A mole corresponds to the mass of a substance that contains 6.023 x 10 23 particles of the substance. The mole is the SI unit for the amount of a substance. Its symbol is mol. By definition: 1 mol of carbon-12 has a mass of 12 grams and contains 6.022140857 x 10 23 of carbon atoms (to 10 significant figures). Students know one mole equals 6.02 x 1023 particles (atoms or molecules). Students know how to determine the molar mass of a molecule from its chemical formula and a table of atomic masses and how to convert the mass of a molecular substance to moles, number of particles, or volume of gas at standard temperature and pressure.
There are about 20 species of fuzzy moles (the kind that crawl around on the ground), and one kind of mole that might appear on your face, but today is a day for celebrating a different kind of mole. Today’s mole is a unit — one invented by a man named Avogadro.
Really, a mole is just a group of objects. You can think of “a mole” the same way you think of “a dozen.” You’re probably familiar with a dozen eggs, or chickens or planets. Moles are no different. You can have a mole of molecules or people or cheeseburgers. But there are a lot more than twelve things in a mole — there are 6.02 x 1023. That’s 602,000,000,000,000,000,000,000 things. Because the mole contains so many units, they’re most often used in chemistry is a way of measuring really really small things like atoms or molecules.
So a mole of water is 6.02 x 1023 molecules of water, which works out to be about 18 grams, or 18 mL. A mole of aluminum is about 26 grams. But to really appreciate how many molecules are in a mole it helps to think about things we can see. To do that, let’s try these comparisons from Daniel Dulek’s lesson about how big a mole is.
A way to think about the relative size of a mole?
If you had a mole of doughnuts, they would cover the entire Earth in a doughnut-layer five miles deep.
If you had a mole of basketballs, you could create a new planet the size of the Earth!
If you received a mole of pennies on the day you were born, and spent a million dollars a second until you died at 100, you’d still have over 99.99% of your money in the bank.
One mole of red blood cells is more red blood cells than exist in every human on earth right now. A mole of cereal boxes stacked end to end would reach from the Sun to Pluto 7.5 million times. A mole of turkeys could form sixteen earths.
Okay, so now that we know why a mole has 6.02 x 1023 things in it, what can we do with that information? Moles in chemistry are far more useful than moles in the ground, or on your face. They factor into all kinds of equations and important concepts in chemistry. Chemists think of moles or atoms like you and I think of a dozen eggs – we add them to recipes, order them from the store and calculate what we need based on how many we have.
What would a mole of fuzzy moles look like? Well, the pile of animals would weigh a little over half of the mass of our moon. Thankfully, there’s no chemistry equation in the world that calls for that many mammals. But if there was, you’d now know just how many mammals that would be.
Learning Objectives
- Describe the unit mole.
- Relate the mole quantity of substance to its mass.
So far, we have been talking about chemical substances in terms of individual atoms and molecules. Yet we don’t typically deal with substances an atom or a molecule at a time; we work with millions, billions, and trillions of atoms and molecules at a time. What we need is a way to deal with macroscopic, rather than microscopic, amounts of matter. We need a unit of amount that relates quantities of substances on a scale that we can interact with.
Chemistry uses a unit called mole. A mole (mol) is a number of things equal to the number of atoms in exactly 12 g of carbon-12. Experimental measurements have determined that this number is very large:
1 mol = 6.02214179 × 1023 things
Understand that a mole means a number of things, just like a dozen means a certain number of things—twelve, in the case of a dozen. But a mole is a much larger number of things. These things can be atoms, or molecules, or eggs; however, in chemistry, we usually use the mole to refer to the amounts of atoms or molecules. Although the number of things in a mole is known to eight decimal places, it is usually fine to use only two or three decimal places in calculations. The numerical value of things in a mole is often called Avogadro’s number (NA), which is also known as the Avogadro constant, after Amadeo Avogadro, an Italian chemist who first proposed its importance.
Example 3
How many molecules are present in 2.76 mol of H2O? How many atoms is this?
Solution
The definition of a mole is an equality that can be used to construct a conversion factor. Also, because we know that there are three atoms in each molecule of H2O, we can also determine the number of atoms in the sample.
To determine the total number of atoms, we have
Test Yourself
How many molecules are present in 4.61 × 10−2 mol of O2?
Answer
2.78 × 1022 molecules
How big is a mole? It is very large. Suppose you had a mole of dollar bills that need to be counted. If everyone on earth (about 6 billion people) counted one bill per second, it would take about 3.2 million years to count all the bills. A mole of sand would fill a cube about 32 km on a side. A mole of pennies stacked on top of each other would have about the same diameter as our galaxy, the Milky Way. A mole is a lot of things—but atoms and molecules are very tiny. One mole of carbon atoms would make a cube that is 1.74 cm on a side, small enough to carry in your pocket.
Why is the mole unit so important? It represents the link between the microscopic and the macroscopic, especially in terms of mass. A mole of a substance has the same mass in grams as one unit (atom or molecules) has in atomic mass units. The mole unit allows us to express amounts of atoms and molecules in visible amounts that we can understand.
