In daily life, there are words that are implicitly defined in groups. A basketball team has five players in the court at a time; if you order a dozen of donuts, a baker might interpret it as you wanting 12 donuts; a “strike” in bowling means that you hit all 10 pins in the lane. 🎳

How does this connect to chemistry? Chemistry frequently deals with particles, atoms, molecules, and compounds, to name a few. To make life easier, chemists have devised a term called the mole instead of calling out “a million atoms” or “20 billion molecules.” This study guide will introduce what a mole is and how we can use it as a tool to navigate the language of chemistry. Woo-hoo! 🧪

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🌉 The Mole: Bridging the Microscopic and Macroscopic Worlds

Definition and Importance of the Mole

Let’s take a look at the actual definition of the mole and where it comes from:

This definition sounds too convoluted for a first-time read, don’t you think? Let’s make this definition simpler! 😵‍💫

That’s all you need to remember when defining moles!

Image Courtesy of National Institute of Standards & Technology

Learning to Convert Between Moles and Particles

To further elaborate: In chemistry, these 6.022 x 10²³ particles could be anything small: atoms, molecules, ions, or electrons. The mole serves as a connector between what we can measure (like grams or liters) and the complex world of atoms and molecules which are too tiny to count individually. See if you notice a pattern in the following examples:

• How many electrons are in a mole of electrons? 6.022 x 10²³!
• How many water molecules are in a mole of $H_2O$? 6.022 x 10²³!
• What about bananas in a mole of bananas? 6.022 x 10²³! 🍌

Let’s formalize what we’ve been talking about so far:

1. To go from moles to particles:

   • Multiply by Avogadro's number:
   $$moles * \frac{6.022*10^{23\,} particles}{mole}=number \,of\,particles$$

2. To go from particles to moles:

   • Divide by Avogadro's number:

You’ll notice in the set up above that it’s set up so that the unit at the numerator cancels out with the unit at the denominator. We call this strategy Dimensional Analysis! This technique helps you keep track of units and make sure they cancel out properly during conversions. 😁

For more information about this technique, check out our study guide all about Dimensional Analysis here.

❓Practice Question

How many atoms are in 3 moles of helium?

Our handy, dandy dimensional analysis set up will help us here! We’re going from moles (what’s given) of Helium to atoms, and our friend Avogadro will save the day.

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⚖️ Mastering Molar Mass

Let’s define a couple terms!

Molar Mass: The mass of one mole of a substance, determined from its atomic mass on the periodic table.

Image courtesy of PubChem

Looking at the periodic table above, you’ll see that oxygen (O, element #8) has an atomic mass of 15.999 g/mol. Meanwhile, magnesium (Mg, #12) has an atomic mass of 24.305 g/mol. What about lead? (That’s Pb, #82.) 207 g/mol!

🏎️ Formula Mass: The sum total mass based on combining individual elements' molar masses according to their proportion in the compound.

❓Molar Mass Practice Question

What is the mass in grams of one mole of water (H₂O)?

Therefore, one mole of water weighs 18 grams!

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🔍 Going Beyond Basic Understanding of Moles

No need to know the following concepts now, but you’ll see the concept of the mole pop up in these areas of chemistry in later units!

📊 Stoichiometry

Stoichiometry uses balanced equations to calculate quantities in chemical reactions based on mole ratios. Again, dimensional analysis comes up a lot in this area in relating moles of reactants to products (and vice versa).

❓Stoichiometry Practice Question

If you react two moles of hydrogen gas with one mole of oxygen gas, how many moles of water will be produced?

Balanced equation: $2H_2+O_2→H_2O$

For every two moles H₂ used, two moles H₂O are produced, so 2 mols $H_2$ produce 1 mol $H_2O$.

Concentration and Molarity

When we talk about how concentrated a solution is, we use molarity (M) to quantify in moles per volume (for example, moles per liter solution). A sample simple description would be that 5 moles of solute in a liter of solution is more concentrated than 3 moles of solute in that same liter of solution.

❓Molarity Practice Question

You have a solution containing five moles solute dissolved into two liters solution; what is its molarity?

Ideal Gases and Moles

When learning chemistry for the first time, we use simpler models of gases called ideal gases to avoid overcomplicating the learning process. For now, all you need to know is that Ideal gases have no volume nor intermolecular interactions; in fact, real gases behave like ideal gases at high temperatures and low pressures!

To model ideal gas behavior, we use the Ideal Gas Law to relate gas volume, pressure, temperature, and number of moles: $PV=nRT$

❓Gas Laws Practice Question

What volume will one mole of gas occupy at standard temperature and pressure (STP) conditions?

Let’s use Ideal Gas Law where R is a gas constant with the value 0.0821 L·atm/(mol·K):

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⭐ Wrapping Up Everything About Moles

You finally know what a mole is and hopefully get to appreciate its versatility across concepts like stoichiometry, molecular formulas, and ideal gases. You’ll also see moles pop up a lot when doing dimensional analysis to calculate molar masses, concentrations, and such, so it’s encouraged that you practice with a lot of questions to this study guide’s.

The more you’re familiar with the mole, the more of a head start you’ll get coming into the deeper parts of chemistry later on! 😉