Use this tool to easily calculate the average atomic mass of an element given the isotopic masses and their relative percent abundances. Ensure the total abundance sums to 100% for an accurate result.
Average Atomic Mass Calculator
Average Atomic Mass Formula
Variables
- Isotope Mass (amu): The exact atomic mass of a specific isotope of the element.
- Percent Abundance (%): The percentage of atoms of that specific isotope in a natural sample of the element.
- i: Index representing each distinct isotope.
- $\sum$: The summation symbol, indicating that the products of all isotope masses and fractional abundances must be added together.
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What is Average Atomic Mass?
The average atomic mass is the weighted average of the atomic masses of the naturally occurring isotopes of an element. This value is what you see listed for each element on the periodic table. Since most elements have several isotopes—atoms with the same number of protons but different numbers of neutrons—a simple average won’t work.
The weighting factor is the natural abundance of each isotope. For instance, carbon naturally occurs as carbon-12 (about 98.9%) and carbon-13 (about 1.1%). The average atomic mass calculation takes these percentages into account, ensuring the final number is closer to the mass of the most abundant isotope (in this case, carbon-12).
It is a crucial concept in chemistry because reactions and mass measurements in a lab setting always involve a bulk sample containing the natural distribution of all isotopes. The average atomic mass allows chemists to make accurate mass-to-mole conversions for calculations like stoichiometry.
How to Calculate Average Atomic Mass (Example)
Let’s calculate the average atomic mass of Chlorine (Cl), which has two major isotopes:
- Identify the Isotopes and Abundances:
- Chlorine-35: Mass = 34.9688 amu, Abundance = 75.77%
- Chlorine-37: Mass = 36.9659 amu, Abundance = 24.23%
- Convert Abundances to Fractional Values:
$$ \text{Fractional Abundance} = \frac{\text{Percent Abundance}}{100} $$
$35$: $75.77 / 100 = 0.7577$
$37$: $24.23 / 100 = 0.2423$ - Calculate the Contribution of Each Isotope:
$$ \text{Contribution} = \text{Mass} \times \text{Fractional Abundance} $$
$35$: $34.9688 \times 0.7577 \approx 26.4940$ amu
$37$: $36.9659 \times 0.2423 \approx 8.9563$ amu - Sum the Contributions: $$ \text{Average Atomic Mass} = 26.4940 + 8.9563 \approx 35.4503 \text{ amu} $$
Frequently Asked Questions (FAQ)
The average atomic mass is typically not a whole number because it represents a weighted average of the masses of all isotopes, and these masses are not exactly integers. The mass of a proton or neutron is not exactly 1.0 amu due to binding energy (mass defect).
The mass number is a count of the total number of protons and neutrons in a single atom and is always a whole number (e.g., 12 for Carbon-12). The average atomic mass is a weighted average of the masses of all naturally occurring isotopes of an element, and it includes the mass defect.
In theory, yes. In practice, due to rounding and measurement limitations, the sum of all known percent abundances might be slightly above or below 100% (e.g., 99.99% or 100.01%). The calculator will check if the sum is reasonably close to 100% (within 0.1%).
Isotope masses are determined experimentally using a mass spectrometer, a device that separates atoms based on their mass-to-charge ratio. These masses are measured with high precision.