1.7.2. Average Atomic Mass

Many naturally occurring elements exist as more than one isotope. When we take into account the existence of these isotopes and their relative abundance (per cent occurrence), the average atomic mass of that element can be computed.

When we talk about elements, some of them have different versions called isotopes. Isotopes are atoms of the same element that have the same number of protons but a different number of neutrons, which gives them different masses. For example, carbon has three isotopes: carbon-12, carbon-13, and carbon-14. To find the average atomic mass of an element, you take into account how much of each isotope is naturally present in a sample of that element.

Imagine a classroom where students are taking a quiz. Some students are writing in blue pens (isotopes with one mass), while others are using black pens (isotopes with a different mass). At the end of the quiz, you want to know the average score of all students. You can't just average the number of students without considering how many used each pen color; similarly, when calculating the average atomic mass, we must consider how many of each isotope there are.

For example, carbon has the following three isotopes with relative abundances and masses as shown against each of them. isotope | relative abundance (%) | atomic mass (amu)
12C | 98.892 | 12.000
13C | 1.108 | 13.00335
14C | 0.0002 | 14.00317
From the above data, the average atomic mass of carbon will come out to be: (0.98892)(12 u) + (0.01108)(13.00335 u) + (2 x 10–12)(14.00317 u) = 12.011 u

To calculate the average atomic mass of carbon, we multiply the atomic mass of each isotope by its relative abundance (expressed as a fraction) and then add them all together. Each isotope's contribution to the average mass depends on how common it is and how heavy it is. The formula shown combines these contributions to arrive at a single average value, which in this case is approximately 12.011 atomic mass units (u).

Think of making a smoothie with different fruits. If you mix a lot of bananas (the most abundant isotope) and just a little bit of strawberries (the rare isotope), your smoothie will taste more like bananas. Each fruit's amount influences the overall flavor just as the abundance of each isotope influences the average atomic mass.

Similarly, average atomic masses for other elements can be calculated. In the periodic table of elements, the atomic masses mentioned for different elements actually represent their average atomic masses.

Every element in the periodic table has an atomic mass listed, which reflects the average mass of all the isotopes of that element found in nature. This average is calculated just like the one for carbon and is useful because it allows chemists to understand how much of an element they are working with in various reactions. Hence, what you see in the periodic table is not the mass of a single atom but an average based on the natural isotopic distribution.

Consider a box of chocolates with different types (dark, milk, white). If you take the weighted average of flavors based on how many of each type there are, you will arrive at a general idea of what flavor most pieces will have. Likewise, the atomic mass of an element gives a broad idea of what to expect when you're using it in a chemical situation.

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