Mole Concept - Online Tutor, Practice Problems & Exam Prep

The mole is defined as the mass of a substance containing the same number of units as atoms in 12 grams of carbon-12. It connects concepts like atoms, ions, molecules, and formula units. Avogadro's number (6.022 × 10²³) allows conversion between moles and particles. For example, 1 mole of Cl₂ equals 6.022 × 10²³ molecules. Additionally, 1 mole of a substance equals its molar mass, serving as a conversion factor. For chlorine, 1 mole weighs 70.90 grams, derived from its atomic mass of 35.45 grams per atom.

Mole Concept

So at this point, we know that the mole represents the amount of a substance. But if we were to take a look at its formal definition, we'd say that the mole is the mass of substance containing the same number of units as atoms in 12 grams of carbon-twelve isotope. And we're going to say here that the mole also acts as a way of connecting together different terms. These terms include atoms, ions, molecules, and formula units. Some of these terms we've seen before, some of them are new. So let's investigate each of them. An atom, remember, we've used the term atom interchangeably with neutral elements. So we're gonna say here an atom is a single element with no charge. Ion, an ion is also a single element, but it possesses a charge. That charge can be either positive or negative. A molecule we're gonna find as a compound with 2 or more nonmetals together. Those nonmetals could be the same or they could be different from one another. And then finally, formula units. A formula unit is just a general term for a compound composed of a metal and nonmetal. So as we delve deeper into the mole concept, just realize that the mole kind of acts as a bridge that connects together these different ideas when it comes to the elements and how they arrange with one another.

Mole Concept Example 1

So in this example question, it says, which of the following compounds would not be associated with the term formula unit? So remember, a formula unit is just a general term we use in terms of a compound that possesses a metal plus nonmetal. So we must look for the choice that does not contain a metal with a nonmetal. If we look at option A, we have Na, C, and O. Na is a metal (sodium). Carbon and oxygen are both nonmetals. So, this would represent a compound that could be termed a formula unit. Next, we have this long compound here, but again, it contains sodium, and all these elements here are nonmetals. So, this could also use the term formula unit. However, option C has B, which is boron (a metalloid), and it has F, which is fluorine (a nonmetal). So, this would be our answer. We cannot associate the term formula unit with this compound because it contains a metalloid and not a metal. And finally, we have Mn and Cl. Mn is manganese, which is a transition metal, and Cl is chlorine, which is a nonmetal. So, this could be associated with the term formula unit. Therefore, out of all the choices, only option C couldn't be associated with the term formula unit.

Mole Concept

Now in order to convert between moles and particles, we have to utilize what's called Avogadro's number. Avogadro's number states that 1 mole of a substance is equal to 6.022×1023 particles. This value of 6.022×1023, that is Avogadro's number. When we say the term particles, it's just a general term used for ions, atoms, molecules, or formula units. If we want to combine them all into one idea, we can use the term particles.

We are going to say here that 1 mole of a substance is equal to Avogadro's number. Right? So, that would mean that 1 mole of chlorine, remember chlorine is a diatomic element in its natural form, equals 6.022×1023 molecules of Cl2. We need to realize here that this can be a conversion factor because it's combining two different units together. So we can say here that 1 mole of Cl2 is 6.022×1023 molecules of Cl2. And remember, conversion factors allow us to do the reciprocal, where we flip it. So, we could say Avogadro's number on top, moles of Cl2 on the bottom, depending on if we want units to cancel out in a certain way.

Before we move on to the next section, let's investigate this conversion factor a little more. We have one mole of chlorine, which in its natural form is Cl2. We are using the term molecules because the term molecules is used when we have a compound that has two or more nonmetals together. Chlorine is a nonmetal, and there are two of them. That's why we're using the term molecules, not using ions, atoms, or formula units. It can't be an ion because it doesn't possess a positive or negative charge. It can't be an atom, as we would only use the term atom if it was just one chlorine by itself. We can't use the term formula unit because formula units imply a metal connected to the nonmetal, which is not the case here. So, again, if we're trying to go between moles and particles, we have to utilize Avogadro's number, and we're using the term molecules here because we have two nonmetals together.

