# How To Calculate Molar Mass

Imagine you want to perform a chemical reaction. In order to do so, you will probably need to consult the reaction’s chemical equation. These expressions show which reactants are needed to produce a specific product. Furthermore, they indicate the amount needed of each reactant to obtain a certain amount of product.

These amounts are shown in moles, a unit that refers to a certain number of atoms or molecules. Nevertheless, chemical compounds are usually measured in grams or milliliters. So, how do you determine the correct amounts to use for your reaction?

This is done using each reactant’s molar mass. Let’s learn what this basic concept is about and the critical role it plays when implementing chemical reactions.

## How to calculate molar mass

The molar mass is calculated by measuring the mass and the number of moles in a sample of the substance of interest, and then dividing both amounts:

Where m is the mass, n the number of moles and M the resulting molar mass.

## What is the molar mass

Almost all matter on Earth is made of atoms. These are very small entities which are, in turn, made of even smaller particles: protons, neutrons and electrons. These are called subatomic particles, and each one has their own characteristics, such as electric charge and mass.

For example, all protons are positively charged, while all electrons are negatively charged. Neutrons, as the name implies, are electrically neutral. Furthermore, protons have a mass of 1,67×10^-27kg, very similar to that of neutrons (1,675×10^-27kg). The smallest of the subatomic particles is the electron, with a mass of 9,11×10^-31kg.

All protons are the same, as are neutrons and electrons. So, how is it possible that different kinds of atoms exist —like the hydrogen, carbon and oxygen atoms that make up all living beings on the planet—, if they are made of the same subatomic particles? The answer is simple: the number of protons and neutrons that constitute the atom’s nucleus form the different elements.

For example, all of the oxygen atoms in the universe have 8 protons. Depending on the number of neutrons that accompany them, different types of oxygen atoms are produced. These are called oxygen isotopes, and the most common ones are oxygen-16, oxygen-17, and oxygen-18. The number next to the element’s name indicates the total number of particles in the nucleus.

Since all oxygen atoms in the universe must have 8 protons to be called so, the three most common oxygen isotopes therefore have 8, 9 and 10 neutrons in their nuclei, respectively. Protons and neutrons sum, in these three cases, 8+8 = 16, 8+9 = 17, and 8+10 = 18, respectively. Their names can also be written as 16O, 17O and 18O. Lastly, the number of electrons in an atom depends on its total charge, but it will tend to match the number of protons so the atom remains electrically neutral.

Since different numbers of protons, neutrons and electrons come together to build an atom, the resulting mass of samples of different elements, made of the same number of atoms, will be different. Let us use an example to understand this better:

Imagine we take a sample of 10 hydrogen-1 atoms. These are called protium atoms, which is a hydrogen isotope with just 1 proton and no neutrons in its nucleus. In this sample you can find a total of 10 protons and 10 electrons. Since the mass of protons is over 1800 times bigger than that of electrons, we can ignore the latter. Those 10 protons present in our sample account for a total mass of  1,67×10^-26kg. Now, if we prepare a sample of 10 oxygen-16 atoms, we would have a total mass of 26,8×10^-26kg, since the number of protons and neutrons is bigger than in the case of our hydrogen-1 sample. Go ahead and try to do the calculation yourself!

The difference in mass between samples of the same number of atoms of different elements is a consequence of the different amounts of subatomic particles that build up each nucleus. This characteristic is what gives different substances different volumes, even if they have the same mass.

Think about our previous example: if we prepare hydrogen-1 and oxygen-16 samples of equal mass, the latter will definitely occupy more space, and will therefore have a greater volume.

Keep in mind that we have been discussing mass and not weight! Mass is the amount of matter present in a sample of any substance. For example, a nitrogen atom has more mass than a hydrogen atom because there are 7 protons in the former and only 1 in the latter. On the other hand, weight is a force that arises from the gravitational attraction between the Earth and the mass in the sample.

We tend to mix up both concepts because of language: it is very common to hear things like “that car weighs 1000 kgs”. Kilograms are units of mass, and not weight. Nevertheless, we are used to experiencing weight as a function of the amount of mass: the more mass, the greater the weight. Although this is correct, it is not completely precise. Just to keep in mind!

We have established that the mass of a sample depends on the atomic species that constitute it. We now know that, the more atoms we have, the greater the resulting mass will be. This also applies for molecules: the greater the number of molecules in a sample, the bigger its mass will be. Actually, the relation between the number of atoms or molecules and the resulting mass is constant for any given substance, and is called its molar mass.

Molar mass is the ratio between the mass of a sample and the number of atoms or molecules in it. It is defined as shown in equation 1. Now, how do we measure the number of atoms or molecules in a sample? If we could count them one by one, given that they are so small, we would end up with an immensely big number. This is what we use moles for.

