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2. Atoms & Elements

The **Mole Concept** involves the interconversions between different unit amounts of a substance.

Mole Concept

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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 Adams in 12 g 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. And Adam, Remember, we've used the term Adam interchangeably with neutral elements. So we're going to stay here in Adam is a single element with no charge. Ion and ion is also a single element, but it possesses a charge. That charge could be either positive or negative. Ah, molecule, we're gonna find as a compound with two or mawr non metals together. Those non metals could be the same, or they could be different from one another and then finally, formally unit formally unit is just a general term for a compound composed of a metal and nonmetal. So as we delve deeper into the mold concept, just realized that the mole kind acts as a bridge that connects together these different ideas when it comes to the elements and how they arranged with one another.

**Mole **connects together atoms, ions, molecules and formula units.

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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 consists, possesses ah, metal plus nonmetal. So we just have to look for the choice that does not contain a medal with nonmetal. If you look at Option A, we have N a C and O. N A is a medalist, 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 non metals. So this could also use the term formula unit. See, though, see has B, which is boron. Boron is a metal Lloyd, and it has F, which is flooring, which is a non metal. So this would be our answer we could not call. We cannot associate the term formula unit with this compound because it contains a metal Lloyd and not a metal. And then finally we have m n and C. L M n is mag unease, which is a transition metal, and see Ellis chlorine, which is a non metal, so this could be associated with the term formula unit. So, out of all the choices on Lee, Option C couldn't be associated with the term Formula unit.

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Now, in order to convert between moles and particles, we have to utilize what's called alpha god Rose number now, avocados Number says that one mole of a substance is equal to 6.22 times 10 to the particles. Now this value here of 6.22 times 10 to the 23. That is avocados number. And we're gonna 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 until one idea we can use the term particles. Now we're going to say here that one mole of a substance is equal to avocados number right. So that would mean that one mole off chlorine remember, chlorine is a dye atomic element in its natural form equals 6.22 times 10 to the 23 molecules of CL, too. Now we need to realize here that this could be a conversion factor because it's combining two different units together. So we can say here that one mole off the L two is 6.22 times 10 to the 23 molecules off cl, too. And remember, conversion factors weaken. Do the reciprocal where we flip it so we could say avocados. Number on top moles of CO two 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 cl two. Why are we using the term molecules, though? Remember the term molecules is used when we have ah, compound that has two or mawr non metals together. Chlorine is a non metal, 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 Adam. We'd only use the term Adam 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, 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 avocados number on. We're using the term molecules here because we have to non metals together.

Converting between moles and particles requires Avogadro's Number:**1 mole = 6.022x10 ^{23 }particles.**

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So in this example question, it says how many moles of chlorine gas are an 8.33 times 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 two moles, right? And to be able to do that, we're gonna have to utilize the conversion factor that we have up here. Alright, so that those molecules are are 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 on on videos on dimensional analysis. All right, so are giving them out is 8.33 times 10 to the 37 molecules off the L two and we need to get to our end amount, which will be in moles. Moles of cool, too. 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 Afghan drills number in molecules have to go on the bottom. So we're gonna put molecules of CL to here on the bottom, and that's equal toe one more of cl two on the top. So here molecules will cancel out, and we'll be left with moles at the end. So what you're gonna 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 to the 37 divided by avocados number. Now, if you do this correctly, what you'll get as your answer at the end will be 1.38 times 10 to the 14 moles off. CL too. So that would mean that option C would be are 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 Ah, 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 gonna have to utilize avocados number at some point.

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Just as the mall connect is the connection toe particles, we can use moles as the connection to Mass. Now we're going to stay here. One mole of a substance is equal to the molar mass of that substance. Remember the term Mueller, Mass. We can use Moeller Wait. Molecular weight or molecular mass? They all mean the same thing here. We're told that one mole off still chlorine weighs 70.90 g. What does that 70.90 g 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 ah, value of 35.45. That's the mass of one chlorine. But here we're dealing with two chlorine that be 35. times to, which gives us that value of 70.90 now. Here again, this can serve as a conversion factor in itself, where one mole of C L two is 70. g C. L two, and since it's a conversion factor, we can also flip it where 70.90 g of C. L two on top and one mole of CL two 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 off element or compound. Now that we've seen this, let's move on to our example problem.

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So in this example question, it says, how many grams of chlorine gas are there in 2. moles? All right, so the 2.34 moles represents are 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 Gramps. Okay, so here we need to determine the grams off chlorine gas now to go from given amount to 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. So let's write down are given amount of 2.34 moles of C l two. We need to cancel moles of CL too. 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 C L two is equal to 70.90 g of c l two So now moles of CL to cancel out and we'll be left with grams of C L two at the end. So when you punch that into your calculator, you should get 65.906 and out of the choices presented be 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 off chlorine gas.

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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 seal to contain 9.25 times 10 to the 24 molecules off all too. All right, so we're going to start out with are given amount, which is 9.25 times 10 to the molecules off CL too. 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 gonna have to utilize some conversion factors and our end amount that we want to get to is grams off. CL too. So if we take a look here, we need to get rid off molecules first. So our first conversion factor, we're going to say that we do 6.22 times 10 to the molecules of C l two. I remember that connects us to moles, so for every one mole of C l two. Then we're going to realize that molecules air 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 CL to here on the bottom is 70.90 g of C l two here on the top. Here are moles would cancel out, and we have our answer Ingram's. 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 times 10 to 24 times 70.90 divided by avocados Number here. Now, if you did this correctly, what you get initially is 1089.48 g off. CL too. 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 write that in scientific notation, asked one point 100 actually, we could do 1.9 times 10 to the g of C. L two. So here, writing in scientific notation gives us our three significant figures, which we had in the original question. 9.25 times 10 to the 24 given to us has three sig figs. So are answered. Must have three sig figs.

Mole also serves to connect mass units to particles.

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Problem

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

A

6.12 x 10^{25} formula units

B

8.42 x 10^{25} formula units

C

1.09 x 10^{26} formula units

D

7.53 x 10^{26} formula units

9

Problem

Calculate the number of oxygen atoms found in 783.9 g NiCl_{2} • 6 H_{2}O.

A

1.192 x 10^{25} O atoms

B

2.314 x 10^{25} O atoms

C

5.833 x 10^{26} O atoms

D

8.849 x 10^{26} O atoms

10

Problem

If the density of water is 1.00 g/mL at 25°C, calculate the number of water molecules found in 1.50 x 10^{3} µL of water.

A

3.993 x 10^{21} molecules

B

5.013 x 10^{22} molecules

C

7.411 x 10^{23} molecules

D

6.291 x 10^{24} molecules

11

Problem

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/cm^{3}. (V = π • r^{2} • h)

A

2.01 x 10^{22} Cu atoms

B

6.36 x 10^{21} Cu atoms

C

9.91 x 10^{21} Cu atoms

D

1.25 x 10^{22} Cu atoms

Additional resources for Mole Concept

PRACTICE PROBLEMS AND ACTIVITIES (108)

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