Calculating the atomic mass of an element involves considering the masses of its different isotopes and their natural abundances, which is distinct from the mass number of a single isotope.
Understanding Mass Number (as per reference)
The provided reference explains how to determine the mass number of a specific atom or isotope, not the element's atomic mass as typically found on the periodic table.
According to the reference:
- Together, the number of protons and the number of neutrons determine an element's mass number.
- The formula is: mass number = protons + neutrons.
- If you want to calculate how many neutrons an atom has, you can simply subtract the number of protons (which is the atomic number) from the mass number.
For example, a carbon atom with 6 protons and 6 neutrons has a mass number of 12 (6 + 6 = 12). A carbon atom with 6 protons and 7 neutrons has a mass number of 13 (6 + 7 = 13). These are different isotopes of carbon. The mass number is always a whole number and refers to a specific isotope.
Calculating Atomic Mass (Weighted Average)
Unlike the mass number which pertains to a single isotope, the atomic mass (often called the average atomic mass or atomic weight) listed on the periodic table is a weighted average of the masses of all naturally occurring isotopes of that element. This is because most elements exist as a mixture of several isotopes, each having a different mass number due to a different number of neutrons.
To calculate the average atomic mass of an element, you need:
- The mass of each naturally occurring isotope.
- The natural abundance (percentage) of each isotope.
The formula for calculating average atomic mass is:
$$ \text{Average Atomic Mass} = \sum (\text{Isotope Mass} \times \text{Fractional Abundance}) $$
Where:
- "Isotope Mass" is the atomic mass unit (amu) value for a specific isotope.
- "Fractional Abundance" is the natural abundance percentage expressed as a decimal (e.g., 75% abundance is 0.75).
- The summation ($\sum$) means you add up the results for each isotope.
Example: Calculating the Atomic Mass of Chlorine
Chlorine ($\text{Cl}$) has two main naturally occurring isotopes: Chlorine-35 and Chlorine-37.
| Isotope | Isotopic Mass (amu) | Natural Abundance | Fractional Abundance |
|---|---|---|---|
| Chlorine-35 | 34.96885 | 75.76% | 0.7576 |
| Chlorine-37 | 36.96590 | 24.24% | 0.2424 |
Using the formula:
Average Atomic Mass of Cl = (34.96885 amu $\times$ 0.7576) + (36.96590 amu $\times$ 0.2424)
Average Atomic Mass of Cl = 26.496 amu + 8.960 amu
Average Atomic Mass of Cl $\approx$ 35.456 amu
This calculated value (approximately 35.45 amu) is the atomic mass typically found on the periodic table for chlorine.
Key Differences: Mass Number vs. Atomic Mass
It's important to distinguish between these two related concepts:
| Feature | Mass Number | Atomic Mass (Average) |
|---|---|---|
| What it is | Protons + Neutrons | Weighted average of isotopic masses |
| Refers to | A specific isotope | An element as found in nature |
| Units | Unitless integer | Atomic mass units (amu) |
| How calculated | Summing protons and neutrons for one atom (as per reference) | Weighted average based on isotopic masses and abundances |
In summary, while the mass number (protons + neutrons) identifies a specific isotope, the atomic mass is a weighted average that accounts for the relative abundance of all isotopes of an element.