A mol is a specific number of constituent particles, which can be atoms or molecules. It equals 6.02 x 10^23 particles. Sample amounts of a substance are usually expressed in terms of moles or fractions of them. For example, when we say we have 1 mol of oxygen, we mean we have 6.02 x 10^23 atoms of oxygen. Similarly, if we say we have 1 mol of carbon dioxide, we mean we have 6.02 x 10^23 molecules of CO2.

In consequence, a substance’s molar mass has units of kg/mol or g/mol. This basic concept tells us right away how much mass is added to a sample for each mol in it, or similarly, how much mass we would find in 1 mol of any substance.

This is very useful when performing chemical reactions, since it allows you to determine the required amounts based on their chemical equations. This is done by multiplying the stoichiometric coefficient of each chemical compound with its respective molar mass:

Where m is the chemical compound’s mass in grams, M its molar mass in g/mol and n its stoichiometric coefficient in the chemical equation.

## Difference between molar mass and molecular mass

Although their names are similar, molar mass and molecular mass refer to slightly different concepts. Molar mass relates the mass of a given substance to the number of atoms or molecules in it, measured in moles. Since every element can have several isotopes, the molar masses that are usually found in periodic tables are calculated using each atom’s standard atomic weight.

The standard atomic weight (Ar) of an element is the weighted average of the masses of each of their existing isotopes, where the weights used to calculate it come from their abundance on Earth. Let’s use an example to grasp this concept: silicon has 3 common isotopes: silicon-28, silicon-29, and silicon-30. Of all silicon on Earth, 92,23% is silicon-28, 4,68% is silicon-29 and 3,09% is silicon-30.

Each silicon isotope has a slightly different mass due to the difference in the number of neutrons present in their nuclei. Since atomic masses are so small, they are usually expressed in units called Dalton, also written as u, instead of kilograms. 1 Dalton equals 1/12 of the mass of a carbon-12 atom at rest, which equals 1,66×10^-27kg. The three most common silicon isotopes have atomic masses of 27,98 u, 28,98 u, and 29,97 u, respectively.

In order to calculate silicon’s standard atomic weight, which is then used to calculate its molar mass, we need to calculate the weighted average of the isotopes’ individual atomic masses:

Look at the following summary table, it might come in handy to understand the calculation:

The molar mass of an element is therefore calculated by averaging the masses of all of its existing isotopes on Earth, taking their abundances into account. When this parameter is used to calculate the mass of a given number of moles of any element or compound, it only provides an approximate value. This is because at no point it is specified which isotopes are present and in which amount in the sample.

On the other hand, the molecular mass of a chemical compound provides a more precise value for a molecule’s mass, since it takes into account the specific isotopes that constitute it. Nevertheless, this parameter refers to individual molecules’ masses measured in Dalton, and not to the bulk mass of a sample made of billions of molecules.

For example, a molecule of CO2 made of one carbon-12 atom and two oxygen-16 atoms has a molecular mass of 12 u + 2 x 15,99 u = 43,98 u. On the other hand, a molecule made of a carbon-14 atom and two oxygen-16 atoms has a molecular mass of 14 u + 2 x 15,99 u = 45,98 u, which is slightly higher than the first one due to the extra neutrons present in the carbon-14 nucleus.

## How to use molar mass

Molar mass is a very useful parameter when performing chemical reactions because it allows you to convert the number of moles of a certain substance into grams of said substance.

Elements’ molar masses are usually found in most periodic tables. Since it refers to the mass per mol of an element, a molecule containing several elements will have a molar mass equal to the sum of each element’s molar mass. For this, the total number of atoms of each element in the molecule need to be taken into account.

For example, a carbon dioxide molecule is made up of 1 carbon atom and 2 oxygen atoms. The former has a molar mass of 12 g/mol, and the latter a molar mass of 16 g/mol. Since there are 2 moles of oxygen atoms in every mol of carbon dioxide, the total molar mass due to oxygen is 2 x 16 g/mol = 32 g/mol. The resulting molar mass of carbon dioxide is therefore 12 g/mol + 32 g/mol = 44 g/mol.

When examining a chemical equation, one of the most important parameters in it are the stoichiometric coefficients. These indicate the amounts of reactants and products in moles. Nevertheless, chemical substances are usually measured in grams or milliliters, not in moles. This is where the molar mass comes in handy.

Consider the following chemical reaction:

You need 1 mol of Mg and 2 moles of water to produce 1 mol of magnesium hydroxide and 1 mol of hydrogen gas. In order to find the necessary amounts of the reactants in grams, you need to find their molar masses. In the case of Mg, it is 24,3 g/mol. In the case of water, the molar mass is:

Let’s say you want to prepare 2 moles of magnesium hydroxide. You therefore need to measure 2 moles of magnesium. To calculate the required amount of Mg in grams, you need to multiply the amount in moles by its molar mass.

In the case of water, the required amount is 4 moles. In grams, this equals to:

If you need a quick tool to find the molar masses of both elements and common molecules, you can use this simple molar mass calculator by The University of Sydney. Just input the chemical symbol or formula of the element or compound of interest and click “calculate” to obtain its molar mass.

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