Atoms of the same element are typically thought of as identical, yet subtle differences can exist within them. These variations occur in what are known as isotopes, which are atoms of the same chemical element that possess the same number of protons but differ in their number of neutrons. This difference in neutron count leads to a variation in their atomic mass. For instance, carbon atoms always have six protons, but some may have six neutrons (carbon-12), while others have seven (carbon-13) or eight (carbon-14). These distinct forms are all carbon, but they carry different masses.
Understanding Isotopic Abundance
Isotopic abundance refers to the relative amount of each specific isotope present in a naturally occurring sample of an element. Elements in nature exist as a mixture of various isotopes, each contributing a certain percentage to the total. These percentages are generally consistent for a given element across different natural samples on Earth, though slight variations can occur.
These variations in isotopic composition arise from the natural processes of element formation, such as those occurring in stars. For example, chlorine found in nature is not composed solely of atoms with one specific mass. It is a blend of chlorine-35 and chlorine-37, each present in a particular ratio.
Connecting Isotopic Abundance to Average Atomic Mass
The atomic mass value listed for each element on the periodic table is not the mass of a single isotope. Instead, it represents a weighted average of the masses of all naturally occurring isotopes of that element. This average takes into account not only the mass of each isotope but also its relative abundance in nature. It essentially reflects the typical mass you would encounter if you were to pick up a random atom of that element.
A weighted average is used because some isotopes are far more common than others. For example, if an element has two isotopes, and one is 90% abundant while the other is 10% abundant, the average atomic mass will be much closer to the mass of the more abundant isotope. This relationship highlights how the individual masses of isotopes, combined with their fractional abundances, collectively determine the element’s overall average atomic mass. This average atomic mass provides the foundational information needed to determine the specific percentage abundance of each isotope.
The Calculation Method for Percent Abundance
Determining the percent abundance of isotopes involves using the average atomic mass of an element, along with the precise masses of its individual isotopes. This calculation is commonly applied when an element has two primary isotopes. The sum of the fractional abundances of all isotopes must equal 1 (or 100% when expressed as percentages).
To illustrate, consider an element with two isotopes, Isotope A and Isotope B. Let ‘x’ represent the fractional abundance of Isotope A. Consequently, the fractional abundance of Isotope B would be (1 – x). The formula connecting these values to the average atomic mass (AAM) is:
AAM = (Mass of Isotope A x) + (Mass of Isotope B (1 – x))
As an example, let’s use chlorine, which has an average atomic mass of 35.453 atomic mass units (amu). Its two main isotopes are chlorine-35 (with a mass of 34.969 amu) and chlorine-37 (with a mass of 36.966 amu). If ‘x’ is the fractional abundance of chlorine-35, then (1-x) is the fractional abundance of chlorine-37.
Substituting these values into the formula:
35.453 = (34.969 x) + (36.966 (1 – x))
35.453 = 34.969x + 36.966 – 36.966x
35.453 = 36.966 – 1.997x
-1.513 = -1.997x
x = -1.513 / -1.997 ≈ 0.7576
The fractional abundance of chlorine-35 is approximately 0.7576, which translates to 75.76%. The fractional abundance of chlorine-37 is (1 – 0.7576) = 0.2424, or 24.24%.