# Converting Among Grams, Moles, and Number: The Mole Road

Ok, I lied. We’ll actually be going to the number of atoms or molecules as well. The Mole Road is a concept I learned in high school chemistry that can be very useful in learning how to convert back and forth among grams, moles, and number. The graphic shown below is the mole road:

## Why is this important?

The ability to do conversions with grams, moles, and number of atoms/molecules is an essential skill for chemistry and life science students. These types of conversions come up again and again throughout typical General Chemistry sequences and can be applied to limiting reagent problems, concentration problems, and much more. The gram-to-mole and mole-to-gram conversion in particular is used constantly in both academic and real world chemistry and biology.

## What is it?

“The Mole Road” shows three quantities, mass, moles, and number of atoms or molecules, and how they are related to each other by atomic/molecular weight and Avogadro’s Number. Notice that the arrows show the direction of the conversion and the operation required is given above or below the arrow.

## First Steps Down the Mole Road

Though I’ve since seen this pictured in other ways, I learned to first walk the Mole Road from left to right, going from grams to moles. The value that relates grams and moles is the **atomic weight** (if dealing with single elements) or **molecular weight** (if dealing with a molecule). (Please see my hub, Calculating Molecular Weights, if you would like a review of finding these values.)

To move from grams to moles, we’ll simply **divide grams by molecular weight**. Let’s take an example to start:

Convert 15 grams of oxygen gas (O_{2}) to moles.

24 g O_{2 }÷ (32 g / mol) = 0.75 mol O_{2}

## And back to grams!

To go from moles back to grams, all we need to do is perform the reciprocal operation - **multiply moles by molecular weight.**

0.75 mol O_{2} × (32 g / mol) = 24 g O_{2} - Success!

## Let’s tackle this number of atoms/molecules thing...

Another common problem type in General Chemistry-type courses, and the next stop on the mole road, is the conversion from moles to number of atoms/molecules. The value that relates moles and number of [stuff] is **Avogadro’s Number (6.022 × 10 ^{23})**. There are exactly Avogadro’s Number of [things] in a mole of [thing]. One mole of chairs has the same number of chairs as a mole of pencils has pencils and a mole of an element has atoms. It’s 6.022 × 10

^{23}every time. Two moles? Twice Avogadro’s Number - 1.2044 x 10

^{24}. Got it? Good!

Up above, we calculated that we had 0.75 moles of oxygen gas in 24 grams of that substance, but how many atoms of oxygen are there? We’ll find that by **multiplying the number of moles by Avogadro’s Number.**

0.75 mol O_{2} × (6.022 × 10^{23 }molecules / mol) = 4.5 × 10^{23} molecules O_{2}

(The number of digits in our answer changed due to the rules of **significant figures**.)

## Bring it back to the moles.

To go back to the amount of our substance in moles when we have the number of molecules/atoms, all we need to do is divide that value by **Avogadro’s Number.**

4.5 x 10^{23} molecules O_{2} ÷ (6.022 x 10^{23} molecules / mol) = 0.75 mol O_{2}.

Phew! It worked, and we’re done!

## Now you try! (Test Your Knowledge)

## Related Hubs from phriot

- Calculating Molecular Weights

Molecular weights are needed for all kinds of chemistry problems. Don't know how to find one? Don't worry! I'll show you how to calculate this value here with some review material and a worked-out example! - Conversions for Science Courses: Temperature, Conversion Factors, and the Metric System

Having trouble with conversions? Perhaps you're taking a General Chemistry class in college. I take you through converting step-by-step with discussion and examples!

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