Relative atomic mass is calculated by determining the weighted average mass of an element's atoms, considering the masses of its isotopes and their natural abundances. It provides an estimate of the average mass of an atom for a given element as found in nature.
Understanding Relative Atomic Mass
Elements exist as different forms called isotopes. Isotopes of an element have the same number of protons but different numbers of neutrons, leading to different atomic masses. Since elements in nature are typically a mixture of these isotopes, the relative atomic mass reflects this natural composition. It's not a simple average, but a weighted average, meaning the abundance of each isotope significantly influences the final value.
The relative atomic mass is essentially the sum of the products of each isotope's mass and its relative abundance. This value is often found on the periodic table for each element.
The Formula for Relative Atomic Mass
To calculate the relative atomic mass, you use the following formula:
Relative Atomic Mass = Σ (Isotope Mass × Fractional Abundance)
Where:
- Σ (sigma) means "the sum of"
- Isotope Mass is the atomic mass unit (amu) of a specific isotope.
- Fractional Abundance is the percentage abundance of that isotope divided by 100.
Step-by-Step Calculation Guide
Calculating the relative atomic mass involves a few straightforward steps:
- Identify Isotopes and Their Data: For the element in question, list all its naturally occurring isotopes, their individual atomic masses (in amu), and their natural percentage abundances.
- Convert Percentage to Fractional Abundance: Divide each isotope's percentage abundance by 100 to convert it into a decimal (fractional) value.
- Multiply Mass by Fractional Abundance: For each isotope, multiply its atomic mass by its corresponding fractional abundance. This gives you the contribution of that isotope to the total average mass.
- Sum the Contributions: Add up the results from Step 3 for all the isotopes. The total sum will be the relative atomic mass of the element.
Practical Example: Calculating the Relative Atomic Mass of Chlorine
Let's illustrate this with an example using Chlorine (Cl), which has two main naturally occurring isotopes: Chlorine-35 and Chlorine-37.
| Isotope | Isotope Mass (amu) | Natural Abundance (%) |
|---|---|---|
| Chlorine-35 | 34.96885 | 75.77 |
| Chlorine-37 | 36.96590 | 24.23 |
Calculation Steps:
-
Convert Abundances to Fractional:
- Chlorine-35: 75.77% ÷ 100 = 0.7577
- Chlorine-37: 24.23% ÷ 100 = 0.2423
-
Multiply Mass by Fractional Abundance for Each Isotope:
- For Chlorine-35: 34.96885 amu × 0.7577 = 26.4958 amu
- For Chlorine-37: 36.96590 amu × 0.2423 = 8.9568 amu
-
Sum the Contributions:
- Relative Atomic Mass = 26.4958 amu + 8.9568 amu = 35.4526 amu
Therefore, the relative atomic mass of Chlorine is approximately 35.45 amu, which aligns with the value found on the periodic table. This demonstrates how the more abundant isotope (Chlorine-35) contributes more significantly to the overall average mass.
