How to Calculate the Average Atomic Mass of an Element
Understanding atomic mass is fundamental in chemistry and physics. While individual atoms have a specific mass number (the sum of protons and neutrons), elements as found in nature are often a mixture of different isotopes, each with a slightly different mass. The "atomic mass" listed on the periodic table is actually the average atomic mass, which is a weighted average of the masses of all naturally occurring isotopes of that element.
What is Atomic Mass?
Before diving into calculations, let's clarify some terms:
- Mass Number: This is the total number of protons and neutrons in a specific isotope of an atom. It's always a whole number (e.g., Carbon-12, Carbon-13).
- Isotopic Mass: This is the actual mass of a specific isotope, measured in atomic mass units (amu). Due to the mass defect (energy released when nucleons bind together), the isotopic mass is usually very close to, but not exactly, the mass number. For example, Carbon-12 has an isotopic mass of exactly 12.000000 amu by definition, but Carbon-13 has an isotopic mass of 13.003355 amu.
- Average Atomic Mass: This is the weighted average of the isotopic masses of all naturally occurring isotopes of an element, taking into account their relative abundances. This is the value typically found on the periodic table.
The unit for atomic mass is the atomic mass unit (amu), defined as 1/12th the mass of a carbon-12 atom.
Why is Average Atomic Mass Important?
The average atomic mass is crucial for several reasons:
- It allows chemists to work with elements in bulk, knowing the average mass of their atoms.
- It's used in stoichiometry to convert between mass and moles of a substance.
- It reflects the natural composition of an element, which is consistent across the globe.
How to Calculate Average Atomic Mass
The average atomic mass is calculated using a weighted average formula. For each isotope of an element, you need two pieces of information:
- Its isotopic mass (in amu).
- Its natural abundance (as a percentage or decimal fraction).
The formula is:
Average Atomic Mass = (Isotope 1 Mass × Isotope 1 Abundance) + (Isotope 2 Mass × Isotope 2 Abundance) + ...
Remember to convert the percentage abundances to decimal form by dividing by 100 before multiplying.
Step-by-Step Example: Calculating the Average Atomic Mass of Carbon
Carbon has two main stable isotopes:
- Carbon-12: Isotopic Mass = 12.000000 amu, Natural Abundance = 98.90%
- Carbon-13: Isotopic Mass = 13.003355 amu, Natural Abundance = 1.10%
Let's calculate the average atomic mass:
- Convert abundances to decimal:
- Carbon-12: 98.90% / 100 = 0.9890
- Carbon-13: 1.10% / 100 = 0.0110
- Multiply each isotopic mass by its decimal abundance:
- Carbon-12 contribution: 12.000000 amu × 0.9890 = 11.868000 amu
- Carbon-13 contribution: 13.003355 amu × 0.0110 = 0.143036805 amu
- Sum the contributions:
- Average Atomic Mass = 11.868000 amu + 0.143036805 amu = 12.011036805 amu
Rounding to a typical number of decimal places, the average atomic mass of Carbon is approximately 12.011 amu, which matches the value on the periodic table.
Use the calculator below to determine the average atomic mass for elements with up to three isotopes.
Average Atomic Mass Calculator
Enter the isotopic mass and natural abundance for each isotope. You can use up to three isotopes.