To calculate the mass weighted average, you multiply the percent of natural abundance of each isotope by its actual mass, then sum these values. This process is crucial for determining the average atomic mass of an element.
Understanding Mass Weighted Average
The mass weighted average, often referred to when discussing average atomic mass, isn't simply an average of different masses. Instead, it considers the relative abundance or percentage of each component when calculating the average. This is particularly important in chemistry, specifically when dealing with isotopes.
Steps to Calculate Mass Weighted Average:
- Identify the Isotopes: Determine all the isotopes of the element you are considering, along with their respective atomic masses.
- Determine Natural Abundance: Find the natural abundance of each isotope, usually expressed as a percentage.
- Multiply Mass by Abundance: For each isotope, multiply its atomic mass by its percentage of natural abundance (expressed as a decimal).
- Sum the Results: Add up all the products from step 3. This final sum is the mass weighted average, or atomic mass of the element.
Example Calculation:
Let's calculate a mass weighted average with a hypothetical example:
- Element X has two isotopes:
- Isotope X-20 (mass = 19.99 amu), abundance is 75%
- Isotope X-22 (mass = 21.99 amu), abundance is 25%
| Isotope | Mass (amu) | Abundance (%) | Abundance (decimal) | Mass x Abundance |
|---|---|---|---|---|
| X-20 | 19.99 | 75 | 0.75 | 14.9925 |
| X-22 | 21.99 | 25 | 0.25 | 5.4975 |
| Total | 100 | 20.49 |
Therefore, the weighted average atomic mass of element X is 20.49 amu.
Key Takeaways:
- The reference states: "The weighted average is determined by multiplying the percent of natural abundance by the actual mass of the isotope." This is precisely how the calculation is performed.
- This weighted average gives a more accurate representation of an element's average atomic mass because it accounts for the natural variation in isotopic abundance.
- This concept is primarily used in determining average atomic masses from isotopic masses.
