The numerical value for atomic mass found on the periodic table is not a simple whole number. This non-integer mass is a calculated value that accounts for natural variations in the element’s structure. Every element exists in nature as a mixture of different forms, which affects the overall mass measured for any bulk sample. This article explains the mathematical method used to determine this single, representative figure.
Defining the Components: Isotopes and Mass Units
The variations in an element’s structure that influence its mass are known as isotopes. Isotopes are atoms of the same element that share the identical number of protons but possess a different number of neutrons in their nucleus. Since neutrons contribute significantly to an atom’s mass, a varying neutron count means that each isotope has a slightly different atomic mass. For instance, a sample of chlorine contains atoms with two distinct masses.
To express these tiny quantities of matter, scientists use the atomic mass unit (amu or u), sometimes called the Dalton (Da). One atomic mass unit is defined as exactly one-twelfth the mass of a single carbon-12 atom. This standard unit allows for accurate comparison of the masses of different atoms and their isotopes.
The final piece of information required for the calculation is the relative abundance, which is the percentage of each specific isotope that occurs naturally on Earth. If an isotope has a 75% relative abundance, three out of every four atoms of that element encountered in nature will have that particular mass. The masses and abundances are determined experimentally, often through mass spectrometry.
The Weighted Average Formula: Step-by-Step Calculation
The process of calculating the atomic mass seen on the periodic table relies on the weighted average principle. A simple average would treat all isotopic masses equally, which would not accurately represent a natural sample because isotopes are not found in equal amounts. The weighted average mathematically accounts for the differing relative abundances of each isotope.
The general formula for this calculation is the sum of the products of each isotope’s mass and its fractional abundance. The fractional abundance is the percentage abundance expressed as a decimal, achieved by dividing the percentage by 100.
Consider the element chlorine, which primarily exists as two isotopes: chlorine-35 and chlorine-37. Chlorine-35 has an exact atomic mass of 34.969 u with a natural abundance of 75.77%. Chlorine-37 has an atomic mass of 36.966 u and a natural abundance of 24.23%.
The first step is to convert the percentage abundances into their fractional forms. For chlorine-35, the fractional abundance is 0.7577, and for chlorine-37, it is 0.2423. The sum of all fractional abundances must always equal 1.00.
Next, the mass of each isotope is multiplied by its corresponding fractional abundance. For chlorine-35, the product is 34.969 u multiplied by 0.7577, which equals 26.496 u. For chlorine-37, the product is 36.966 u multiplied by 0.2423, which results in 8.957 u.
The final step is to sum the products from each isotope to find the average atomic mass. Adding the two products (26.496 u + 8.957 u) yields a result of 35.453 u. This value is the weighted average atomic mass for chlorine and is the number displayed on the periodic table. This result is closer to the mass of chlorine-35 because the lighter isotope is significantly more abundant in nature, weighting the average toward its mass.
Why the Periodic Table Uses Average Atomic Mass
The calculated average atomic mass is the standard value used by chemists because it accurately reflects the composition of elements as they are encountered in the real world. In practical laboratory settings, scientists work with macroscopic samples that contain billions of atoms. Any natural sample of an element will contain its isotopes mixed together in their characteristic, fixed proportions.
The average atomic mass serves as the representative mass for an element’s natural mixture of isotopes. This figure is indispensable for stoichiometric calculations, which involve measuring the quantities of reactants and products in chemical reactions. Using the average atomic mass ensures that calculations accurately reflect the total mass of the natural isotopic mix in any sample.
If the periodic table used the mass of only the most common isotope, chemical calculations involving bulk quantities would be inaccurate. The weighted average provides a single, reliable figure equivalent to the molar mass of the element, simplifying the conversion between mass and moles for all naturally occurring samples.