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Group Activity: the Mole

Introduction

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In your everyday life you deal with groups of things. In chemistry you deal with groups of atoms and molecules. You put on a pair of socks in the morning. In the afternoon you might go out and buy a six-pack of soda. Your teacher goes through a dozen eggs about every five days. In the chemistry lab you might find it a bit harder to characterize the number of atoms or molecules that participate in a reaction.

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In this lesson we will discuss how to come to grips with the vast numbers of extremely tiny particles that do the evaporating, condensing, reacting, and dissolving in the study of chemistry. For example, the tiniest speck of dust that you can see without a magnifying glass or a microscope is built of about 1 × 1016 atoms. An 8 oz. glass of water contains about 8 × 1024 water molecules. There are more carbon atoms in the lead of your pencil than there are stars visible in the night sky.


Conservation of Atoms

You are familiar with the conservation of mass in chemical reactions. The conservation of mass is the direct result of the conservation of individual atoms and molecules. In a chemical reaction atoms and molecules become reorganized. They never disappear or become converted completely into energy.

The fact that atoms are never destroyed can have important consequences. For example, climate change due to the emission of carbon dioxide through the burning of fossil fuels is a direct result of the rule that atoms cannot be destroyed. Carbon compounds in the form of petroleum and natural gas are excellent fuels. Hydrocarbons (compounds that are made of C and H) release a lot of energy when those compounds are burned. This is because carbon and hydrogen have a chemical affinity for oxygen that is very strong.

When plain carbon burns, say in the form of charcoal, the reaction is written this way:

C + O2 Arrowsngl CO2
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This symbolic notation tells the love story of carbon and oxygen. Under the right conditions (say, in a well-burning, well-ventilated charcoal grill) carbon combines easily with oxygen and releases quite a bit of heat in the process. Perhaps disappointingly for some, this love story is a romance by the numbers. It says that every individual carbon atom always combines with exactly two oxygen atoms—one oxygen molecule. (Notice that the oxygen does not appear as a single atom but as a diatomic molecule: it nearly always does). Furthermore, the chemical equation shows that this process always results in exactly one molecule of carbon dioxide.

The power of the equation is not really obvious from this notion of single atoms and molecules. In the real world we never deal with atoms and molecules one at a time (there isn’t a pair of tweezers small enough). Instead we always have billions upon billions upon billions. So the equation really shows how useful it is when you consider that it says that no matter how many carbon atoms you have they will always react with as many oxygen molecules as there are carbon atoms.

Well, actually, that was a simplification. (The teaching of science is full of simplifications). Carbon and oxygen can work things out a different way if conditions require it. Under normal circumstances, when there is plenty of oxygen around, carbon will always combine with oxygen to form carbon dioxide. But when there is not enough oxygen, such as when someone runs a gas-powered electricity generator in a closed-up space, something much less romantic happens. Instead of making relatively harmless CO2 the reaction becomes:

2C + O2 Arrowsngl 2CO

Carbon dioxide is bad enough, considering the damage it is doing to the climate as a result of our insatiable energy requirements. Even so, it is relatively harmless in low concentrations. But CO (carbon monoxide) is downright hazardous.

Carbon monoxide binds to the oxygen-carrying protein hemoglobin in the blood 200 times more strongly than oxygen. When present, it prevents oxygen from binding to hemoglobin and this prevents it from reaching the body’s tissues. At a level of just 100 parts per million by volume in air it can cause dizziness and headaches. When its concentration reaches 667 ppm it can be fatal. The moral of the story: never run a generator (or burn charcoal) in an unventilated room.

Incidentally, take notice of the fact that both equations for the burning of pure carbon are what are called balanced chemical equations. A balanced chemical equation has exactly the same number and kinds of atoms before and after the arrow. In other words, the number of atoms that react (the reactants) is the same as the number of atoms the are produced (the products). This is really an expression of the Law of Conservation of Matter For example, there is one atom of carbon and there are two atoms of oxygen on both sides of the equation showing the product CO2.


