Mole Concept - Online Tutor, Practice Problems & Exam Prep

The mole is a fundamental unit in chemistry that represents a quantity of substance containing the same number of entities as there are atoms in 12 grams of carbon-12. It serves as a bridge between atoms, ions, molecules, and formula units, facilitating conversions between these forms of matter. Avogadro's number (

$6.022\times {10}^{23}\text{particles}$

) is crucial for converting between moles and particles, whether they are atoms, ions, molecules, or formula units. Additionally, the molar mass of a substance, which can be calculated from the periodic table, allows for the conversion between moles and mass. For instance, one mole of chlorine (Cl₂) has a molar mass of 70.90 grams, derived from the atomic mass of chlorine. These relationships enable chemists to quantify and convert substances in chemical reactions, emphasizing the mole's role as a central concept in stoichiometry and chemical calculations.

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 massive substance containing the same number of units as atoms in 12 grams of carbon 12 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 going to say here an atom is a single element with no charge.

An ion is also a single element, but it possesses a charge. That charge can be either positive or negative. A molecule we're going to find as a compound with two or more non metals together. Those nonmetals could be the same, or they could be different from one another.

And then finally, 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 formula unit is just a general term we're going to use in terms of a compound that possesses a metal plus nonmetal. So we just have to look for the choice that does not contain a metal with nonmetal.

If we look at option A, we have Na₂CO₃, Na is a metallic sodium. Carbon and oxygen are both non metals, so this would represent a compound that could be termed a formula unit. Next we have this long compound here, but again it has sodium in it and all these elements here are nonmetals. So this could also use the term formula unit.

See though, see has B which is boron. Boron is a metalloid and it has F which is fluorine which is a nonmetal. So this would be our answer. We could not call. We cannot associate the term formula unit with this compound because it contains a metalloid and not a metal. And then 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.

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. Now Avogadro's number says that one mole of a substance is equal to 6.022×1023 particles. Now this value here of 6.022×1023, that is Avogadro's number and we're going to say the term particles. It's just a general term that is used for ions, atoms, molecules or formula units. We talked about each of these four terms up above. If we want to just combine them all into one idea, we can use the term particles.

Now we're going to say here that one mole of a substance is equal to Avogadro's number, right? So that would mean that one mole of chlorine. And remember, chlorine is a diatomic element in its natural form equals 6.022×1023 molecules of CL₂. Now 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 one mole of CL₂ is 6.022×1023 molecules of CL₂. And remember conversion factors we can 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.

Now before we move on to the next section, just let's investigate this conversion factor a little bit more. We have one mole of chlorine. Chlorine, remember its natural form of CL₂. Why are we using the term molecules though? Remember, 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, right. So that's why we're using the term molecules. That's why we're 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. We'd only use the term atom if it was just one chlorine. By itself, we can't use the term formula unit because formula unit would mean that we need to have a metal connected to that chlorine. Because remember, a formula unit is when you have a metal and nonmetal together. 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 an 8.33 * 10 to the 37 molecules. All right. 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, all right, so that 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 mole 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 on our videos on dimensional analysis.

All right. So our given amount is 8.33 * 10 to the 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 * 10 to the 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 * 10 to the 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, OK. 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 connected the connection to particles, we can use moles as the connection to mass. Now we're going to say here 1 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 one mole of still chlorine weighs 70.90 grams. What does that 70.90g come from? Well, if you look on the periodic table, you'll see chlorine, and you'll see that underneath chlorine or above it, you'll see a value of 35.45. That's the mass of 1 chlorine. But here we're dealing with two chlorines, so that would be 35.45 * 2, which gives us that value of 70.90.

Now here again, this can serve as a conversion factor in itself, where one mole of CL₂ is 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 one 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 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. All right, 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. OK, so here we need to determine the grams of chlorine gas.

Now to go from given amount to end amount, we know we have to utilize conversion factor. So the conversion factor we have up above is the one that we're going to use. So 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. 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.

2.34 ⁢ 70.90   g   Cl 2 1   mol   Cl 2 = 165.906   g   Cl 2

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.

All right. 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 one 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 one mole of CL₂ here on the bottom is 70.90 grams of CL₂ here on the top here are moles would cancel out and we'd have our answer in grams.

Now when you do the math, make sure you put these in parentheses, otherwise your calculator may give you the incorrect answer. So we do 9.25×1024 * 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 three sig figs in our original value given to us. So we need this answer also to be in three sig figs. 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 three significant figures which we had in the original question. 9.25×1024 given to us has three sig figs. So our answer must have three sig figs.