For example, we already know that, by definition, a mole of carbon has a mass of exactly 12 g. This means that exactly 12 g of C has 6.022 × 1023 atoms:
12 g C = 6.022 × 1023 atoms C
We can use this equality as a conversion factor between the number of atoms of carbon and the number of grams of carbon. How many grams are there, say, in 1.50 × 1025 atoms of carbon? This is a one-step conversion:
But it also goes beyond carbon. Previously we defined atomic and molecular masses as the number of atomic mass units per atom or molecule. Now we can do so in terms of grams. The atomic mass of an element is the number of grams in 1 mol of atoms of that element, while the molecular mass of a compound is the number of grams in 1 mol of molecules of that compound. Sometimes these masses are called molar masses to emphasize the fact that they are the mass for 1 mol of things. (The term molar is the adjective form of mole and has nothing to do with teeth.)
Here are some examples. The mass of a hydrogen atom is 1.0079 u; the mass of 1 mol of hydrogen atoms is 1.0079 g. Elemental hydrogen exists as a diatomic molecule, H2. One molecule has a mass of 1.0079 + 1.0079 = 2.0158 u, while 1 mol H2 has a mass of 2.0158 g. A molecule of H2O has a mass of about 18.01 u; 1 mol H2O has a mass of 18.01 g. A single unit of NaCl has a mass of 58.45 u; NaCl has a molar mass of 58.45 g. In each of these moles of substances, there are 6.022 × 1023 units: 6.022 × 1023 atoms of H, 6.022 × 1023 molecules of H2 and H2O, 6.022 × 1023 units of NaCl ions. These relationships give us plenty of opportunities to construct conversion factors for simple calculations.
Example 4
What is the molar mass of C6H12O6?
Solution
To determine the molar mass, we simply add the atomic masses of the atoms in the molecular formula but express the total in grams per mole, not atomic mass units. The masses of the atoms can be taken from the periodic table or the list of elements in Chapter 17 “Appendix: Periodic Table of the Elements”:
| 6 C = 6 × 12.011 | = 72.066 |
| 12 H = 12 × 1.0079 | = 12.0948 |
| 6 O = 6 × 15.999 | = 95.994 |
| TOTAL | = 180.155 g/mol |
Per convention, the unit grams per mole is written as a fraction.
Test Yourself
What is the molar mass of AgNO3?
Answer
169.87 g/mol
Knowing the molar mass of a substance, we can calculate the number of moles in a certain mass of a substance and vice versa, as these examples illustrate. The molar mass is used as the conversion factor.
Example 5
What is the mass of 3.56 mol of HgCl2? The molar mass of HgCl2 is 271.49 g/mol.
Solution
Use the molar mass as a conversion factor between moles and grams. Because we want to cancel the mole unit and introduce the gram unit, we can use the molar mass as given:
Test Yourself
What is the mass of 33.7 mol of H2O?
Answer
607 g
Example 6
How many moles of H2O are present in 240.0 g of water (about the mass of a cup of water)?
Solution
Use the molar mass of H2O as a conversion factor from mass to moles. The molar mass of water is (1.0079 + 1.0079 + 15.999) = 18.015 g/mol. However, because we want to cancel the gram unit and introduce moles, we need to take the reciprocal of this quantity, or 1 mol/18.015 g:
Test Yourself
How many moles are present in 35.6 g of H2SO4 (molar mass = 98.08 g/mol)?
Answer
0.363 mol
Other conversion factors can be combined with the definition of mole—density, for example.
Example 7
The density of ethanol is 0.789 g/mL. How many moles are in 100.0 mL of ethanol? The molar mass of ethanol is 46.08 g/mol.
Solution
Here, we use density to convert from volume to mass and then use the molar mass to determine the number of moles.
Test Yourself
If the density of benzene, C6H6, is 0.879 g/mL, how many moles are present in 17.9 mL of benzene?
Answer
0.201 mol
Key Takeaways
- The mole is a key unit in chemistry.
- The molar mass of a substance, in grams, is numerically equal to one atom’s or molecule’s mass in atomic mass units.
Exercises
How many atoms are present in 0.0665 mol of K?
How many molecules are present in 2.509 mol of H2S?
How many molecules are present in 0.336 mol of acetylene (C2H2)?
How many moles are present in 3.55 × 1024 Pb atoms?
How many moles are present in 2.09 × 1022 Ti atoms?
How many moles are present in 1.00 × 1023 PF3 molecules?
How many moles are present in 5.52 × 1025 penicillin molecules?
a) Si
b) SiH4
c) K2O
10. Determine the molar mass of each substance.
a) Cl2
b) SeCl2
c) Ca(C2H3O2)2
11. Determine the molar mass of each substance.
a) Al
b) Al2O3
c) CoCl3
12. Determine the molar mass of each substance.
a) O3
b) NaI
c) C12H22O11
14. What is the mass of 0.311 mol of Xe?
16. What is the mass of 0.0656 mol of PbCl2?
18. How many moles are present in 0.00339 g of LiF?
20. How many moles are present in 48.8 g of BaCO3?
21. How many moles are present in 54.8 mL of mercury if the density of mercury is 13.6 g/mL?
22. How many moles are present in 56.83 mL of O2 if the density of O2 is 0.00133 g/mL?
Answers
9.
a) 28.086 g
Chemistry Mole And Avogadro's Number
b) 32.118 g
The Mole In Chemistry Number
c) 94.195 g
Define Mole