Conservation of Matter

Atoms and molecules are unimaginably small: a CO2 molecule is about 0.29 nm long. That is 0.29 billionths of a meter long or 0.29 millionths of a millimeter. Written in decimal notation the length of the molecule is 0.000 000 000 29 m. Their masses are also incredibly tiny: a single molecule of O2 has a mass of 5.3 × 10-23 g. No lab balance ever made could possibly measure such a tiny mass. The amount of air you breathe in for each breath is about 0.5 L. This is actually a staggeringly large number of gas molecules: about 1.2 × 1022. Normal amounts of everyday materials are made of many, many incredibly tiny particles.

Because atoms and molecules are so small the only way to count them is to figure out a relationship between their mass and how many there are. In this way we can count them by weighing them. To do this we use correct chemical formulas and balanced chemical equations. Chemical formulas and equations relate numbers of atoms to each other based on how they bind to each other and react. By knowing their atomic masses and measuring the masses we work with the in the lab we can use chemical formulas and equations to count atoms. Here’s how:

Carbon monoxide results from burning fuel without enough oxygen. So how much oxygen do you need to make sure that all the carbon burns to form CO2 and not to form CO? This is a question chemistry can help us to answer. We know that in a balanced chemical equation the number of atoms that react are the same as the number of atoms after the reaction is over.

C + O2 Arrowsngl CO2
(reactants—one carbon atom and two oxygen atoms— react to make
products—a compound made of one carbon atom and two oxygen atoms)
We also know that one atom of carbon has a mass of 12 amu and that one molecule of oxygen (2 × 16 amu) has a mass of 32 amu. So the answer is that it takes a mass of 32 amu of oxygen to react with 12 amu of carbon if 44 amu of CO2 is the product. To summarize: because we know that atoms are not created or destroyed, and we know the masses of those atoms, we know the mass of oxygen necessary to react with a given mass of carbon: 32 amu of oxygen for 12 amu of carbon, a ratio of  8/3.

The ratio  8/3 is a ratio of masses. That means that for any size mass of carbon you can figure out how much oxygen you need (by mass, if not by number of molecules). So say you have exactly 12 g of carbon (grams can be measured using a simple lab balance; atomic mass units are not so easy to measure). That means that you need 32 g of oxygen to react with it to make carbon dioxide: 12 g ×  8/3 = 32 g. By putting oxygen into a container of known mass sitting on a balance you can measure out 32 g of the gas. If you ignite the 12 g of carbon inside the container holding 32 g of oxygen they will both be used up and the container will then be filled with carbon dioxide.

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Take notice of what just happened here. The ratio of masses depends on the idea that an individual carbon reacts with exactly one oxygen molecule. That is, because you know how many atoms of each element react you also know what mass of each element reacts. By using the ratio of the masses you can figure out what measurable mass, in grams, of each element will be needed for the reaction. So by weighing out twelve grams of carbon and 32 grams of oxygen you have in effect guaranteed that there are the same number of carbon atoms in twelve grams of carbon as there are oxygen molecules in 32 grams of oxygen. Another way to say it is this: The ratio of the number of particles is 1 O2 to 1 C. The ratio of masses that matches this ratio of numbers is 32 amu/12 amu (8/3). If you take the same ratio of masses in grams (32 g/ 12 g) then the ratio of the number of particles must also be the same. Therefore the number of molecules of oxygen is equal to the number of atoms of carbon for 32 g of oxygen and 12 g of carbon. This result is very important because it shows how it is possible to count atoms and molecules by weighing them. The mass of a chemical sample is proportional to the number of atoms or molecules of that sample.


The Mole

Chemists have to deal with astonishingly small sizes and inconceivably large numbers if they want to understand what is going on in chemical reactions and physical changes. They do it by the simple method of weighing in order to count things. If you go to the hardware store to buy nails there is a good chance that they will weigh your purchase and not count each individual nail. If you have a stack of paper and you want to know how many sheets you have the simplest way to find out is to weigh the stack and divide by the weight of one sheet.

In the same way chemists use the mass of a pile of atoms or molecules to figure out how many atoms or molecules are there. They take one more step to simplify things even further. Chemists use a unit called the mole to keep track of the number of atoms or molecules. The mole is a unit like the dozen, the pair, the six-pack or the ream (a ream of paper is 500 sheets). There are twelve things in a dozen, two in a pair, six in a six-pack and 500 in a ream.

