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The calculation of molar mass is essential to carry out any stoichiometric calculation involving the mass or volume of chemical compounds. This includes calculations related to both chemical reactions and the composition of the different types of compounds known to science.
What is molar mass?
As its name implies, the molar mass is nothing more than the mass of one mole of atoms, molecules, or formula units. That is, it represents the sum of the masses of an Avogadro number of these particles, or, what is the same, of 6,022.10 23 particles.
Molar mass is expressed in units of mass per mole or mass per mole -1 . The most commonly used units in the scientific field and in most countries that have adopted the International System of Units are g/mol.
However, there are other units that are frequently used in engineering, such as kg/mol; In countries like the United States and Liberia, where the imperial system of units is used, lb/lb-mol is often used.
Steps to Calculate Molar Mass
Calculating the molar mass is very simple. All we need is to add up the molar masses of all the atoms that make up a chemical substance. To do this, we only need a periodic table and know the chemical formula of the substance. Below are the steps necessary to calculate the molar mass of any compound or chemical substance.
Step 1: Write the chemical formula and determine what elements are present
Chemical substances, both elements and chemical compounds, can be represented by different types of chemical formulas. In the simplest case, the formula is simply an ordered list of the elements that make up the substance along with the number of atoms of each element that are present.
However, there are cases where structural formulas are presented that make it difficult to calculate the molar mass, so it is preferable to convert such structural formulas into easier-to-read molecular formulas.
Example:
The following figure shows the structural formula of sodium 2-oxopropanoate. As the structure is written, it is difficult to determine the molar mass, so the first step is to take the structural formula and determine its molecular formula.
As you can see, in this case the compound is made up of carbon, hydrogen, oxygen and sodium atoms.
Step 2: Count the number of atoms of each element present
The second important piece of information we need is the number of atoms of each type in the compound. This number is evident in cases where we have the simple molecular formula. This happens because the simple molecular formula consists precisely of a list of the symbols of each element that makes up the substance, with a subscript that indicates the number of times that said element appears in the structure. However, care must be taken with molecular formulas that have parentheses and other grouping signs, since the subscripts of these parentheses multiply all internal subscripts.
It is convenient to arrange this information in a small table to facilitate calculations later. In addition to the symbol of each element and the number of atoms of each type, we will also add another two columns and one row:
- A column for the atomic mass of each element
- Another column for the total molar mass that each element contributes to the molar mass of the compound.
- One row at the end for the calculation of the total molar mass.
Example:
In the case of sodium 2-oxopropanoate shown above, the formula is C 3 H 3 NaO 3 , so this compound contains 3 C atoms, 3 H atoms, 1 Na atom, and 3 O atoms. The table would look like this:
| Element | number of atoms | Atomic mass (relative) | Total mass per element (relative) |
| C. | 3 | ||
| h | 3 | ||
| na | 1 | ||
| EITHER | 3 | ||
| TOTAL MOLAR MASS = |
The total number of atoms is not relevant to the calculation of the molar mass, but in some stoichiometric calculations it is useful.
NOTE: Care should be taken with compound formulas containing waters of hydration. Firstly, because it is very common to forget to add the hydrogen and oxygen atoms of the water to the total number of these atoms during the calculation of the molar mass. Secondly, because hydration waters usually have a coefficient that indicates the number of water molecules present per unit of the anhydrous compound, which implies that the total number of H and O atoms present in the water must be multiplied by said coefficient to calculate the molar mass correctly.
Example:
In the case of copper (II) sulfate pentahydrate, each copper sulfate unit is associated with 5 water molecules, as shown by the complete formula: CuSO 4 ·5H 2 O. In this case, the total number of hydrogens is 5 x 2 = 10 and the total number of oxygens is 4 + 5 x 1 = 9.
Step 3: Find the atomic masses of the elements on a periodic table
The values of the respective molar atomic masses can be found in any periodic table. These actually show the relative atomic mass of each element, but this is numerically equal to the molar mass, so all you need to do is add the units of g/mol (or lb/lb-mol if you’re using the system). imperial) when placing the result of the calculations.
The periodic table lists all known elements ordered by their atomic number. Each element is in a cell that contains varying amounts of information, but almost all include the relative atomic masses somewhere. To know which data corresponds to the atomic mass, you should look at the legend, which is generally found in the blank space above the transition metals.
The following figure shows an example of this legend, highlighting the field where the relative atomic mass of each element appears on that particular periodic table.
As we can see, in this case the atomic masses correspond to the data found in the upper left corner of each cell. However, this is not always the case, so it is important to always review the legend to avoid using the wrong data.
Once all the elements we need are located, we fill in the table with the respective atomic masses.
