You calculate relative atomic mass by determining the weighted average of the masses of the isotopes of an element, taking into account their relative abundances.
Here's a step-by-step breakdown:
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Determine the isotopic mass of each isotope. Isotopic mass is usually provided or can be found in isotopic data tables.
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Determine the relative abundance of each isotope. Relative abundance is usually expressed as a percentage or a decimal fraction. If given as a percentage, divide by 100 to convert to a decimal.
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Multiply the isotopic mass of each isotope by its relative abundance (as a decimal). This gives you the contribution of each isotope to the overall relative atomic mass.
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Add up the contributions from all the isotopes. The sum is the relative atomic mass of the element.
Formula:
Relative Atomic Mass = (Isotope 1 Mass * Isotope 1 Abundance) + (Isotope 2 Mass * Isotope 2 Abundance) + ... + (Isotope n Mass * Isotope n Abundance)
Example:
Let's say we have an element, X, with two isotopes:
- Isotope X-20 has a mass of 20 amu and an abundance of 90%.
- Isotope X-22 has a mass of 22 amu and an abundance of 10%.
To calculate the relative atomic mass of element X:
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Convert percentages to decimals: 90% = 0.90 and 10% = 0.10
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Multiply each isotopic mass by its decimal abundance:
- X-20: 20 amu * 0.90 = 18 amu
- X-22: 22 amu * 0.10 = 2.2 amu
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Add the results: 18 amu + 2.2 amu = 20.2 amu
Therefore, the relative atomic mass of element X is 20.2 amu.
In essence, the relative atomic mass is a weighted average, where the "weights" are the relative abundances of the isotopes. This accounts for the fact that some isotopes are more common than others, and thus contribute more to the overall atomic mass of the element.