How many things are there in a mole? There are as many things in a mole as there are carbon-12 atoms in exactly 12 g of pure carbon-12. This definition alone would be enough for the mole to be a useful unit since carbon can be reacted with other elements and compounds, the results analyzed and in this way the mass of a mole of other chemicals can be determined. The number of things in a mole is a fundamental constant and has the value: 6.02 × 1023/1 mol. The unit is in the denominator to reflect that this is the number of things per mole.

A mole is a collection of 6.02 × 1023 items. In theory, you could have a mole of any kind of thing. A mole of water molecules has the same number of items as a mole of elephants. The elephants take up a lot more space, however. But the point is not really how many items there are in a mole. The point is what the mole can do. We saw earlier that 12 g of carbon and 32 g of oxygen have the same number of particles. These numbers were not selected at random: they are the mass of one mole of each of those substances.

For any singular atom or molecule it is easy to figure out the mass measured in atomic mass units (amu). The mass of a CO2 molecule is 12 amu + 2 × 16 amu = 44 amu. The mass of an O2 molecule is 2 × 16 amu = 32 amu. The mass of a single unit of NaCl is 23 amu + 35 amu = 58 amu. The great thing about the mole is that there are a mole of atoms or molecules in the mass of a substance in grams that is equal to the mass of a single unit of that substance in atomic mass units. In other words, there is a mole of CO2 molecules in 44 g of CO2. Likewise, 32 g of O2 is a collection of a mole of oxygen molecules. Similarly, if you measure out 58 g of NaCl you have, at the same time, counted out a mole of NaCl units.

It is interesting to play around with the number of things in a mole to see just how big of a number the it is. If it were possible to have a mole of chicken eggs they would cover the entire surface area of the Earth…four miles deep. If you were rich enough to own a mole of pennies then they could be stacked in groups 400 pennies high in a disk that reaches from the surface of the Earth all the way to the orbit of the moon. (The bank teller would hate you for bringing them in for a deposit; it is enough money so that if distributed evenly every person on Earth would have over 1 trillion dollars.) One more illustration: the volume of the Earth is about 1021 m3. It takes about 500 grapefruit to fill up a box one meter on a side (1 m3). So a mole of grapefruit would be large enough to fill the entire volume of the planet Earth.

For many people the mole is a difficult concept. Perhaps this illustration might help. Say you have a dozen crocodiles and a dozen mice. There are twelve of each animal but you could never say that the two groups of animals have the same mass. It would only take one crocodile one snap of its jaws to consume the dozen mice! On the other hand, if you have 1,000 kg of crocodiles and 1,000 kg of mice you would have the same mass of each one. But you would certainly not have the same number of each animal. How many mice (weighing in at 25 g) would that be? A single average adult crocodile might have a mass of 1,000 kg.

To summarize: The mole is a quantity used by chemistry to count atoms, molecules, and particles of all kinds. The number of items in a mole is called Avogadro’s number and equals 6.022 × 1023 per mole (/1 mol). The most useful aspect of the mole is that it relates the atomic mass of atoms to a measurable mass in grams. Specifically, a mole of any chemical substance has a mass in grams equal to the sum of the atomic masses of its atoms. For example, 1 mol of C has a mass of 12.011 g and 1 mol of KCl has a mass of 74.55 g.




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Examples of Problems

Finding Molar Mass

The molar mass of a chemical substance is the molecular weight of the substance expressed in units of grams per mole (g/mol). It is calculated by adding up the atomic masses of all the atoms in the molecular formula of the substance. Here are two examples:

Molar Mass of H2 (elemental hydrogen)
From the periodic table: H atoms have an atomic mass of 1.00794 g/mol
2 × 1.00794 g/mol = 2.01559 g/mol                         2.01559 g
                                  The molar mass of H2 is ----------
                                                            1 mol
Molar Mass of Fe2O3 (iron(III) oxide, aka rust)
Fe: 55.845 g/mol and O: 15.9994 g/mol
2 × 55.845 g/mol + 3 × 15.9994 g/mol = 159.69 g/mol          159.69 g
                                  The molar mass of Fe2O3 is ----------
                                                               1 mol

Converting between Mass and Number of Moles

Since atoms and molecules are far to small to see, much less count, scientists count them by weighing them. This is the value of the molar mass. If you know the molar mass of a substance then you can calculate the number of moles or the mass of that substance.