Mole Concept Example 2

So in this example question, it says, how many moles of chlorine gas are in \( 8.33 \times 10^{37} \) molecules? Alright. So to be able to do this question, we need to realize that we're trying to go from molecules to moles. Right? And to be able to do that, we're going to have to utilize the conversion factor that we have up here. Alright. So those molecules are our given amount. Remember, we're setting this up as though it is a dimensional analysis question. Although we're dealing with more concept, it still hinges on the idea of dimensional analysis, where we have our given amount, and then we need to get to our end amount, and to do that we utilize conversion factors. So if you don't quite remember the steps necessary to do this, go back and take a look at our videos on dimensional analysis. Alright. So our given amount is \( 8.33 \times 10^{37} \) molecules of Cl₂, and we need to get to our end amount which will be in moles. Moles of Cl₂. Now to be able to go from given amount to end amount, we have to utilize our conversion factor. So our conversion factor is this part up here. Now we need molecules to cancel out, so Avogadro's number in molecules have to go on the bottom. So we're going to put molecules of Cl₂ here on the bottom, and that's equal to 1 mole of Cl₂ on the top. So here molecules will cancel out, and we'll be left with moles at the end. So what you're going to do is make sure you put these in parentheses in your calculator, otherwise, you may get an incorrect answer. So it's going to be \( 8.33 \times 10^{37} \) divided by Avogadro's number. Now if you do this correctly, what you'll get as your answer at the end will be \( 1.38 \times 10^{14} \) moles of Cl₂. So that would mean that option c would be our correct answer. So again, we're setting this up as though it's a dimensional analysis question where we have our given amount, we have to know what our end amount will be, and to get from the given amount to the end amount we have to utilize a conversion factor or two. In this particular case, it was just one conversion factor that was utilized in order to get to our final answer. Okay? But keep in mind, if we're trying to go between moles and particles, meaning any one of these terms here, we're going to have to utilize Avogadro's number at some point.

Mole Concept

Just as the mole connects to particles, we can use moles as the connection to mass. Now, we're going to say here, one mole of a substance is equal to the molar mass of that substance. Remember the term molar mass, we can use molar weight, molecular weight, or molecular mass. They all mean the same thing. Here we're told that 1 mole of diatomic chlorine weighs 70.90 grams. Where does that 70.90 grams come from? Well, if you look on the periodic table, you'll see chlorine, and you'll see that underneath or above chlorine, you'll see a value of 35.45. That's the mass of 1 chlorine atom. But here we're dealing with 2 chlorine atoms, so that'd be 35.45 times 2, which gives us that value of 70.90. Now, here again, this can serve as a conversion factor in itself, where 1 mole of Cl₂ equals 70.90 grams Cl₂. And since it's a conversion factor, we can also flip it, where 70.90 grams of Cl₂ on top, and 1 mole of Cl₂ on the bottom. Remember, we do this based on if we need to cancel out certain units. So just remember the moles can serve as a bridge to connect us to the mass of an element or compound. Now that we've seen this, let's move on to our example problem.

Mole Concept Example 3

So, in this example question, it says, how many grams of chlorine gas are there in 2.34 moles? Alright. So, the 2.34 moles represents our given amount, and we have to determine what our end amount will be. What are we trying to get to? So, our end amount that we need to find is grams. Okay. So here we need to determine the grams of chlorine gas. Now, to go from the given amount to the end amount, we know we have to utilize a conversion factor. So the conversion factor we have up above is the one that we're going to use.

Let's write down our given amount of 2.34 moles of CL₂. We need to cancel moles of CL₂ so it goes on the bottom. So, just like I said earlier, you can invert your conversion factor. You do that to make sure that units cancel out. To cancel out these moles in red, I need to put these moles in blue on the bottom, and then that one mole of CL₂ is equal to 70.90 grams of CL₂. So now, moles of CL₂ cancel out and we'll be left with grams of CL₂ at the end. So when you punch that into your calculator, you should get 165.906, and out of the choices presented, b would be the best choice.

So just remember, our moles we've seen act as a bridge to connect us to particles earlier, and now we're seeing it connecting us to the mass of chlorine gas.

Mole Concept Example 4

As we stated earlier, the unit of moles can act as a bridge that connects together the other units. So here we can see that moles rise right in the middle between grams and all the terms that we collectively call particles. Now if we take a look here at this example question, it says, how many grams of Cl₂ contain 9.25×1024 molecules of Cl₂? Alright. So we're going to start out with our given amount, which is 9.25×1024 molecules of Cl₂, and we have to get to our end amount over here. Now remember, we're going to say in order to get there, we're going to have to utilize some conversion factors, and our end amount that we want to get to is grams of Cl₂. So if we take a look here, we need to get rid of molecules first. So our first conversion factor, we're going to say that we do 6.022×1023 molecules of Cl₂, and remember that connects us to moles, so for every 1 mole of Cl₂. Then we're going to realize that molecules are out. Now we have moles. We're not there yet though because we don't want moles at the end as our answer. We want grams. So our second conversion factor, which we saw earlier, would be that 1 mole of Cl₂ here on the bottom is 70.90 grams of Cl₂ here on the top. Here, our moles would cancel out, and we'd have our answer in grams. Now when you do the math, make sure to put these in parentheses. Otherwise, your calculator may give you the incorrect answer. So, we do 9.25×1024 times 70.90 divided by Avogadro's number here. Now if you did this correctly, what you get initially is 1089.048 grams of Cl₂. But realize at this point we have 3 significant figures in our original value given to us, so we need this answer also to be in 3 significant figures. So we'd write that in scientific notation as 1.09×103 grams of Cl₂. So here, writing it in scientific notation gives us our 3 significant figures, which we had in the original question. 9.25×1024 given to us has 3 significant figures, so our answer must have 3 significant figures.

