
The image to the right is a representation atomic symbol from the periodic table. The element symbol is that of boron (atomic number 5). The decimal number below the symbol represents the average atomic mass of that element. The question then becomes: Why is it an average? What is it an average of? You may recall from your previous chemistry course that the atomic nucleus of each element is comprised of both protons and neutrons. The number of protons in the nucleus of an atom is what gives an element its identity, however the number of neutrons can vary. Because of this variance in the number of neutrons, most elements exist naturally as a mixture of different isotopes. Click HERE
Links to an external site. for a brief refresher on atomic structure if necessary.
Average Atomic Mass
Elements with multiple naturally occurring isotopes exist in different abundances. For example, Boron, shown above, exists as two naturally occurring isotopes; however, those isotopes have different natural abundancies. In other words, it is not a 50/50 ratio of each of the naturally occurring isotopes. Therefore, calculating the average atomic mass requires the calculation of what is referred to as a weighted average. One of the most common ways to experimentally determine these natural abundancies is through the use of mass spectrometry.
Mass Spectrometry
Mass spectrometry (MS) is a widely used technique used in chemistry, forensics, medicine, environmental science, and many other fields to analyze and help identify the substances in a sample of material. To determine natural abundances a sample of an element is vaporized and exposed to a high-energy electron beam that causes the sample’s atoms (or molecules) to become electrically charged, typically by losing one or more electrons. These cations then pass through an electric or magnetic field that deflects each cation’s path that depends on the mass and charge.
The degree to which an ion is deflected is interpreted by the instrument as different masses corresponding to different isotopes. When graphed, the height of each vertical feature or peak in a mass spectrum is proportional to the fraction of isotopes with the specified mass-to-charge ratio. And since the only source of mass difference is the number of neutrons, each peak represents an isotope of that element.
The data from a mass spectrum is visualized in a bar chart. A bar is created for each isotope on the independent axis and the height of each bar is determined by the frequency of that isotope being found in the sample.
The example shown above is for the element chlorine which has two isotopes as indicated by the two bars. The mass number for these two isotopes are 35 and 37, indicating both have 17 protons and the chlorine-35 isotope has 18 neutrons while the chlorine-37 isotope has 20 neutrons. Some sources will report the isotopes with a mass/charge ratio rather than mass number or even actual atomic mass, using the atomic mass units for the slightly differing masses between neutrons and protons.
Percent abundance found on the y-axis is a way of indicating the total number of particles found as a percent of the total number in the sample. Sometimes a graph may not use percent but the fractional proportions.
Practice
Skill 1: Estimate Atomic Mass From Mass Spectrum
Example: What is the approximate average atomic mass of chlorine from the data shown?
The first step is to identify the isotope masses or mass number and percent abundances from the graph.
Uranium - 35 is 75% and Uranium -37 amu is at 25%
Secondly, multiply each isotope's mass by its relative abundance, not percent abundance.
35 amu x 0.75 = 26.25 amu
37 amu x 0.25 = 9.25 amu
Thirdly, add the results.
26.25 amu + 9.25 amu = 35.5 amu
With respect to significant figures limited by the mass number to two significant figures, this answer rounds to 36 amu.
Skill 2. Identify The Element From Mass Spectrum
Example: Which element's mass spectrum is shown in the graph?
The first step is to estimate the average atomic mass roughly from the data provided. Secondly, use the periodic table to find elements that have average atomic masses shown near your estimate. And lastly, if there are multiple possibilities still, select the element that has the average atomic mass closest to the most abundant isotope.
In this example, there are 3 isotopes, with something close to 90% having a mass number of 20. There are far fewer of the larger isotopes. So you are looking for an element with a mass number slightly greater than 20.
Take a look at the periodic table you will be provided while you take the AP Exam. Click HERE Links to an external site. to access a copy to print out and have handy throughout the course.
Which elements have atomic mass near 20? F has 19.00, Ne 20.18, and Na 22.99.
Fluorine is too small - the mass spec data has nothing lower than 20 and sodium is too large since the isotopes with the larger masses have very low abundance. So the answer must be neon.
You Try It!
Identify the element and the number of neutrons in the circled isotope of the element. Click on the check mark to check your answer.
Data From Table Formats
Sometimes the information from mass spectroscopy is provided in table form instead of graphically. The same method of calculation demonstrated in Skill 1 above can be done with this data. In table form, the actual atomic mass in atomic mass units (u) is given with great precision. When provided, using this exact isotope mass will give you a number closer to that reflected in a periodic table. This abundance data is found using the mass spectrometer.
| Mass Number | Exact Mass (u) | Percent Abundance |
|---|---|---|
|
12 |
12.000000 | 98.90% |
| 13 | 13.003355 |
1.100% |
(12.000000 u x .9890) + (13.003355 u x .0110) = 12.001
The answer should have the same number of significant digits found in the factor with the fewest. That is reflected in the four sig figs in the percent abundance data.
Practice Problems
Complete the following two practice problems. Slide to the right to reveal the answer!
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