In this explainer, we will learn how to define formula mass and calculate its value for given molecular formulas using atomic masses.
Atoms, molecules, and compounds all have mass. However, the mass of a single atom or molecule is incredibly small. The mass of a carbon-12 atom is approximately grams. In order to make this number more convenient to work with in calculations, chemists developed the unified atomic mass unit. They decided that an atom of carbon-12 weighs exactly 12 unified atomic mass units, 12 u. Unified atomic mass units (u) are similar to atomic mass units (amu). However, the atomic mass unit (amu) is defined relative to oxygen-16 and is not commonly used anymore.
The atomic mass of carbon-12 is 12 u by definition, but it also corresponds to the number of combined protons and neutrons. One atomic mass unit is approximately the mass of a single neutron or a single proton. Carbon-12 atoms have 6 protons and 6 neutrons with a mass number of 12, while the heavier isotope carbon-13 has atoms with 6 protons and 7 neutrons and a mass number of 13. The identifying number of an isotope refers to the mass number of that isotope.
Definition: Atomic Mass
Atomic mass is the mass of one atom of an element in unified atomic mass units.
Definition: Mass Number
Mass number is the sum of the protons and neutrons in the nucleus of an atom of an element.
Example 1: Determining the Mass of a Fluorine Atom in Unified Atomic Mass Units
The unified atomic mass unit (u) is defined as th of the mass of an atom of carbon-12. What is the mass of a fluorine-19 atom in unified atomic mass units?
A fluorine-19 atom has a mass of 19 unified atomic mass units. Each neutron and proton has an atomic mass of approximately 1 unified atomic mass unit, so the protons and neutrons of fluorine-19 have a mass of 19 unified atomic mass units. The “19” in fluorine-19 refers to its atomic mass, so the correct answer is 19 u.
The atomic mass for a carbon-12 atom is 12 u. If we look at some periodic tables, we will actually find that the atomic mass of carbon is given as 12.011 u. This number is the average of all of the atomic masses of the atoms in a sample of carbon. Most carbon atoms are carbon-12 atoms, but small amounts of heavier carbon-13 and carbon-14 atoms boost the average mass above 12 u. Since the ratio of these various isotopes is fixed, we can reliably use 12.011 u as the average mass of a carbon atom when looking at a sample of carbon. Often, the average atomic mass is rounded to integer values.
When atoms combine to form molecules or compounds, we can calculate the average mass of those molecules or compounds. We do so by adding together the atomic masses of the constituent atoms. For a molecular compound, we call this value the “molecular mass.” For the formula unit of an ionic compound, we call this value the “formula mass.”
Sometimes, we call these values “relative molecular mass” or “relative formula mass” using the symbol “” although with a key difference. The relative values are ratios that are unitless, while the nonrelative values use unified atomic mass units.
Definition: Relative Atomic Mass
Relative atomic mass is the average mass of one atom of an element on a scale where an atom of carbon-12 has a mass of 12.
The formula mass or molecular mass of a compound is simply the sum of the atomic masses of its constituent atoms. For example, a molecule of water contains two hydrogen atoms and one oxygen atom. According to a periodic table that uses integer values, the atomic mass of hydrogen is 1 u, while the atomic mass of oxygen is 16 u. The molecular mass of a water molecule can be calculated using the following equation:
When we combine the mass of one oxygen atom and two hydrogen atoms, we end up with 18 u, which is the molecular mass of water. Note that different periodic tables round atomic masses to different decimal places. You may see the atomic mass of hydrogen listed as 1.01, 1.008, or 1. Rounding to a different decimal place may slightly change the final answer of a calculation.
Definition: Molecular Mass
Molecular mass is the average mass of one molecule of an element or compound in unified atomic mass units.
Definition: Relative Molecular Mass
Relative molecular mass is the ratio of the average mass of one molecule of an element or compound to one-twelfth of the mass of an atom of carbon-12.
Example 2: Calculating the Relative Molecular Mass of Xenon Difluoride from Its Chemical Formula
What is the of xenon difluoride ? [, ]
To find , or the relative molecular mass of , we need to reference the periodic table to find the relative atomic masses of its constituent atoms. Then, we need to add the relative atomic masses of the atoms in the compound.
The relative atomic mass of xenon is 131. The relative atomic mass of fluorine is 19. We can use these values to calculate the relative molecular mass of the compound with the following equation:
Since relative molecular mass is a unitless value, 169 is the correct answer.
The process of calculating the mass of the compound works essentially the same way for ionic compounds, only we use the name “formula mass” instead of “molecular mass.” For example, to calculate the formula mass of sodium chloride, we need to know that the atomic mass of sodium is 23 u, while the atomic mass of chlorine is 35.5 u. The mass of the formula unit of that contains one atom of sodium and one atom of chlorine can be calculated by adding those two values together:
Thus, 58.5 u is the formula mass of sodium chloride.
Definition: Formula Mass
Formula mass is the average mass in unified atomic mass units of the formula unit of an ionic compound.
Example 3: Calculating the Relative Formula Mass of Magnesium Fluoride
What is the relative formula mass of magnesium fluoride ? [, ]
To find the relative formula mass of a compound, we need to add together the relative atomic masses of its constituent atoms. In this problem, the relative atomic masses of the elements are provided.
For magnesium, the relative atomic mass is 24, and for fluorine, the relative atomic mass is 19.
A formula unit of consists of one magnesium ion and two fluoride ions. We can calculate the relative formula mass accordingly:
Note that relative formula mass is a unitless measure. Thus, the correct answer is 62.
Example 4: Calculating the Relative Formula Mass of 1, 3, 5-Tribromocyclohexane from Its Structural Formula
The displayed formula for 1, 3, 5-tribromocyclohexane is shown below. What is its relative formula mass? Give your answer to the nearest whole number. [, , ]
To calculate the relative formula mass of this compound, we need to determine the compound’s chemical formula. Then, we need to calculate the relative formula mass by adding together the relative atomic masses of the atoms in the compound.
First, we need to find the chemical formula of the compound. We can determine this through a visual count. There is a ring of six carbon atoms in the center, nine hydrogen atoms around the outside, and another three bromine atoms around the outside. The chemical formula for this compound is .
From the periodic table, we can find the relative atomic masses of these three elements. Rounded to the nearest whole number, the relative atomic mass of carbon is 12, that of hydrogen is 1, and that of bromine is 80.
To calculate the relative formula mass, we can add together the relative atomic masses of the individual atoms in the compound by multiplying each relative atomic mass by the number of atoms of that type in the compound:
Since relative formula mass is a unitless value, the correct answer is 321.
Let us summarize what we have learned in this explainer.
- The unified atomic mass unit is th of the mass of a carbon-12 atom.
- One unified atomic mass unit approximately corresponds to the mass of a proton or a neutron.
- The atomic mass of an element is the average mass of an atom in a sample of that element.
- The molecular mass of a molecule is the combined atomic mass of its constituent atoms.
- The formula mass of an ionic compound is the combined atomic mass of the atoms that make up one formula unit of the compound.
- Relative molecular mass and relative formula mass are the same values as the nonrelative molecular and formula masses, only the relative versions are unitless instead of using unified atomic mass units.
- The symbol for relative molecular mass or relative formula mass is .