Average Atomic Mass Calculator
Enter the mass and natural abundance for each isotope. You can use up to three isotopes.
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Understanding and Calculating Average Atomic Mass
The atomic mass listed on the periodic table for each element isn't simply the mass of a single atom. Instead, it represents the average atomic mass, which is a weighted average of the masses of all naturally occurring isotopes of that element. This concept is crucial in chemistry for understanding the properties of elements and performing stoichiometric calculations.
What is Atomic Mass?
An atom is composed of protons, neutrons, and electrons. The mass of an atom is primarily determined by its protons and neutrons, as electrons have negligible mass. The atomic mass unit (amu) is used to express these masses, where 1 amu is approximately the mass of one proton or one neutron.
- Mass Number: This is the total number of protons and neutrons in a specific isotope of an element. For example, Carbon-12 has 6 protons and 6 neutrons, so its mass number is 12.
- Isotopes: Atoms of the same element (same number of protons) but with different numbers of neutrons are called isotopes. This means isotopes of an element have different mass numbers. For instance, Carbon-12 and Carbon-14 are isotopes of carbon.
- Natural Abundance: In nature, elements usually exist as a mixture of their isotopes. The natural abundance refers to the percentage of each isotope found in a typical sample of the element.
Why a Weighted Average?
Because elements exist as mixtures of isotopes, and each isotope has a slightly different mass, the atomic mass on the periodic table reflects the average mass of these isotopes, weighted by their natural abundance. This ensures that when you take a macroscopic sample of an element, its average atomic mass accurately represents the mass of its atoms.
The Formula for Average Atomic Mass
To calculate the average atomic mass, you use the following formula:
Average Atomic Mass = Σ (Isotope Mass × Fractional Abundance)
Where:
- Isotope Mass: The exact mass of a specific isotope (usually given in amu).
- Fractional Abundance: The natural abundance of that isotope divided by 100 (to convert the percentage to a decimal).
- Σ (Sigma): Represents the sum of these products for all naturally occurring isotopes of the element.
Step-by-Step Example: Calculating the Average Atomic Mass of Chlorine
Let's calculate the average atomic mass of Chlorine, which has two main naturally occurring isotopes:
- Chlorine-35: Has an isotopic mass of 34.96885 amu and a natural abundance of 75.77%.
- Chlorine-37: Has an isotopic mass of 36.96590 amu and a natural abundance of 24.23%.
Here's how to apply the formula:
- Convert abundances to fractional abundances:
- Chlorine-35: 75.77% ÷ 100 = 0.7577
- Chlorine-37: 24.23% ÷ 100 = 0.2423
- Multiply each isotope's mass by its fractional abundance:
- For Chlorine-35: 34.96885 amu × 0.7577 = 26.4959 amu
- For Chlorine-37: 36.96590 amu × 0.2423 = 8.9563 amu
- Sum the results:
- Average Atomic Mass = 26.4959 amu + 8.9563 amu = 35.4522 amu
Therefore, the average atomic mass of Chlorine is approximately 35.4522 amu, which matches the value found on the periodic table.
Using the Calculator
Our Average Atomic Mass Calculator simplifies this process. Simply input the isotopic mass (in amu) and the natural abundance (as a percentage) for each isotope of the element you are interested in. The calculator will then perform the weighted average calculation and display the average atomic mass for you.
Remember to ensure that the sum of the natural abundances for all isotopes of an element should ideally be 100% for an accurate average atomic mass calculation. If you enter fewer than 100%, the calculator will still provide a result based on the data provided, but it will also issue a warning.