AP® Chemistry review sheet from Aim for Five (aimforfive.com/chem/units/1/1-2)
Unit 1 · Topic 1.2
1.2 Mass Spectra of Elements
Most elements exist as a mix of isotopes, atoms with the same number of protons but different numbers of neutrons. A mass spectrum shows each isotope as a peak, and the element's average atomic mass is the weighted average of those isotope masses.
Key terms
- isotope
- mass spectrum
- relative abundance
- average atomic mass
- weighted average
Isotopes
Every atom of an element has the same number of protons; that number (the atomic number) defines the element. Isotopes of an element differ in their number of neutrons, so they have different masses. Chlorine-35 and chlorine-37 both have 17 protons, but they have 18 and 20 neutrons.
Isotopes of an element behave almost identically in chemical reactions, because reactions depend on electrons, and isotopes have the same number of electrons.
Reading a mass spectrum
A mass spectrometer turns atoms into ions and sorts them by mass. For a sample of one element, the spectrum is a set of vertical lines (peaks).
The horizontal axis is mass (strictly, mass-to-charge ratio, but for the singly charged ions you'll see, it's just the mass in amu). The vertical axis is relative abundance: how common each isotope is.
So each peak tells you two things: where it sits gives the mass of one isotope, and how tall it is tells you what fraction of the atoms are that isotope. Count the peaks to count the isotopes.
Example: a spectrum of magnesium has three peaks, at about 24, 25 and 26 amu, with the 24 peak far taller than the other two. Three peaks means three isotopes, and the tall one at 24 tells you most magnesium atoms are magnesium-24. That's why magnesium's average atomic mass, 24.31, sits just above 24.
- Abundance may be given as percentages that add to 100%.
- Or the tallest peak may be set to 100, with the others scaled to it. Then the heights don't add to 100, and you must convert them to fractions first.
Average atomic mass is a weighted average
The atomic mass printed on the periodic table is an average over all the isotopes, weighted by how common each one is. To calculate it, multiply each isotope's mass by its fractional abundance (percent ÷ 100) and add the results.
Average atomic mass = Σ (isotope mass × fractional abundance)
Because it's weighted, the average always lands closest to the most abundant isotope. Chlorine's average, 35.45, is much nearer 35 than 37, so you can tell chlorine-35 is the more common isotope without doing any math. That kind of estimate is often all a multiple-choice question needs.
The same weighted average is what makes molar mass work. When you use 35.45 g/mol for chlorine in topic 1.1, you're using this average, so any real sample of chlorine, with its natural mix of isotopes, contains 6.022 × 10²³ atoms in 35.45 g.
What you won't be tested on
The exam only uses spectra of single elements. You won't need to interpret spectra of compounds or mixtures of elements, or peaks from fragments and ions with charges other than 1+.
Worked examples
Try each one yourself first, then open the solution.
- Example 1Calculator allowed
Average atomic mass from percentages
Chlorine's mass spectrum has two peaks: 34.969 amu (75.78%) and 36.966 amu (24.22%). Calculate chlorine's average atomic mass.
Show the solutionHide the solution
- Step 1: Change percentages to fractions: 0.7578 and 0.2422.
- Step 2: Multiply and add: (34.969)(0.7578) + (36.966)(0.2422) = 26.50 + 8.953 = 35.45 amu.
- Step 3: Check: the answer is between 35 and 37 and closer to 35, which matches chlorine-35 being more common.
Answer: 35.45 amu
- Example 2Calculator allowed
Peak heights that don't add to 100 (classic trap)
A mass spectrum of copper shows a peak at 62.93 amu with relative height 100 and a peak at 64.93 amu with relative height 44.6. Calculate the average atomic mass of copper.
Show the solutionHide the solution
- Step 1: The heights add to 144.6, not 100, so they aren't percentages. Convert each to a fraction of the total.
- Step 2: Fraction of copper-63 = 100 ÷ 144.6 = 0.6916. Fraction of copper-65 = 44.6 ÷ 144.6 = 0.3084.
- Step 3: Weighted average = (62.93)(0.6916) + (64.93)(0.3084) = 63.55 amu.
- Step 4: If you had used 1.00 and 0.446 as the fractions, you'd get about 91.9 amu, which is impossible because it's bigger than both isotope masses.
Answer: 63.55 amu
- Example 3Calculator allowed
Working backward to an abundance
Boron has two isotopes, boron-10 (10.013 amu) and boron-11 (11.009 amu). Its average atomic mass is 10.81 amu. What percent of boron atoms are boron-10?
Show the solutionHide the solution
- Step 1: Let x be the fraction of boron-10. Then the fraction of boron-11 is 1 − x, because the fractions must add to 1.
- Step 2: Set up the weighted average: 10.013x + 11.009(1 − x) = 10.81.
- Step 3: Expand: 10.013x + 11.009 − 11.009x = 10.81, so −0.996x = −0.199 and x = 0.200.
- Step 4: Sense check: 10.81 is closer to 11 than to 10, so boron-11 should be the majority. It is (80%).
Answer: About 20.0% boron-10
Common mistakes
- Using mass numbers (35, 37) when exact isotope masses are given. Use the masses on the spectrum.
- Treating relative peak heights as percentages when they don't add to 100. Divide each height by the total first.
- Thinking the average atomic mass must equal the mass of a real atom. No chlorine atom has a mass of 35.45 amu; it's an average.
- Saying isotopes differ in protons or electrons. They differ only in neutrons.
On the exam
- Expect to read a spectrum and either calculate an average atomic mass or identify the element by comparing your answer to the periodic table. Show the weighted-average setup, not just the result.
- Many questions can be answered by estimation: if the average is close to one peak, that isotope is the most abundant.
Connected topics
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Check yourself
4 questions on 1.2 Mass Spectra of Elements. Pick an answer to see if you got it, and why.
| Mass of isotope (amu) | Relative abundance (%) |
|---|---|
| 24 | 79.0 |
| 25 | 10.0 |
| 26 | 11.0 |
A mass spectrum of a pure sample of an element shows three peaks, summarized in the table. Isotope masses are rounded to whole numbers.
Based on the data, the average atomic mass of the element is closest to which of the following?
How many neutrons are in the nucleus of an atom that produces the peak at 26 amu?
Which of the following best explains why all three peaks can come from atoms of a single element?
Gallium has two naturally occurring isotopes, ⁶⁹Ga (68.93 amu) and ⁷¹Ga (70.92 amu). The average atomic mass of gallium is 69.72 amu. Which of the following is closest to the percent abundance of ⁶⁹Ga?
0 of 4 answered