The atomic mass of chlorine is calculated as the weighted average of the masses of its naturally occurring isotopes. Here's how:
Understanding Isotopes and Weighted Averages
Chlorine exists in nature primarily as two isotopes: chlorine-35 (35Cl) and chlorine-37 (37Cl). Isotopes are atoms of the same element with the same number of protons but different numbers of neutrons, resulting in different mass numbers. The atomic mass on the periodic table is not a whole number because it reflects the average mass, considering the relative abundance of each isotope. This is a weighted average.
Calculation Steps
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Identify the Isotopes and Their Masses:
- Chlorine-35 (35Cl) has a mass of approximately 35 atomic mass units (amu).
- Chlorine-37 (37Cl) has a mass of approximately 37 atomic mass units (amu).
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Determine the Natural Abundance of Each Isotope:
- Chlorine-35 (35Cl) has a natural abundance of about 75.76% (or 0.7576 as a decimal).
- Chlorine-37 (37Cl) has a natural abundance of about 24.24% (or 0.2424 as a decimal).
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Multiply the Mass of Each Isotope by its Abundance:
- (Mass of 35Cl) x (Abundance of 35Cl) = 35 amu x 0.7576 = 26.516 amu
- (Mass of 37Cl) x (Abundance of 37Cl) = 37 amu x 0.2424 = 8.9688 amu
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Sum the Results:
- Atomic mass of chlorine = 26.516 amu + 8.9688 amu = 35.4848 amu
Therefore, the atomic mass of chlorine is approximately 35.48 amu.
Formula
The general formula for calculating atomic mass is:
Atomic Mass = (Mass of Isotope 1 x Abundance of Isotope 1) + (Mass of Isotope 2 x Abundance of Isotope 2) + ...
Example
Let's recalculate using the simplified abundances given in the references: 75% for chlorine-35 and 25% for chlorine-37.
Atomic Mass = (35 amu x 0.75) + (37 amu x 0.25) = 26.25 amu + 9.25 amu = 35.5 amu
This simplified calculation gives an atomic mass of 35.5 amu, which is a common approximation. The more precise value, accounting for the exact natural abundances, is closer to 35.45 amu on the periodic table.
