Число Авогадро: моль

Since atoms are so small, and there are so many atoms in any sample of matter, scientists have established a unit of measure called the mole to count atoms.

A mole is equal to the number of carbon atoms in exactly 12 g of pure Carbon-12.

Okay, so now we know what a mole is. But how many atoms are in a mole? 1000? 3148382 million? 1 googolplex?

Techniques such as mass spectrometry have counted atoms very precisely to determine the number of atoms in a mole to be $6.02214 * 10^{23}$. In most chemistry courses, $6.022 * 10^{23}$ would be sufficient. This number is known as Avogadro's number or Avogadro's constant.

*Avogadro's number equals $6.022 * 10^{23}$. One mole of something is $6.022 * 10^{23}$ units of that substance.

(Video) The Mole

by Bozeman Science

In this video, Mr. Andersen describes the mole. You'll learn that a mole is just a number. But, it's a massive number! What's its purpose? To help us quantify chemical reactions. The video also shows you how to use the molar mass and Avagadro's number to calculate the number of particles. If you want a better understanding of the mole, this video is for you.

Right now, I'm drinking a cup of coffee. Have you ever wondered how many water molecules are in your morning mug of coffee? Maybe every morning before leaving home, you fill a water bottle. If it's a Nalgene brand, it holds one liter. How many water molecules is that? That's a great question!

Atoms and molecules are unbelievably tiny. Remember, we measure their size in angstroms. An angstrom, in scientific notation, is $10^{-10}$ meters! It takes a lot of water molecules to fill up your water bottle. But what about chemical reactions? They're impossible to observe between two atoms. We can't see or measure what's happening! To recognize a chemical reaction, we need a usable amount. So, chemists use the mole.

What is the mole?

The mole is the SI base unit for the number of particles in a substance. A particle is intentionally left vague. Why? Because it depends on what we're measuring. If we have a pure element, the particles are atoms. In a water bottle, it's water molecules. In electrochemistry, we can calculate moles of electrons! So, how many particles are in a mole? One mole equal $6.02214076\times 10^{23}$ particles. That's six hundred and two sextillion! For practical purposes, we use $6.02\times 10^{23}$. We call it Avagadro's Number.

Using the Mole

So, when do we use moles? For chemical reactions, we need a usable quantity. So, we often work in moles. For example, let's write a balanced chemical equation between hydrogen and oxygen gas.

$2H_{2(g)} + O_{2(g)} \rightarrow 2H_{2}O_{(l)}$

The coefficients in front of the numbers are the moles. So, what do we get if we react two moles of hydrogen with one mole of oxygen? We generate two moles of water. In this reaction, our mole ratio is two-one-two.

So, how do we know if we have a mole of a substance? We use the molar mass! The molar mass and the atomic mass are the same quantity. We calculate both using the mass number on the periodic table. But, they have different units. We measure the atomic mass in amu. The molar mass is in grams. So, one atom of water is 18.02 amu. One mole of water is 18.02 grams. Most often, to perform a chemical reaction, we weigh out the moles of our reactants based on the mole ratios. But what about gas reactions? It's not practical to weigh out a gas. So, we have to use volume and pressure. At STP, gasses have a molar volume of 22.4 liters per mole. What if we don't have standard conditions? We have to use the ideal gas law.

The History of the Mole

Amedeo Avagadro hypothesized the mole in 1811. Why? He wanted to explain why two different gases have the same volume at equivalent pressures and temperatures. He proposed that the two gases had an equal number of particles. But, we didn't have evidence of atoms or molecules. So, his hypothesis got ignored. It wasn't until after he died that his contributions became accepted.

Mole Calculations

You'll need to learn a few basic calculations. Thankfully, they're easy, and you'll use them in almost every chemistry class. They are examples of dimensional analysis.

Grams to Moles to Particles

The least complicated calculation is grams to moles to particles. You use the molar mass and Avagadro's number.

Let's say we had 250.00 grams of sucrose. It's molecular formula is $C_{12}H_{22}O_{11}$. How many particles do we have?

First, we need to find the molar mass.

$MM=(12\times 12.01 )+ (22\times 1.01) + (11\times 15.99) =342.23 \frac{g}{mol}$

Next, we can calculate the number of moles.

$moles= \frac{mass}{molar mass}=\frac{250.00g}{342.23\frac{g}{mol}}=0.73 moles$

Now, we can use Avagadro's number to find the number of molecules.

$0.73 moles \times 6.02\times10^{23}\frac{molecules}{mole}=4.40\times10^{23}$

Molarity

We'll also use the mole when we study solutions. A solution is a mixture where a solute dissolves in a solvent. Typically, we dissolve an ionic compound in a polar solvent like water. The amount of solute in a solvent is its concentration. The most common way we measure concentration is molarity. That's $\frac{mols\, solute}{liters\, solvent}$.

Let's do an example problem. Let's say we dissolve 30.00 grams of sodium chloride in 1.5 liters of water. What's the concentration?

First, we need to calculate the moles of sodium chloride.

$Moles=\frac{mass}{molar\,mass}=\frac{30.00grams}{58.44 \frac{g}{mol}}=0.51 mols$.

Now, we can calculate the concentration.

$Molarity=\frac{mols\, solute}{liters\, solvent}=\frac{0.51 mols}{1.5L}=0.34\frac{mol}{L}$.

Happy Mole Day!

Now you understand the mole! With that knowledge comes a great honor. You get to celebrate Mole Day. Every year chemists celebrate Mole Day on October 23rd between 6:02 am and 6:02 pm. Why October 23rd? Because, all together, it's 6:02 10/23. That looks like Avagadro's number! Many people will celebrate with a mole-shaped cake. Others like to read a translation of Avagadro's original paper. If you really enjoy mole day, you can look at the National Mole Day Foundation website. Each year they come up with a theme and resources for celebrating. Past themes include...

• May the Moles be with You.
• The Molevengers.
• Moley Potter.
• HaMOLEton.

Maybe it gets a little weird. But, I highly recommend getting your chemistry teacher to bring a cake.