How To Convert Atoms To Grams With A Calculator

It's really difficult to count the number of atoms in any measurement of material because you can't see them! You also can't simply pick up five atoms and put them on a scale to find the weight. For this reason, scientists use Avogadro's number in order to talk about atoms.

Avogadro's number is 6.022x10²³ particles, which is also known as one mole (abbreviated mol). These particles can be molecules, atoms, ions, etc. Avogadro's number tells you that there are 6.022x10²³ particles in one mole of a substance. If there is one mole of ping pong balls this means there are 6.022x10²³ ping pong balls. It also means that if there is one mole of nitrogen that means there are 6.022x10²³ atoms of nitrogen.

In other words:

\(\Biggl(\dfrac{6.022\times10^{23}\enspace molecules}{1\enspace mol}\Biggr)\)

Avogadro's number tells you the number of particles there are in one mole of a substance.

How many grams of a substance there are in one mole depends on the substance in question.

The molar mass of an element or compound is the mass per mole of that substance. This value is reported in gram/mol or g/mol. You can find the molar mass by looking at the periodic table at the number under the element name. For example, the molar mass of chlorine is 35.45 g/mol.

If you need to find the molar mass of a compound you will need to add the molar mass of the individual elements together. For example, the molar mass of water requires you to take twice the molar mass of hydrogen and add the molar mass of oxygen to get 18.02 g/mol.

Now that you know the number of particles in one mole, and how to calculate the number of grams in one mol of that substance, you can convert from atoms to grams.

Say you have 3x10²⁴ atoms of chlorine. How many grams of chlorine is that?

First, you need to begin by converting from atoms to mols.

\(3\times 10^{24}\enspace atoms\enspace chlorine\Biggl(\dfrac{1\enspace mol\enspace chlorine}{6.022\times10^{23}\enspace atoms\enspace chlorine}\Biggr)=4.98\enspace mol\enspace chlorine\)

Now that you know how many mol of chlorine 3x10²⁴ atoms is equal to, you can use the molar mass to convert from mol to grams.

\(4.98\enspace mol\enspace chlorine\Biggl(\dfrac{35.45g\enspace chlorine}{1\enspace mol\enspace chlorine}\Biggr)=176.6g\enspace chlorine\)

This means that if you have 3x10²⁴ atoms of chlorine, it is the same as having 176.6 grams of chlorine.

What about if you know how many atoms you have of an element, but the actual compound you're talking about isn't just that element? For example, let's say you know you have 5.55x10²³ atoms of oxygen, but the compound you want to find the mass of is CO₂. How would you do that?

You know that there are two oxygen atoms per CO₂ molecules. This means that for each oxygen atom you have, there is an entire CO₂ molecule. You can now use this conversion factor to get to the mass of CO₂.

Take a look:

The only difference between what was done before and this problem is the first step. You will need to figure out how many molecules of CO₂ there are:

\(5.98\times 10^{23}\enspace atoms\enspace oxygen\Biggl(\dfrac{1molecule\enspace CO_2}{2\enspace atoms\enspace oxygen}\Biggr)=2.99\times 10^{23}\enspace molecules\enspace CO_2\)

Now you can do exactly what you did before!

\(2.99\times 10^{23}\enspace molecules\enspace CO_2 \Biggl(\dfrac{1\enspace mol\enspace CO_2}{6.022\times10^{23}\enspace molecules\enspace CO_2}\Biggr)\Biggl(\dfrac{44.01g\enspace CO_2}{1\enspace mol\enspace CO_2}\Biggr)=21.9g\enspace CO_2\)

Knowing only the number of atoms of oxygen, you can find the grams of CO₂.

When converting from atoms to grams always make sure to keep track of your units!