The average atomic mass of an element is calculated by taking a weighted average of the masses of its naturally occurring isotopes. This involves multiplying the mass of each isotope by its relative abundance (expressed as a decimal) and then summing these products.
Here's a breakdown of the process:
Understanding Isotopes and Abundance
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Isotopes: Isotopes are variants of a chemical element which have the same number of protons but different numbers of neutrons, resulting in different mass numbers. For example, Chlorine has two common isotopes: Chlorine-35 and Chlorine-37.
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Natural Abundance: Natural abundance refers to the percentage of each isotope that naturally occurs on Earth. For instance, Chlorine-35 has a natural abundance of approximately 75.76%, and Chlorine-37 has a natural abundance of approximately 24.24%.
Calculation Steps
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Determine the Mass of Each Isotope: The mass of each isotope is typically expressed in atomic mass units (amu). This information is often provided or can be found in a periodic table or isotope table.
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Convert Natural Abundance to Decimal Form: Divide the percentage abundance of each isotope by 100 to obtain its decimal abundance.
- Example: If an isotope has a natural abundance of 75%, its decimal abundance is 75/100 = 0.75.
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Multiply Isotope Mass by Decimal Abundance: For each isotope, multiply its mass (in amu) by its decimal abundance.
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Sum the Results: Add up the values obtained in step 3 for all isotopes of the element. The result is the average atomic mass of the element.
Example Calculation: Chlorine
Let's calculate the average atomic mass of chlorine, given the following information:
| Isotope | Mass (amu) | Natural Abundance (%) | Decimal Abundance |
|---|---|---|---|
| Chlorine-35 | 34.9688 | 75.76 | 0.7576 |
| Chlorine-37 | 36.9659 | 24.24 | 0.2424 |
Average Atomic Mass = (34.9688 amu 0.7576) + (36.9659 amu 0.2424)
Average Atomic Mass = 26.4925 amu + 8.9598 amu
Average Atomic Mass = 35.4523 amu
Therefore, the average atomic mass of chlorine is approximately 35.45 amu. This value is what you typically see listed on the periodic table.
In summary, calculating the average atomic mass involves weighting the mass of each isotope by its prevalence in nature and then summing the results. This weighted average gives us a more accurate representation of the atomic mass of an element than simply using the mass of the most common isotope.
