What is Percent Abundance?
Percent abundance refers to the proportion of a specific isotope of an element relative to all its isotopes. It is expressed as a percentage and is used to calculate the average atomic mass of an element.
Formula for Percent Abundance
To find the percent abundance of an isotope when the average atomic mass and mass of the isotope are known, we use the formula:
Percent Abundance = (Average Atomic Mass × 100) / Mass of Isotope
To find the average atomic mass when the mass of an isotope and its percent abundance are known:
Average Atomic Mass = (Percent Abundance × Mass of Isotope) / 100
To find the mass of an isotope when the average atomic mass and percent abundance are known:
Mass of Isotope = (Average Atomic Mass × 100) / Percent Abundance
Example Calculation
Scenario:
Imagine an element, “X,” that has two isotopes:
- X-20: Mass = 20 amu
- X-22: Mass = 22 amu
We know the average atomic mass of X is 20.4 amu.
How to find the percent abundances:
- Set up equations:
- Let “x” be the percent abundance of X-20.
- Then, “1 – x” (or 100-x when using percentages) is the percent abundance of X-22.
- The average atomic mass is the sum of (isotope mass × relative abundance):
- 20x + 22(1 – x) = 20.4
- Solve for x:
- 20x + 22 – 22x = 20.4
- -2x = -1.6
- x = 0.8
- Convert to percentages:
- X-20 abundance: 0.8 × 100% = 80%
- X-22 abundance: (1-0.8) * 100% = 20%
