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

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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:

the-mole-road-from-grams-to-moles-and-back-again

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.

the-mole-road-from-grams-to-moles-and-back-again

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 (O2) to moles.

24 g O2 ÷ (32 g / mol) = 0.75 mol O2

the-mole-road-from-grams-to-moles-and-back-again

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 O2 × (32 g / mol) = 24 g O2 - 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 × 1023). 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 × 1023 every time. Two moles? Twice Avogadro’s Number - 1.2044 x 1024. 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.

the-mole-road-from-grams-to-moles-and-back-again

0.75 mol O2 × (6.022 × 1023 molecules / mol) = 4.5 × 1023 molecules O2

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

the-mole-road-from-grams-to-moles-and-back-again

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 1023 molecules O2 ÷ (6.022 x 1023 molecules / mol) = 0.75 mol O2.

Phew! It worked, and we’re done!

Now you try! (Test Your Knowledge)

For each question, choose the best answer. The answer key is below.

  1. Convert 5.05 grams of hydrogen (single atoms) to moles.
    • 3 mol
    • 1.75 mol
    • 5 mol
  2. If I have 2.00 x 10^23 nitrogen atoms, how many moles do I have?
    • 0.750 mol
    • 0.332 mol
    • 1.030 mol
  3. How many molecules are in an 18 gram sample of glucose?
    • 0.0999 molecules
    • 6.0 x 10^22 molecules
    • 0.0999 x 10^23 molecules

Answer Key

  1. 5 mol
  2. 0.332 mol
  3. 6.0 x 10^22 molecules
calculating-molecular-weights

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Comments

Chella P. Maniquiz BSTM (7:30-12:00 TF) on February 26, 2017:

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. It also shows the conversion factors needed to interconvert between mass, number of particles, and volume of a gas. 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. The mole is at the center of any calculation involving amount of a substance.

The mole road can be very useful in learning how to convert back and forth among grams, moles, and number.

Frances Birco on February 25, 2017:

Frances Birco

BAC-II

This lecture pertains in giving us the ability to do conversions with grams, moles and number of atoms/molecules is an essential skill for chemistry and life science students. It can be applied to limiting reagent problems, concetration problems and much more. The gram-to-mole and mole-to-gram conversion in particular is used constantly in both academic and real worl chemistry and biology. In the platform of Mass communication, we converted raw materials into finish products through finding the right news to cover for the media, using our voice in a responsible way to deliver the news, having the discernment if the news might affect, hurt, or wrong should not be shared to others but it should be right, would not hurt the people emotionally and should benefit them, and lastly we report not just to talk and share what we know but convert our knowledge to action, to act and be a part of the solution to the rapid negative changes in our society.

Jerson G Maniego BSHM-4 (7:30-12:00 T\F) on February 25, 2017:

The number of atoms or other particles in a mole is the same for all substances. The mole is related to the mass of an element in the following way: one mole of carbon-12 atoms has 6.02214179 × 1023 atoms and a mass of 12 grams. In comparison, one mole of oxygen consists, by definition, of the same number of atoms as carbon-12, but it has a mass of 16 grams. Oxygen, therefore, has a greater mass than carbon. This reasoning also can be applied to molecular or formula weights.

Rafael Adriano on February 24, 2017:

In this particular lesson, the moles of the substance (lower left) will be the unknown (which will be signified by the letter x). The exact same proportion is used in the moles-to-grams conversion lesson. Then the "x" will reside in the upper left.

This proportion is a symbolic equation. When you solve a particular problem, you insert the proper numbers & units into the proper places of the symbolic equation and then you solve using cross-multiplication and division. Also, do not attach units to the unknown. Let it be simply the letter "x." The proper unit should evolve naturally from solving the proportion and cancellation of units.

Make sure you have a periodic table and a calculator handy. AS AN ABCOM STUDENT LIKE IN GATHERING INFORMATION OR DATAS WE SHOULD BE ACCURATE IN EVERYTHING THAT HAS DONE.

Mary Grace Gonzales on February 24, 2017:

BU BSTM-4 Sci 202 T-F 7:30-12:00

Moles are a standard unit of measurement in chemistry that take into account the different elements in a chemical compound.[1] Often, amounts of compounds are given in grams and need to be converted to moles. Although the conversion is simple, there are a number of important steps that need to be followed. Using this method, you can learn how to convert grams into moles.

Liwayway Memije-Cruz from Bulacan, Philippines on February 24, 2015:

I found this hub very useful for my students...