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

Here’s what students ask on this topic:

What is the mole concept?

The mole concept is a fundamental principle in chemistry that provides a method for quantifying substances. It is based on Avogadro's number, which is $6.022\times {10}^{23}$, the number of atoms, ions, or molecules in one mole of a substance. The mole allows chemists to convert between the mass of a substance and the number of particles it contains.

To understand the mole concept, consider it as a counting unit, similar to a dozen for counting eggs. Just as a dozen represents 12 items, a mole represents approximately $6.022\times {10}^{23}$ particles. This large number is used because atoms and molecules are extremely small and it takes an enormous number of them to make up substances that we can interact with on a macroscopic scale.

The mass of one mole of a substance is equal to its relative molecular or atomic mass in grams. This is known as the molar mass and is used in stoichiometric calculations to relate the masses of reactants and products in a chemical reaction.

What is Avogadro's number?

Avogadro's number, also known as Avogadro's constant, is a fundamental scientific constant that represents the number of atoms, ions, or molecules in one mole of a substance. It is named after the Italian scientist Amedeo Avogadro, who, in 1811, hypothesized that equal volumes of gases, at the same temperature and pressure, contain an equal number of particles. This number is crucial in chemistry for converting between atomic mass units and grams.

The value of Avogadro's number is approximately $6.022\times {10}^{23}\text{particles per mole}$. This means that one mole of any substance contains exactly $6.022\times {10}^{23}$ of its fundamental units (like atoms for elements or molecules for compounds). For example, one mole of carbon-12 atoms has a mass of exactly 12 grams and contains $6.022\times {10}^{23}$ carbon atoms. Avogadro's number allows chemists to work with the macroscopic amounts of substances in a laboratory while referencing the microscopic scale of atoms and molecules.

How do you convert moles to particles?

To convert moles to particles, you'll need to use Avogadro's number, which is 6.022 x 10²³. This number represents the number of particles, usually atoms or molecules, in one mole of a substance. The process is straightforward:

1. Determine the number of moles you have.
2. Multiply that number by Avogadro's number.

Here's the formula:

$\text{Number of particles}=\text{Number of moles}x\text{Avogadro's number}$

For example, if you have 2 moles of a substance and you want to find out how many particles that is, you would calculate it as follows:

$2\text{moles}x(6.022x{10}^{23}\text{particles/mole})=1.2044x{10}^{24}\text{particles}$

So, 2 moles of the substance contain 1.2044 x 10²⁴ particles. Remember that the type of particle will depend on the substance you're dealing with – it could be atoms, molecules, ions, or others.

How to convert mass to moles?

To convert mass to moles, you need to use the molar mass of the substance, which is the mass of one mole of that substance. The molar mass is usually found on the periodic table or can be calculated by adding the atomic masses of the elements in a compound. Here's the step-by-step process:

1. Determine the molar mass of the substance. If it's an element, use the atomic mass from the periodic table. If it's a compound, calculate the molar mass by adding the atomic masses of all the atoms in the compound according to its chemical formula.
2. Measure the mass of the substance that you want to convert to moles.
3. Use the following formula to convert mass to moles:

$\text{Number of moles}=\frac{\text{Mass of substance (in grams)}}{\text{Molar mass of substance (in grams per mole)}}$

For example, if you have 18 grams of water (H₂O), and the molar mass of water is approximately 18 g/mol, you would calculate the moles of water as follows:

$\text{Number of moles}=\frac{18\text{g}}{18\text{g/mol}}=1\text{mole}$

Therefore, 18 grams of water is equivalent to 1 mole of water.

How to calculate mass from moles?

To calculate mass from moles, you'll need to use the molar mass of the substance, which is the mass of one mole of that substance. The molar mass is typically found on the periodic table and is expressed in grams per mole (g/mol).

Here's the formula you'll use:

$\mathrm{Mass}\left(g\right)=\mathrm{Moles}\left(\mathrm{mol}\right)\times \mathrm{Molar}\mathrm{Mass}(g/\mathrm{mol})$

Here's how you do it step by step:

1. Determine the number of moles you have.
2. Look up the molar mass of the substance you're dealing with. This information can be found on the periodic table or in a chemical database.
3. Multiply the number of moles by the molar mass.

For example, if you have 2 moles of carbon (C), and the molar mass of carbon is 12.01 g/mol, the calculation would be:

$\mathrm{Mass}=2\times 12.01=24.02\mathrm{grams}$

So, you would have 24.02 grams of carbon.