If a sample of sodium chloride, NaCl, contains 73.1 kg, what is its number of formula units?

• A. 6.12 x 10²⁵ formula units
• B. 8.42 x 10²⁵ formula units
• C. 1.09 x 10²⁶ formula units
• D. 7.53 x 10²⁶ formula units

Calculate the number of oxygen atoms found in 783.9 g NiCl₂ • 6 H₂O.

• A. 1.192 x 10²⁵ O atoms
• B. 2.314 x 10²⁵ O atoms
• C. 5.833 x 10²⁶ O atoms
• D. 8.849 x 10²⁶ O atoms

If the density of water is 1.00 g/mL at 25°C, calculate the number of water molecules found in 1.50 x 10³ µL of water.

• A. 3.99 x 10²¹ molecules
• B. 5.01 x 10²² molecules
• C. 7.41 x 10²³ molecules
• D. 6.29 x 10²⁴ molecules

A cylindrical copper wire is used for the fences around a house. The copper wire has a diameter of 0.0750 in. How many copper atoms are found in 5.160 cm piece? The density of copper is 8.96 g/cm³. (V = π • r² • h)

• A. 2.01 x 10²² Cu atoms
• B. 6.36 x 10²¹ Cu atoms
• C. 9.91 x 10²¹ Cu atoms
• D. 1.25 x 10²² Cu atoms

The density of the sun is 1.41 g/cm³ and its volume is 1.41 x 10²⁷ m³. How many hydrogen molecules are in the sun if we assume all the mass is hydrogen gas?

• A. 5.94 x 10⁵⁶ H₂ molecules
• B. 8.13 x 10⁵⁷ H₂ molecules
• C. 3.04 x 10⁵⁸ H₂ molecules
• D. 7.46 x 10⁵⁹ H₂ molecules

Here’s what students ask on this topic:

What is the mole concept in chemistry?

The mole concept in chemistry is a fundamental principle that defines the amount of a substance. One mole is the mass of a substance containing the same number of units as there are atoms in 12 grams of carbon-12. This number is known as Avogadro's number, which is 6.022 × 10²³ particles. The mole serves as a bridge connecting various chemical concepts such as atoms, ions, molecules, and formula units. It allows chemists to convert between the mass of a substance and the number of particles it contains, facilitating calculations in chemical reactions and stoichiometry.

How do you convert between moles and particles using Avogadro's number?

To convert between moles and particles, you use Avogadro's number, which is 6.022 × 10²³ particles per mole. For example, to find the number of particles in 2 moles of a substance, you multiply the number of moles by Avogadro's number: $2\times 6.022\times {10}^{23}$. Conversely, to find the number of moles from particles, you divide the number of particles by Avogadro's number: $\frac{\mathrm{particles}}{6.022\times {10}^{23}}$.

What is Avogadro's number and why is it important?

Avogadro's number is 6.022 × 10²³ particles per mole. It is a fundamental constant in chemistry that allows for the conversion between the number of particles (atoms, ions, molecules, or formula units) and the amount of substance in moles. This number is crucial because it standardizes the quantity of particles in a mole, making it easier to perform calculations involving chemical reactions, stoichiometry, and the determination of molecular and formula masses.

How is the molar mass of a substance determined?

The molar mass of a substance is determined by summing the atomic masses of all the atoms in its chemical formula. For example, the molar mass of chlorine gas (Cl₂) is calculated by adding the atomic masses of two chlorine atoms. Each chlorine atom has an atomic mass of 35.45 grams per mole, so the molar mass of Cl₂ is 35.45 × 2 = 70.90 grams per mole. This value can be used as a conversion factor to relate the mass of the substance to the number of moles.

What is the relationship between moles and molar mass?

The relationship between moles and molar mass is that one mole of a substance is equal to its molar mass in grams. The molar mass is the mass of one mole of a substance and is expressed in grams per mole (g/mol). For example, one mole of chlorine gas (Cl₂) has a molar mass of 70.90 grams. This relationship allows chemists to convert between the mass of a substance and the number of moles, facilitating calculations in chemical reactions and stoichiometry.