Finding Mass from Moles: What is the mass of 2.00 moles of H2?
               2.01559 g
2.00 mol H2 × ---------- = 4.03 g H2
                1 mol
Finding Moles from Mass: How many moles are in 399.22 g Fe2O3?
                   1 mol
399.22 g Fe2O3 × ---------- = 2.5000 mol Fe2O3
                  159.69 g

Comparing Numbers of Moles

It is important to remember that for the purpose of studying chemistry the important quantity is the number of moles, not the mass. It is the number of molecules reacting with each other that predicts the outcome, not the mass. For that reason it is valuable to have an understanding of relative numbers of particles.

Which sample has a larger number of particles (that is, number of moles):
8.06 g H2 or 79.85 g Fe2O3?
              1 mol
8.06 g H2 × ---------- = 4.00 mol H2
             2.01559 g
                  1 mol
79.85 g Fe2O3 × ---------- = 0.5000 mol Fe2O3
                 159.69 g              
Don't be surprised by the fact that there are 8 times more particles of
H2 than there are particles of Fe2O3!

The Mole is a Very Big Number

It is instructive to take note of just how many particles there are in a mole because it gives you an appreciation for the incredibly tiny size of the molecular world. To accomplish the purpose of giving you this appreciation you will calculate the number of particles there are in various samples. This is done by using the definition of the mole: there are 6.02 × 1023 objects in a mole. Mathematically the number is expressed with the unit mol in the denominator: 6.02 × 1023/1 mol.

Finding Number of Particles from Mass
                   1 mol      6.02 × 1023
399.22 g Fe2O3 × ---------- × ---------- = 1.505 × 1024 particles of Fe2O3
                  159.69 g      1 mol
Number of particles can be calculated starting with moles, too. Just
leave off the molar mass conversion ratio.



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Questions and Problems

Comprehension Questions

Answer the following questions using one or more complete sentences. Everyone in the group must write down complete answers. Discuss among your group members what the best way to answer the question is and then write it down.

  1. How is it that a balanced chemical equation is an expression of the law of conservation of matter? Before answering this question, consider the following:
    1. Balance this chemical equation:
      C3H8 +      O2 →      CO2 +      H2O
    2. When you balance a chemical equation, how do you know that it is correctly balanced?
    3. What is the law of conservation of matter?
    4. Put these ideas together and answer the main question.
  2. For the reaction of carbon with oxygen to make carbon dioxide (C + O2CO2) which is simpler:


    Explain.
  3. Based on your answer to the previous question, why is it important to chemists to be able to count atoms and molecules?
  4. Why does the number of things in a mole (6.02 × 1023) have to be so large?
  5. How do you calculate the mass of one mole of a chemical substance? Write a complete sentence to give your answer but also give an example using the chemical formula of an element or compound of your own choice.
  6. How can you calculate the number of actual items in a given number of moles of a substance? Write a complete sentence to give your answer but also give an example by calculating the number of items in 2.5 moles of water.



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  1. Definitions Write definitions in your own words using what you have learned about the concepts listed. Some of these were defined in earlier units in this course. Others are new and are defined in the text of this packet.
    1. chemical reaction:
    2. physical change:
    3. balanced chemical equation:
    4. mole:
    5. mass:
  2. Please explain, in a short paragraph, what the conservation of atoms has to do with the principle of the conservation of mass in chemical reactions and physical changes.
  3. Please explain, using chemical equations, why it is a very bad idea to run a gasoline engine indoors.
  4. From the text you will remember that 1 atom of carbon reacts with 1 molecule of oxygen. You can scale this up to any number: a million atoms of carbon react with a million molecules of oxygen. In reality, you cannot count the atoms and molecules because they are too small. Instead, scientists weigh chemicals to find their mass. Scientists found that twelve grams of carbon always react completely with thirty-two grams of oxygen. What does this information tell you about the number of carbon atoms in 12 g compared to the number of oxygen molecules in 32 g? Why?
  5. You have been given some number of textbooks with a total mass of 1,395 kg. Each text has a mass of 1.5 kg. You have also been given 900 spiral-bound notebooks, each with a mass of 300 g. Do you have more textbooks or more notebooks? Also, do you have a larger mass of textbooks or notebooks?
  6. A chemistry teacher would like to order a mole of sand grains in order to show his students just how big a mole really is. One grain of sand has a volume of about 5 × 10-13 m3 if it has a diameter of 0.1 mm. Dump trucks with a volume capacity of 11 m3 are going to be used to transport the sand to the school. How many dump truck loads will be needed?
  7. An e. coli bacterium is about 1.2 μm long. How long would a line of 6.02 × 1023 e. coli bacteria be? Convert your answer to km (1 × 109 μm = 1 km). About how many times could this line go back and forth from the Earth to the Sun? The sun is 1.5 × 108 km away.

