Atomic mass is the sum of all the protons, neutrons, and electrons in a single atom or molecule. The mass of an electron is so small that it can be ignored and not taken into account. Although technically incorrect, the term atomic mass is also often used to refer to the average atomic mass of all the isotopes of an element. This second definition is actually relative atomic mass, which is also known as atomic weight an element. Atomic weight takes into account the average mass of naturally occurring isotopes of the same element. Chemists must distinguish between these two types of atomic mass to guide their work – for example, an incorrect atomic mass value can lead to incorrect calculation of experimental results.
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Method 1 of 3: Reading the Atomic Mass in the Periodic Table
Step 1. Understand how to represent atomic mass
Atomic mass is the mass of an atom or molecule. Atomic mass can be expressed in standard SI mass units – grams, kilograms, etc. However, because atomic mass is very small when expressed in these units, atomic mass is often expressed in compound atomic mass units (usually abbreviated u or amu). The standard for one atomic mass unit is 1/12 of the mass of the standard carbon-12 isotope.
The atomic mass unit expresses the mass of one mole of an element or molecule in grams. This is a very useful property in practical calculations because this unit makes it easy to convert between masses and moles of quantities of atoms or molecules of the same kind
Step 2. Find the atomic mass in the periodic table
Most periodic tables list the relative atomic mass (atomic weight) of each element. This mass is almost always listed as a number at the bottom of the element grid in the table, below the chemical symbol that reads a letter or two. This number is usually represented as a decimal rather than a whole number.
- Note that the relative atomic masses listed in the periodic table are the average values of the related elements. Chemical elements have different isotopes – chemical forms that have different masses due to the addition or subtraction of one or more neutrons from the atomic nucleus. Thus, the relative atomic mass listed in the periodic table can be used as an average value for the atoms of a particular element, but no as the mass of a single atom of the element.
- Relative atomic masses, such as those found in the periodic table, are used to calculate the molar masses of atoms and molecules. Atomic mass, when denoted in amu as in the periodic table, technically has no units. However, multiplying the atomic mass by 1 g/mol gives us a quantity that can be used for the molar mass of the element – the mass (in grams) of one mole of an atom of the element.
Step 3. Understand that the values in the periodic table are the average atomic masses for an element
As already explained, the relative atomic mass listed for each element in the periodic table is the average value of all the isotopes of the atom. This average is important for many practical calculations – for example, calculating the molar mass of a molecule consisting of several atoms. However, when working with individual atoms, this number is sometimes not sufficient.
- The value in the periodic table is not an exact value for any single atomic mass because it is an average of several different types of isotopes.
- The atomic masses for individual atoms must be calculated taking into account the exact number of protons and neutrons in a single atom.
Method 2 of 3: Calculating Atomic Mass for Individual Atoms
Step 1. Find the atomic number of the element or isotope
The atomic number is the number of protons in an element and does not have a varying number. For example, all hydrogen atoms, and only hydrogen atoms, have one proton. Sodium has an atomic number of 11 because its nucleus has eleven protons, while oxygen has an atomic number of 8 because its nucleus has eight protons. You can find the atomic number of any element in the periodic table – in almost any standard periodic table. The atomic number is the number above the chemical symbol that reads one or two letters. This number is always a positive integer.
- Suppose we are working with carbon atoms. Carbon always has six protons. So, we know that the atomic number is 6. We also see in the periodic table that the box for carbon (C) has the number “6” at the top, indicating that the atomic number of carbon is six.
- Note that the atomic number of an element has no direct effect on its relative atomic mass as it is written in the periodic table. While it seems likely that the atomic mass of an atom is twice its atomic number (especially among elements at the top of the periodic table), atomic mass is never calculated by multiplying an element's atomic number by two.
Step 2. Find the number of neutrons in the nucleus
The number of neutrons can vary for atoms of a particular element. Although two atoms with the same number of protons and different numbers of neutrons are the same element, they are different isotopes of the element. Unlike the number of protons in an element which never changes, the number of neutrons in the atoms of a given element can vary, so the average atomic mass of the element must be represented as a decimal value between two whole numbers.
- The number of neutrons can be determined by determining the isotope of an element. For example, carbon-14 is a naturally occurring radioactive isotope of carbon-12. You'll often see isotopes assigned a small number at the top (superscript) before the element symbol: 14C. The number of neutrons is calculated by subtracting the number of protons from the number of isotopes: 14 – 6 = 8 neutrons.
- Suppose the carbon atom we are working with has six neutrons (12C). It is the most common isotope of carbon, making up nearly 99% of all carbon atoms. However, about 1% of carbon atoms have 7 neutrons (13C). The other types of carbon atoms, which have more or less than 6 or 7 neutrons, are very few in number.
Step 3. Add up the proton and neutron counts
This is the atomic mass of the atom. Don't worry about the number of electrons orbiting the nucleus – the combined mass is so small that in most practical cases this mass won't really affect your answer.
- Our carbon atom has 6 protons + 6 neutrons = 12. The atomic mass of this particular carbon atom is 12. However, if the atom is an isotope of carbon-13, we know that the atom has 6 protons + 7 neutrons = atomic weight of 13.
- The actual atomic weight of carbon-13 is 13,003355, and this weight is more accurate because it was determined experimentally.
- The atomic mass is almost equal to the number of isotopes of an element. For basic calculation purposes, the number of isotopes is equal to the atomic mass. When determined experimentally, the atomic mass is slightly larger than the number of isotopes due to the very small mass contribution of the electrons.
Method 3 of 3: Calculating the Relative Atomic Mass (Atomic Weight) of an Element
Step 1. Determine the isotopes present in the sample
Chemists often determine the relative isotopic proportions in a sample using a special instrument called a mass spectrometer. However, in chemistry lessons for students and college students, this information is often given to you in school tests, etc., in the form of grades that have been determined in the scientific literature.
For our purposes, let's say we're working with the isotopes carbon-12 and carbon-13
Step 2. Determine the relative abundance of each isotope in the sample
In a given element, different isotopes occur in different proportions. This proportion is almost always denoted as a percentage. Some isotopes have very common proportions, while others are extremely rare – sometimes, so rare that these proportions are barely detectable. This information can be determined through mass spectrometry or from reference books.
Suppose the abundance of carbon-12 is 99% and the abundance of carbon-13 is 1%. Other carbon isotopes do exist, but in such small quantities that they can be neglected in this example problem
Step 3. Multiply the atomic mass of each isotope by its proportion in the sample
Multiply the atomic mass of each isotope by its percentage abundance (written in decimal). To convert a percentage to a decimal, simply divide the percentage by 100. The number of percentages that have been converted to a decimal will always be 1.
- Our sample contains carbon-12 and carbon-13. If carbon-12 makes up 99% of the sample and carbon-13 makes up 1% of the sample, multiply 12 (atomic mass of carbon-12) by 0.99 and 13 (atomic mass of carbon-13) by 0.01.
- Reference books will give you percentage proportions based on all known amounts of an element's isotopes. Most chemistry textbooks include this information in a table at the back of the book. The mass spectrometer can also determine the proportion of the sample being tested.
Step 4. Add up the results
Add up the multiplication results you did in the previous step. The result of this sum is the relative atomic mass of your element – the average of the atomic masses of the isotopes of your element. When discussing elements in general, and not specific isotopes of the element, this value is used.
