# Mole Calculator

Created by Davide Borchia
Last updated: Aug 24, 2022

Moles for chemists are not only found in gardens but appear everywhere: our mole calculator teaches you everything you need to know about this concept. A mole is a fundamental quantity in chemistry, slightly challenging our understanding but of utmost importance in every aspect of that science — and not only.

• What is a mole?
• How to calculate the number of moles from grams (or any unit of mass);
• How to convert from moles to grams; and
• Convert grams to molecules and vice-versa.

And much more: keep reading to dive deep into the fundamental aspects of chemistry. Are you also interested in biology? Be sure to visit our protein molecular weight calculator, where you can learn a lot about the molecular weight of organic materials.

## What is a mole? Number of molecules, moles, and Italian scientists

We will introduce the concept of moleand gradually explain all the intricacies associated with it.

A mole is a quantity of a substance that contains exactly an Avogadro's number of molecules (or atoms).

There is a lot to unpack here: we will start with the basics.

• Molecules and atoms are the defining elements of every substance. Technically, if you can split a given amount of substance any number of times, you reach a point where you can't perform a division anymore without losing some of the properties of the substance itself. You found the fundamental unit of that substance: either an atom or a molecule.
• Each atom and molecule has a definite mass. Scientists find it difficult to work with "normal" units of mass when dealing with objects so small, so they created an appropriate unit, the dalton. A dalton is equal to $1/12$ the mass of an atom of carbon-12.

🙋 The definition we used for the mole is the official one chosen by the international bureau for weights and measurements (BIPM): it changed in 2019, so expect many books not to be up to date!

The Avogadro's number is a physical constanthence it has an exact and fixed value:

$N_{\text{A}} = 6.022 140 76\times10^{23}$

A mole of any substance contains $N_{\text{A}}$ atoms or molecules. Why does Avogadro's number have this value? It is a matter of convenience — which got lost a bit with our improved understanding of science.

Avogadro's number's value makes the mass of a molecule/atom in daltons roughly coincide with the mass of a mole of the same substance in grams. Initially, the constant had a value equal to the number of atoms in $12\ \text{g}$ of carbon-12.

With the redefinition, this equality is no longer true but remains roughly valid.

A mole of a substance, thus an Avogadro's number of atoms or molecules, has a weight equal to the molecular weight or molar mass of that substance (visit our molecular weight calculator to find out more). For example, carbon-12 has a molar mass:

$m_{\text{mol,}^{12}\text{C}}=11.999 999 9958(36) \times 10^{-3}\ \frac{\text{kg}}{\text{mol}}$

Of course, this value gets approximated to $12$.

## How do I calculate the number of moles from grams?

Why do we need to calculate the moles? After all, even in chemical reactions, it's easier to measure masses and volumes. Chemical reactions, however, don't compare these quantities directly! Chemists rarely make a gram of a substance react with a gram of another, hoping that this would give them some reference: a gram of mercury contains far fewer atoms than a gram of hydrogen. Converting grams to moles allows us to compare single atoms reacting with single atoms.

🙋 Check how moles are relevant for solutions with our molarity calculator!

To calculate the moles from grams of a substance, we need the molar mass of the substance. The formula to calculate the moles from grams is:

$n = \frac{m}{m_{\text{mol}}}$

Where we can identify:

• $n$ — The number of moles, both of molecules and atoms;
• $m$ — The mass of the substance, in grams; and
• $m_{\text{mol}}$ — The molar mass of the substance, in $\text{g}/\text{mol}$.

We can easily calculate the number of molecules/atoms knowing the number of moles of a substance:

$N = N_{\text{A}}\cdot n$

The relationship between moles and molecules makes use of Avogadro's constant.

## How to convert moles to grams — number of molecules to grams conversion

The inverse calculations are of similar neatness. If you know the number of models (or, by extension, the number of atoms or molecules), and the molar mass, you can calculate the mass of the substance with the formula:

$m = n\cdot m_{\text{mol}} = \frac{N}{N_{\text{A}}}\cdot m_{\text{mol}}$

The conversion from moles to grams is of fundamental importance in chemistry: chemical reactions don't work in terms of masses but of the number of atoms/molecules participating in the reaction.

## Bonus: how much does a mole of moles weight?

We are talking of the adorable, almost blind mammals digging holes in your garden. What do we need to calculate the mass of a mole of moles?

• The average mass of a mole (or the mass of an average mole); and
• A bit of imagination.

An eastern mole weights about $m_{\text{mole}}75\ \text{g}$ (think of a big egg). A mole of moles has a mass equal to an Avogadro's number of masses of a single mole:

\begin{align*} m &= N_{\text{A}}\cdot m_{\text{mole}} \\ &=6.022 140 76\times10^{23} \cdot 0.075\ \text{kg}\\ &=4.52\times 10^{22}\ \text{kg} \end{align*}

That is about half the mass of the Moon: Avogadro's number, even though often associated with the infinitely small, is an astronomical quantity!

Davide Borchia
Mass
g
Molecular weight
g / mol
Moles
mol
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