Moles and Molarity: Counting and Chemistry from Donuts to Soap

Lisa D'Agostino
1 December 2017

Above: A mole holding the number of atoms or molecules in a mole.
Mole Photo © fihu modified by Andi

A dozen donuts in a box. (photo by PunkToad)

Imagine you are working in a donut shop. A customer comes in and asks you for a dozen donuts. There are twelve to a dozen, so you count out twelve donuts. Very quickly, you are finished serving the customer.

Later, another customer comes in with an unusual order. He doesn't want a standard box of twelve donuts. He wants a special order of twenty-four donuts decorated with ten thousand sprinkles to celebrate having ten thousand followers on Instagram.

This is a bit of an outlandish request, but your manager says to do it.

So, there you are in the donut workshop counting out individual sprinkles. By sprinkle 110, you start to think there has to be a better way. An idea occurs to you: "Why not use the kitchen scale to do the counting for me?"

You take the 110 sprinkles you've already counted and put them on the scale. It reads reads 0.19 grams. Now that you know how much 110 sprinkles weigh, you can calculate how much 10,000 sprinkles will weigh.

(0.19 g)/(110 sprinkles) x 10 000 sprinkles = 17.27 g of sprinkles

You carefully weigh out 17.27 grams of sprinkles. You’re pretty pleased with with how much time you have saved by not counting sprinkles!

Scientists use a similar method to determine how many atoms or molecules there are in a substance. They have to do this to combine suitable amounts of different chemicals for reactions to make new chemicals. Unlike sprinkles, it’s physically impossible to simply count atoms or molecules. They’re just too small!

To overcome this, scientists have a quantity that connects amounts of substances people can easily measure with numbers of atoms or molecules. This is similar to the kitchen scale at the donut shop.  Donuts typically come by the dozen, and there are 12 units in a dozen. Similarly, atoms and molecules can be measured by the mole, and there are 602 200 000 000 000 000 000 000 units per mole.

You're probably thinking, “That’s a lot of zeros!” And you’re right! To use large numbers like this, people use scientific notation. This is a way of writing a large number in a shorter way. It reduces the chances of making a mistake!

To use scientific notation:

  • count from the decimal place in the number until there is only one digit remaining to the left
  • move the decimal to this location
  • multiply by 10 to the power of the number you counted to
602 200 000 000 000 000 000 000 per mole = 6.022×〖10〗^23

So, the scientific notation used to calculate a mole is 6.022 x〖10〗^23.

Now, let's get an idea of how big a mole is by figuring out the mass of a mole of sprinkles:

(0.19 g)/(110 sprinkles) x  6.022 x〖10〗^23   sprinkles/mole = 1.04 x〖10〗^21   g/mole   x (1 kg)/(1000 g) = 1.04 x〖10〗^18   kg/mole

  • 110 sprinkles had a mass of 0.19 grams
  • 6.022 x〖10〗^23   is the number of objects in a mole
  • 1.04 x〖10〗^21   g/mole is the mass of a mole of sprinkles in grams
  • (1 kg)/(1000 g) is the conversion from grams to kilograms. There are 1000 grams in a kilogram
  • 1.04 x〖10〗^18   kg/mole is the mass of a mole of sprinkles in kilograms

This mole of sprinkles is over 260,000 times the mass of food produced for human consumption each year on Earth! So, you are never going to see a mole of sprinkles.

Did you know? The number of unit in a mole is so large that if all the people who have ever lived did nothing but count grains of wheat, they would not be able to count to a mole of grains of wheat.

The Tiffany Diamond in Bird on a Rock setting (photo by Shipguy)

But atoms and molecules are much smaller than sprinkles! The mole exists to help scientists deal with such tiny particles. For example, diamonds are made of carbon. A mole of carbon atoms has a mass of about 12 grams. The Tiffany Diamond is a famous yellow diamond weighing about 26 grams. This is more than two moles of carbon. So, a mole of atoms (in this case, carbon) is a reasonable quantity for people to measure.

The number of particles in a mole, 6.022x1023 per mole, is often called Avogadro's constant or Avogadro’s number. It is named after Amedeo Avogadro, an Italian physicist.

So when would anyone use Avogardo’s constant? Likely when making a solution, which involves many chemical reactions. When performing a reaction, you combine appropriate numbers of molecules of each chemical that you base on the number of moles required.

Moles are often abbreviated as mol. To determine how much of a solution to use, chemists use molarity. That’s the number of moles of a chemical in a litre of solution.

A concentration of 1 mole in 1 litre is called 1 molar and abbreviated 1 M or mol/L.

To see this in action, let’s imagine you were a chemist trying to make soap. You’d need to react  vegetable oil or animal fat with sodium hydroxide to produce soap. Imagine you had measured some oil and determined it contained 0.2 moles of a type of fat molecule called triglycerides.

In the soap making reaction, 1 mole of triglyceride reacts with 3 moles of sodium hydroxide. How much 12 molar sodium hydroxide solution would be needed to react with this vegetable oil containing 0.2 moles of triglycerides?  

A bar of soap made from olive oil. (photo by Tommi Nummelin)

Step One: Calculate moles of sodium hydroxide needed

Multiply the moles of triglycerides needed by the ratio of reactants (the number of moles of sodium hydroxide divided by the 1 mol of triglycerides)

0.2 mol of triglyceride x (3 mol of sodium hydroxide)/(1 mol of triglycerides) = 0.6 mol of sodium hydroxide

Step Two: Calculate Volume of 12 molar sodium hydroxide needed

Number of moles = molarity x volume

Rearrange this to find the formula for calculating volume:

Volume = number of moles / molarity

= 0.6 mol of sodium hydroxide / 12  mol/L = 0.05 L of 12 molar sodium hydroxide

Step Three: Convert litres to millilitres

For small amounts, like those used in making soap, millilitres is a more useful measurement than litres. Remember, 1L = 1000ml

0.05 L x 1000 mL/L = 50 mL

50 mL of 12 molar sodium hydroxide would be required.

That was a lot of information! Let’s sum up the key points:

  • A mole is a specific, very large number of things used in describing numbers of very tiny atoms or molecules.
  • In chemistry, knowing how many moles there are is important for performing reactions, such as making soap.
  • Concentrations in molarity or moles in a litre can help you determine the amount of a solution needed.

Did you know? October 23rd (10/23!) from 6:02 am to 6:02 pm is Mole Day. It’s a day to celebrate chemistry!

Learn more!

Avogadro's Number
The Editors of Encyclopædia Britannica, Encyclopædia Britannica

Chemistry: The mole
Higher Bitesize, BBC

Mole Day
American Chemical Society

Lisa D'Agostino

lisa d'agostino
I am originally from southeastern Alberta. While completing an undergraduate degree in chemistry at the University of Alberta, I worked on several research projects involving analytical separations and infrared spectroscopy. Next, while studying for a master’s degree in analytical chemistry at McMaster University, I developed a method for analyzing metabolites associated with oxidative stress. Most recently, I completed a PhD in environmental chemistry at the University of Toronto, where my research focused on fluorinated contaminants in firefighting foams. In addition to research, I enjoy knitting, running and improv comedy.

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