1.2 Mass Spectroscopy of Elements

The Periodic Table and Average Atomic Mass

Understanding the numbers on the periodic table is crucial to mastering chemistry. Let’s break it down, focusing on subatomic particles and how they shape the elements we see on the periodic table.

Review of the Periodic Table ⚗️

Each element on the periodic table provides essential information:

• Element Symbol: Every element is represented by a unique symbol, typically one or two letters—for instance, “C” for carbon.

• Atomic Number: This number, located above the element symbol, represents the number of protons in an atom. It also tells us the number of electrons in a neutral atom.

• Atomic Mass: Below the element symbol, you’ll find the atomic mass, expressed in atomic mass units (amu). It represents the average mass of an atom of that element, accounting for the number of protons and neutrons.

If you’ve ever wondered why the atomic mass is often a messy decimal, like 12.01 for carbon, that’s because it’s an average atomic mass. It considers all naturally occurring isotopes of an element, weighted by how often each isotope appears.

Isotopes and Average Atomic Mass

Isotopes are variations of an element that have the same number of protons but different numbers of neutrons. This means they share the same atomic number but have different atomic masses. The atomic mass listed on the periodic table reflects the weighted average of all isotopes of an element, based on their natural abundances.

Carbon’s Isotopes

Carbon, for example, has three naturally occurring isotopes:

• Carbon-12: The most abundant form, making up about 98.9% of all naturally occurring carbon. It has an atomic mass of 12 amu.

• Carbon-13: Makes up about 1.1% of carbon and has an atomic mass of 13 amu.

• Carbon-14: Rare and present in trace amounts, it is radioactive and has an atomic mass of 14 amu. Carbon-14 is famous for its use in carbon dating, which helps determine the age of ancient organic materials.

The average atomic mass for carbon is calculated like this:

Average Atomic Mass (AAM) = (0.989 × 12) + (0.011 × 13) = 12.01 amu

This explains why the atomic mass of carbon on the periodic table is 12.01 rather than a nice, whole number. The small contribution from Carbon-13 influences the average.

Mass Spectrometry ▶️

Mass spectrometry is a technique used to measure the mass and relative abundance of ions in a sample. It produces a graph called a mass spectrum, which helps identify isotopes and their relative abundances.

Imagine looking at the mass spectrum for carbon. You’d see two main peaks: one representing Carbon-12 and another for Carbon-13. The taller peak for Carbon-12 indicates it’s much more abundant in nature.

Calculating Average Atomic Mass from a Spectrum

Suppose we have a mass spectrum of an unknown element with three peaks:

• Isotope 1 (24 amu): 82.8% abundance

• Isotope 2 (25 amu): 8.1% abundance

• Isotope 3 (26 amu): 9.1% abundance

To calculate the average atomic mass:

AAM = (0.828 × 24) + (0.081 × 25) + (0.091 × 26) = 24.263 amu

The element with an atomic mass close to 24.3 amu is magnesium (Mg), according to the periodic table.

Sample AP Chemistry Question

Consider a question from a past AP Chemistry exam. Let’s break down how to solve it step by step.

Question 2a Part i: Solving for Percent Abundance

• Given: Average atomic mass (AAM) = 20.18, masses of isotopes = 19.99 and 21.99.

• Equation: Set it up as follows:

  20.18 = (x × 19.99) + ((1 – x) × 21.99)

• Solve for x: x = 0.905

• Conclusion: Ne-20 has 90.5% abundance, and Ne-22 has 9.5% abundance.

Question 2a Part ii: Converting Grams to Atoms

Use dimensional analysis to convert from grams to atoms. Start with the mass of neon, convert to moles using the molar mass, and then use Avogadro’s number to find the number of atoms.

Mass Spectrometry in the Lab

Mass spectrometry isn’t just a theoretical concept—it’s a powerful lab technique for analyzing substances. If you want a more in-depth explanation, check out Khan Academy’s excellent resources on mass spectrometry!

Key Takeaways

• The atomic number represents the number of protons, while the atomic mass is an average of all naturally occurring isotopes.

• Isotopes are atoms of the same element with different numbers of neutrons.

• Mass spectrometry helps determine isotope abundance and calculate average atomic mass.

• Calculating average atomic mass involves weighting isotopes by their relative abundances.