How to Calculate Atomic Mass

Steps to Calculate Atomic Mass

Atomic mass
For a single atom, atomic mass is the sum of the protons and neutrons. Electrons are much smaller than protons and neutrons, so their mass isn't factored into the calculation. Science Photo Library / Andrzej Wojcicki / Getty Images

What Is Atomic Mass?

Atomic mass is the sum of the masses of the protons, neutrons, and electrons in an atom, or the average mass, in a group of atoms. However, electrons have so much less mass than protons and neutrons that they don't factor into the calculation. So, the atomic mass is the sum of the masses of protons and neutrons. There are three ways to find atomic mass, depending on your situation.

3 Ways To Find Atomic Mass

1) Look Up Atomic Mass on the Periodic Table

If it's your first encounter with chemistry, your instructor will want you to learn how to use the periodic table to find the atomic mass (atomic weight) of an element. This number usually is given below an element's symbol. Look for the decimal number, which is a weighted average of the atomic masses of all the natural isotopes of an element.

Example: If you are asked to give the atomic mass of carbon, you first need to know its element symbol, C. Look for C on the periodic table. One number is carbon's element number or atomic number. Atomic number increase as you go across the table. This is not the value you want. The atomic mass or atomic weight is the decimal number, The number of significant figures varies according to the table, but the value is around 12.01.

This value on a periodic table is given in atomic mass units or amu, but for chemistry calculations, you usually write atomic mass in terms of grams per mole or g/mol.

The atomic mass of carbon would be 12.01 grams per mole of carbon atoms.

2) Sum of Protons and Neutrons for a Single Atom

To calculate the atomic mass of a single atom of an element, add up the mass of protons and neutrons.

Example: Find the atomic mass of an isotope of carbon that has 7 neutrons. You can see from the periodic table that carbon has an atomic number of 6, which is its number of protons.

The atomic mass of the atom is the mass of the protons plus the mass of the neutrons, 6 + 7, or 13.

3) Weighted Average for All Atoms of an Element

The atomic mass of an element is a weighted average of all the element's isotopes based on their natural abundance. It is simple to calculate the atomic mass of an element with these steps.

Typically, in these problems, you are provided with a list of isotopes with their mass and their natural abundance either as a decimal or percent value.

  1. Multiply each isotope's mass by its abundance. If your abundance is a percent, divide your answer by 100.
  2. Add these values together.

The answer is the total atomic mass or atomic weight of the element.

Example: You are given a sample containing 98% carbon-12 and 2% carbon-13. What is the relative atomic mass of the element?

First, convert the percentages to decimal values by dividing each percentage by 100. The sample becomes 0.98 carbon-12 and 0.02 carbon-13. (Tip: You can check your math by making certain the decimals add up to 1. 0.98 + 0.02 = 1.00).

Next, multiply the atomic mass of each isotope by the proportion of the element in the sample:

0.98 x 12 = 11.76
0.02 x 13 = 0.26

For the final answer, add these together:

11.76 + 0.26 = 12.02 g/mol

Advanced Note: This atomic mass is slightly higher than the value given in the periodic table for the element carbon. What does this tell you? The sample you were given to analyze contained more carbon-13 than average. You know this because your relative atomic mass is higher than the periodic table value, even though the periodic table number includes heavier isotopes, such as carbon-14. Also, note the numbers given on the periodic table apply to the Earth's crust/atmosphere and may have little bearing on the expected isotope ratio in the mantle or core or on other worlds.

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