The average atomic mass is not a direct measure of a single atom. This mass is the average mass per atom of a general sample of a particular element. If you could calculate the mass of a single billionth of an atom, you could calculate this value in the same way as you would any other average. Fortunately, there is an easier way to calculate atomic mass, which is based on known data from the rarities of different isotopes.
Step
Part 1 of 2: Calculating the Average Atomic Mass
Step 1. Understand isotopes and atomic masses
Most elements occur naturally in a variety of forms, called isotopes. The mass number of each isotope is the number of protons and neutrons in its nucleus. Each proton and neutron weighs 1 atomic mass unit (amu). The only difference between two isotopes of an element is the number of neutrons per atom, which affects the atomic mass. However, the elements always have the same number of protons.
- The average atomic mass of an element is affected by variations in the number of its neutrons, and represents the average mass per atom in a general sample of an element.
- For example, elemental silver (Ag) has 2 naturally occurring isotopes, namely Ag-107 and Ag-109 (or 107Ag and 109Ag). Isotopes are named based on their "mass number" or the number of protons and neutrons in an atom. This means, Ag-109 has 2 more neutrons than Ag-107 so its mass is slightly larger.
Step 2. Note the mass of each isotope
You need 2 types of data for each isotope. You can find this data in textbooks or internet sources such as webelements.com. The first data is the atomic mass, or the mass of one atom of each isotope. Isotopes that have more neutrons have a greater mass.
- For example, the silver isotope Ag-107 has an atomic mass of 106, 90509 high school (atomic mass unit). Meanwhile, the isotope Ag-109 has a slightly larger mass, namely 108, 90470.
- The last two decimal places may vary slightly between sources. Do not include any numbers in parentheses after the atomic mass.
Step 3. Write down the abundance of each isotope
This abundance indicates how common an isotope is in terms of a percentage of all the atoms that make up an element. Each isotope is proportional to the element's abundance (the greater the abundance of an isotope the greater the effect on the average atomic mass). You can find this data in the same sources as atomic mass. The abundance of all isotopes should be 100% (although there may be a slight error due to rounding errors).
- The isotope Ag-107 has an abundance of 51.86%, while Ag-109 is slightly less common with an abundance of 48.14%. This means, the general sample of silver is composed of 51.86% Ag-107 and 48.14% Ag-109.
- Ignore any isotopes whose abundance is not listed. Isotopes like these do not occur naturally on Earth.
Step 4. Convert the abundance percentage to a decimal number
Divide the abundance percentage by 100 to get the same value in decimal numbers.
In the same problem, the abundance number is 51.86/100 = 0, 5186 and 48, 14/100 = 0, 4814.
Step 5. Find the weighted average of the atomic masses of the stable isotopes
The average atomic mass of an element with a number of isotopes n is equal to (massisotope 1 * abundanceisotope 1) + (massisotope 2 * abundanceisotope 2) + … + (massn isotope * abundancen isotope . This is an example of a "weighted average", which means, the more mass found (the greater the abundance) the greater the effect on the result. Here's how to use the above formula on silver:
-
Average atomic massAg = (massAug-107 * abundanceAug-107) + (massAg-109 * abundanceAg-109)
=(106, 90509 * 0, 5186) + (108, 90470 * 0, 4814)
= 55, 4410 + 52, 4267
= 107, 8677 high school.
- Look at the elements in the periodic table to check your answer. The average atomic mass is usually listed below the element symbol.
Part 2 of 2: Using Calculation Results
Step 1. Convert mass to atomic number
The average atomic mass shows the relationship between mass and atomic number in a general sample of an element. This is useful in chemistry laboratories because calculating the atomic number directly is nearly impossible, but calculating its mass is fairly easy. For example, you could weigh a sample of silver and estimate that every 107.8677 amu of its mass contains 1 atom of silver.
Step 2. Convert to molar mass
The atomic mass unit is very small. Thus, chemists generally weigh samples in grams. Fortunately, this concept was defined to make conversion easier. Simply multiply the average atomic mass by 1 g/mol (molar mass constant) to get the answer in g/mol. For example, 107.8677 grams of silver contains an average of 1 mole of silver atoms.
Step 3. Find the average molecular mass
Since a molecule is a collection of atoms, you can add up the masses of the atoms to calculate the molecular mass. If you use the average atomic mass (not the mass of a specific isotope), the result is the average mass of molecules found naturally in the sample. Example:
- The water molecule has the chemical formula H2O. So, it is composed of 2 hydrogen atoms (H) and 1 oxygen atom (O).
- Hydrogen has an average atomic mass of 1.00794 amu. Meanwhile, oxygen atoms have an average mass of 15,9994 amu.
- Molecular mass H2The mean O is equal to (1.00794)(2) + 15.9994 = 18.01528 amu, equivalent to 18.01528 g/mol.
Tips
- The term relative atomic mass is sometimes used as a synonym for average atomic mass. However, there is a slight difference between the two because relative atomic mass has no units, but represents mass relative to a C-12 carbon atom. Provided you use atomic mass units in your average mass calculation, these two values are essentially identical.
- With a few special exceptions, the elements to the right of the periodic table have a greater average mass than the elements to the left. This can be an easy way to check if your answer makes sense.
- 1 atomic mass unit is defined as 1/12 the mass of one C-12 carbon atom.
- The abundance of the isotopes is calculated based on samples that occur naturally on Earth. Unusual compounds such as meteorites or laboratory samples may have different isotope ratios, and as a result, different average atomic masses.
- The number in parentheses after the atomic mass represents the uncertainty of the last digit. For example, an atomic mass of 1.0173 (4) means that a general sample of atoms has a mass in the range 1.0173 ± 0.0004. You do not need to use this number unless asked to in the problem.
- Use the average atomic mass when calculating masses involving elements and compounds.
