How To Convert Grams To Molecules

Whenever you convert from one unit to another, you need a conversion factor. For example, when you convert from minutes to seconds, you use the fact that in one minute there are 60 seconds. You need to know the same kind of conversion factors when trying to convert grams of a substance into molecules of that substance.

In finding the conversion factor to get from grams to molecules, you first need to take a look at molar mass. Molar mass tells you the mass of a substance in one mole (abbreviated mol) of that substance. The key unit here is mol.

Why? Avogadro's number (6.022x10²³) tells you how many molecules of a substance are in one mol of that substance. That means the conversion factor between mol and number of molecules is:

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

Given this information, you have a way to convert from mol to molecules.

But what about from grams to a mole?

As mentioned above, the molar mass is the mass of a substance in one mol of a substance. This means that you can always find how many grams there are in a mol of any substance by finding the molar mass. For example, the molar mass of water (H₂O) is 18.02 grams per mol. This means there are 18.02 grams of water in one mol of water.

Given the different conversion factors mentioned above, there is enough information to convert from grams to molecules. You just have to be careful to set it up so that units cancel correctly and that you are left with molecules of the substance at the end.

Say your chemistry lab instructor asks you: How many molecules of methane (CH₄) are there in 105 grams of methane?

Where would you begin?

Knowing that the conversion factor to get to molecules involves the number of mols, the first conversion you need to do from grams is to mol. For this, you need to know the molar mass of methane, which is 16.04 g/mol.

\(105g \enspace CH_4\Biggl(\dfrac{1 mol\enspace CH_4}{16.04g\enspace CH_4}\Biggr)=6.55mol\enspace CH_4\)

Now, you know that in 105 g of methane there are 6.55 mol of methane. Next, you can make use of Avogadro's number to find the number of molecules of methane in 6.55 mol of methane.

\(6.55mol\enspace CH_4\Biggl(\dfrac{6.022\times10^{23}\enspace molecules\enspace CH_4}{1\enspace mol\enspace CH_4}\Biggr)=3.94\times 10^{24}\enspace molecules\enspace CH_4\)

This means that in 105 grams of methane, there are 3.94x10²⁴ molecules of methane. It's hard to even comprehend a number that big!

You can take this kind of dimensional analysis one step further by asking how many atoms of a particular element in a compound there are in some mass of that compound. For example, how many atoms of nitrogen are there in imidazole (C₃H₄N₂)?

You'll need another conversion factor! The conversion factor here is how many nitrogen atoms are there per molecule of imidazole? The molecular formula has the answer! There are two nitrogen atoms in one molecule of imidazole.

Say you have 21 grams of imidazole. How many atoms of nitrogen are there in that 21 grams of imidazole? You will need the following conversion factors: molar mass (68.077 g/mol, the number of molecules per mol, and the number of nitrogen atoms in one molecule (2).

Here's how to set it up:

\(21g\enspace C_3H_4N_2\enspace CH_4\Biggl(\dfrac{1 mol\enspace C_3H_4N_2}{68.077g\enspace C_3H_4N_2}\Biggr)\Biggl(\dfrac{6.022\times10^{23}\enspace molecules\enspace C_3H_4N_2}{1\enspace mol\enspace C_3H_4N_2}\Biggr)\Biggl(\dfrac{2\enspace atoms\enspace N}{1\enspace molecule\enspace C_3H_4N_2}\Biggr)=3.72\times 10^{23}\enspace atoms\enspace N\)

This means that in 21 grams of imidazole there are 3.72x10²³ atoms of nitrogen.

Always remember to think about conversion factors and the units you want to end up with!