Example
Continuing with the example of sodium 2-oxopropanoate, after adding the atomic masses, the table looks like this:
| Element | number of atoms | Atomic mass (relative) | Total mass per element (relative) |
| C. | 3 | 12,011 | |
| h | 3 | 1,008 | |
| na | 1 | 22,990 | |
| EITHER | 3 | 15,999 | |
| TOTAL MOLAR MASS = |
Step 4: Multiply and add
To find the total mass that each element contributes to the molar mass of the compound, we must multiply the atomic mass of each by the number of atoms of that type present in the formula. Once this operation is carried out, all the results are added to obtain the molar mass. At this point, the respective units are added ( g/mol or lb/lb-mol, as the case may be).
Example
In our example, this means multiplying the values in the second and third columns, placing the results in the last column, and then adding these values to get the molar mass:
| Element | number of atoms | Atomic mass (relative) | Total mass per element (relative) |
| C. | 3 | 12,011 | 36,033 |
| h | 3 | 1,008 | 3,024 |
| na | 1 | 22,990 | 22,990 |
| EITHER | 3 | 15,999 | 47,997 |
| TOTAL MOLAR MASS = | 110.044 g/mol |
Molar mass, atomic mass, molecular mass, and formula mass
Before learning how to calculate molar mass, some frequently confused related concepts should be briefly clarified. These are the concepts of atomic mass, molecular mass, and formula mass , which are often used interchangeably with molar mass. However, they are not the same.
As can be deduced from the names, the atomic, molecular, and formula mass correspond to the mass of an atom, a molecule, and a formula unit, respectively. In contrast, the molar mass represents the mass of one mole of such particles. In addition, being masses, these three variables are expressed in mass units that can be grams, kilograms, pounds or any other, although it is customary to use a special unit called the atomic mass unit.
Despite their differences, given the definition of the mole and the atomic mass unit, the latter is numerically equal to the molar mass, which represents the source of the confusion.
Atomic and molecular masses and relative formulas
At a conceptual level, talking about calculating a molar mass by adding atomic masses is a mistake. However, at a practical level it makes no difference, since molar atomic masses and atomic masses expressed in amu (atomic mass units) are numerically equal.
However, both this confusion and any potential problems with imperial units are resolved by using relative mass units instead of absolute values. These relative masses consist of the respective atomic or molecular masses divided by one-twelfth the mass of the carbon-12 isotope. This division causes units to cancel and therefore all relative masses are dimensionless and can be used in any context simply by multiplying by the absolute or molar mass of carbon-12 divided by 12.
Molar Mass Calculation Example
Calculation of the molar mass of ferric sulfate heptahydrate
Step 1: The formula of this compound is Fe 2 (SO 4 ) 3 ·7H 2 O, so it is made up of iron (Fe), sulfur (S), oxygen (O) and hydrogen (H).
Step 2: The total number of each element is:
- Faith = 2
- S = 1 x 3 = 3
- Or = 4 x 3 + 7 x 1 = 19
- H = 7 x 2 = 14
| Element | number of atoms | Atomic mass (relative) | Total mass per element (relative) |
| Faith | 2 | ||
| S | 3 | ||
| EITHER | 19 | ||
| h | 14 | ||
| TOTAL MOLAR MASS = |
Step 3: The relative atomic masses obtained from the periodic table are:
- Faith = 55,845
- S = 32,060
- OR = 15,999
- H = 1,008
| Element | number of atoms | Atomic mass (relative) | Total mass per element (relative) |
| Faith | 2 | 55,845 | |
| S | 3 | 32,060 | |
| EITHER | 19 | 15,999 | |
| h | 14 | 1,008 | |
| TOTAL MOLAR MASS = |
Step 4:
| Element | number of atoms | Atomic mass (relative) | Total mass per element (relative) |
| Faith | 2 | 55,845 | 111,690 |
| S | 3 | 32,060 | 96,180 |
| EITHER | 19 | 15,999 | 303,981 |
| h | 14 | 1,008 | 14,112 |
| TOTAL MOLAR MASS = | 525.963 g/mol |
References
CALCULATION OF THE MOLAR MASS . (2021, January 26). Course for UNAM. https://cursoparalaunam.com/calculo-de-la-masa-molar
How to calculate the Molecular Weight ? Examples and exercises . (2021, May 18). Unibetas. https://unibetas.com/molecular-weight/
Molecular weight concept . (nd). Wow. https://www.guao.org/tercer_ano/quimica/concepto_de_peso_molecular-concepto_de_peso_molecular
Examples of Molar Mass . (2015, October 18). Chemistry.NET. https://www.quimicas.net/2015/10/ejemplos-de-masa-molar_18.html
Guerra M., L. (2019). Stoichiometric reactions . UAEH. https://www.uaeh.edu.mx/docencia/P_Presentaciones/b_sahagun/2019/lgm-quiminorganica.pdf
Meyer. (nd). Safety Data Sheet – Ferric Sulfate Hydrate . Meyer Chemical Reagents. http://reactivosmeyer.com.mx/datos/pdf/reactivos/hds_1345.pdf