Moles: Numbers and Masses

Molar Masses

For each of the following elements or compounds calculate the mass of 1 mole of particles of that substance. Express answers in units of g/mol.For example: the molar mass of HCO3 is H: 1 × 1.008 g/mol + C: 1 × 12.01 g/mol + O: 3 × 16.00 g/mol = 60.02 g/mol

  1. Al
  2. O2
  3. NaCl
  4. H2O
  1. CaCO3
  2. AlPO4
  3. Mg(OH)2
  4. Fe2(CO3)3
Putting Molar Masses to Work

The previous exercise requires you to find the mass in grams of one mole of a chemical substance. This mass has a special name in chemistry: the molar mass. When you work with this number, as with any number in science, you need a unit. The unit of molar mass is grams per mole (g/mol). To have a mole of sand (SiO2) you measure out approximately 60 g. But chemists seldom work with exactly one mole.

How many moles of SiO2 are there in 12 g? How many grams do you weigh out if you need 2.4 moles of SiO2? Just use dimensional analysis to figure it out:

            60 g                              1 mol
2.4 mol × -------- = 144 g           12 g × -------- = 0.20 mol
            1 mol                             60 g

In the following problems, find the number of moles given the number of grams. Find the number of grams given the number of moles.

  1. 47 g of O2
  2. 112 g of NaCl
  3. 91 g of H2
  1. 14 mol of H2O
  2. 0.35 mol of Fe2O3
  3. 42 mol of Mo(PO4)2



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Comparing Numbers of Particles

Write an equal sign (=), a greater than sign (>), or a less-than sign (<) between each of the following pairs. Determine which sign is appropriate by comparing the number of moles of each member of the pair. That is, compare the number of atoms or molecules in each member of the pair. For example, there are more atoms in 28 g of N2 than in 2 g of C. This is because 1 mole of N2 has a mass of 28 g. One mole of C has a mass of 12 g. Since there are only 2 g of C and this is equal to 0.17 mol there are more molecules of N2 in 28 g of N2 than in 2 g of C.

  1. 27 g Al        4 g He
  2. 10 g Fe        10 g Br
  3. 2 mol NaCl        2.1 mol H2O
  4. 14 g Fe2O3        14 g U
  1. 1 mol Au        1 mol Pb
  2. 1 g O2        1 g N2
  3. 2 g H2        10 g PbCl2
  4. 10 g H2O2        20 g CH4
Big Numbers

For each of the following calculate the number of units of a chemical substance (atoms or molecules or ionic unit). For example, 1.5 mol of sugar molecules contains 1.5 × (6.02 × 1023) = 9.03 × 1023 sugar molecules.

  1. 2 mol NaCl
  2. 1.5 mol Fe2O3
  3. 1.0 × 10-6 mol grains of sand
  4. 5.8 × 10-7 mol H2O
  1. 58 g NaCl
  2. 100 g F2
  3. 2 kg C3H8 Hint: 1 kg = 1,000 g
  4. 18 mL H2O Hint: the density of water is 1 g/mL

In writing this lesson I have closely emulated the ideas and order of presentation used by Carl H. Snyder in his excellent text The Extraordinary Chemistry of Ordinary Things
Another source for this lesson is the NPR site and their on-air stories about climate change.

POGIL Summary: Relative Mass and the Mole
Moles Practice Calculations
Homework Assignment: The Mole and Molar Mass
Lab: Moles, Molecules and Grams
Lab: Size of an Aluminum Atom
Activity: Moles of Macroscopic Objects
Homework: Moles Quick Calculations
We have already covered: Balancing Chemical Equations
Homework for Balancing Chemical Equations
Related activities: Basic Stoichiometry
Homework Assignment: Stoichiometry (aka Chemical Ratios)
Moles, Empirical Formulas, Stoichiometry, Limiting Reagents
Last updated: May 28, 2019        Home