In chemistry, there are many applications in which quantifying the amounts of chemicals involved in a reaction is necessary. Let’s say, for example, a forensic investigator is trying to determine the identity of a poisonous substance found in a victim’s bloodstream. A sample would likely be sent off to a laboratory for analysis. A little magic happens, and a few days later, an envelope containing information about the substance arrives identifying it as ricin toxin. That’s how it works, right? On television, yes. But in the real world, that “magic” is a little less mysterious, and actually involves a highly skilled group of analytical chemists. Analytical chemistry makes use of quantitative chemistry, among other disciplines, to identify substances by determining their molecular formula. Such a process is only made possible by employing the concept of the mole.
Quantitative chemistry involves being precise in measuring the amounts of reactants and products involved in a chemical reaction. This allows you to control the amount of product produced, determine the identity of an unknown substance, determine the percentage composition of a mixture, prepare solutions of known concentration, and perform many other tasks critical in a scientific process. In many ways, quantitative chemistry is a lot like cooking. Known amounts of ingredients are combined in order to make a predetermined amount of food. In chemistry, known amounts of chemicals are combined in order to make a predetermined amount of product. However, cooking is a far more difficult discipline to master than chemistry. Before you guffaw loudly, just think about the average recipe for food. It likely involves measuring amounts of ingredients in many different, often obscure units. 2 teaspoons of salt, 1 cup of brown sugar, 4 ounces of vanilla, 1 pint of water, 2 tablespoons of egg yolk, and a pinch of nutmeg. A pinch? Just how much is that? Ounces, fluid ounces, cups, pints, gallons, teaspoons, tablespoons, etc. There can be a dozen different units for one recipe. Sometimes you have to alter a recipe to feed a different amount of people than the recipe calls for.
This involves converting between these obscure units without making mistakes, otherwise your guests will be quite disappointed with the abysmal food you prepared.
In chemistry, amounts of chemicals are really just measured in one unit that we call the mole. It is like any other counting unit, calling for a precise amount of any substance. For example, you might have a food recipe that calls for two dozen eggs (must be a REALLY big omelet!). You know this really means 24 eggs. But it’s easier to go to the grocery store and grab two packages of eggs that each contain one dozen eggs, rather than manually count 24 eggs separately
(and probably drop several as you try to hold on to that many eggs at once). If you’re buying paper, it’s easier to walk in and grab ten reams of paper than to sit there and count out 5,000 individual sheets of paper (one ream contains 500 sheets). In this manner, counting units make our lives easier by taking a larger number of things and organizing them into a smaller number of groups. If we know how many objects are in the group (12 in one dozen, 500 in one ream, etc.), we can count out the groups instead of counting out the individual objects. Such a thing has been done for centuries in society and commerce.
In quantitative chemistry, what we’re counting are extremely small objects called atoms or molecules. It would be impossible for us to count out individual atoms to perform our chemical recipe, because not only are they too small to see, but we would need to count out an extremely large number of them in order to do anything useful. For example, in the synthesis of water, two molecules of hydrogen combine with one molecule of oxygen to make two molecules of water:
2H
2
+ O
2

2H
2
O
But what would be the point of making two molecules of water? Such an amount would be impossibly small to see or do anything with. We’ll need to use larger amounts of hydrogen and oxygen to make larger amounts of water. How about using two dozen molecules of hydrogen and one dozen molecules of oxygen? That should produce two dozen

molecules of water according to the chemical equation. If you look at the coefficients in the balanced equation, it calls for twice as much hydrogen as oxygen. The number of water molecules produced should be equal to the number of hydrogen molecules used, and twice as big as the number of oxygen molecules used. This is because the ratio of hydrogen to oxygen to water is 2 : 1 : 2.
So ok, combining two dozen hydrogen molecules and one dozen oxygen molecules makes two dozen water molecules.
Still, two dozen water molecules? That’s only 24, which still really isn’t enough to work with yet because molecules are
REALLY SMALL! We’re going to need a counting unit that calls for a much, much larger number of things than what a dozen calls for. We’ll need even bigger than a ream. We’ll need one called the mole.
A dozen is 12. A ream is 500. A mole is 602000000000000000000000.
That is not a typo. A mole is really that many objects. Why so many? Because we’re counting REALLY small things, atoms or molecules. If we look at the equation for synthesizing water again, 2 moles of hydrogen molecules combine with one mole of oxygen molecules to make two moles of water molecules. Now two moles of water, that’s actually something we can see. It ends up being around 36 grams, which for water is 36 ml. This would be a small cupful. In fact, the concept of the mole was introduced to give chemists a counting unit they could use to be precisely quantitative about their reactions. As you will see, there are many practical applications to being quantitative in chemistry, from cutting edge medicine to high tech industrial processes like metallurgy or energy production.
Summarize the information above about the MOLE.
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In order for you to get a handle on working with moles, we’ll start by learning how to calculate a quantity known as
formula mass. Specifically, this is the mass that one mole of atoms or molecules would have. This is pretty simple to calculate, because the periodic table lists atomic masses for every element known. For example, one mole of carbon atoms has a mass of 12.011 grams, as is listed on the periodic table. One mole of iron atoms has a mass of 55.845 grams. One mole of hydrogen atoms has a mass of 1.00794 grams. One mole of hydrogen MOLECULES, which have two hydrogen atoms, would have a mass of 2.01588 grams, or 2 x 1.00794.
As stated above, we said that two moles of water molecules would have mass of around 36 grams. Where did that number come from? By calculating the formula mass of water. H
2
O has two hydrogen atoms and one oxygen atom.
One mole of H
2
O would have two moles of hydrogen and one mole of oxygen. If we use the periodic table two add the mass of two moles of hydrogen and one mole of oxygen, we would end up calculating 1.00794 + 1.00794 + 15.9994, which equals 18.01528. This means that one mole of water molecules would have a mass of 18.01528 grams. This is the formula mass of water. Two moles of water would have a mass of 2 x 18.01528 grams, which is close to 36 grams.
The units for formula mass are grams per mole, written as 𝑔
⁄ 𝑚𝑜𝑙
. The formula mass for water is approximately 18 g/mol.
Summarize the information above about FORMULA MASS.
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Find the formula mass for the following elements or compounds.
Show your work:
Ex. CO2 (1 carbon x 12 g/mol) + (2 oxygen x 16 g/mol) = (1 x 12 g/mol) + (2 x 16 g/mol) = 44 g/mol
Ar
Ba(OH)
2
CH
3
COOH
U
NH
4
NO
3
NaCl
(NH
4
)
2
CO
3
Cl
2

Since chemical equations are actually “mole recipes” for a reaction, it is imperative that chemists have a way for determining the number of moles of a substance from its mass. This is easily done after calculating the substance’s formula mass.
For example, how many moles of water molecules are present in 50.0 grams?
Multiply
Given
Unit wanted
50.0 grams H
2
O
Divide
1 mole H
2
O
18 grams H
2
O
Cancel out units
Mole ratio
=2.8 moles H
2
O have a mass of 18 grams because that is water’s formula mass. Then 50 grams would be more than 1 mole. The conversion chart involved dividing grams by grams, which cancelled grams. What is left is moles, which is what we were looking for. Likewise, we could determine the number of grams if given moles by using a conversion chart:
For example, what is the mass of 0.500 moles of zinc (II) chloride?
Given Unit wanted
0.500 moles ZnCl
2
136.4 g ZnCl
1 mole ZnCl
2
2
=
Mole ratio
68.2 grams ZnCl
2
Cancel out units
Determine the number of moles in the following amounts of substance.
37.2 g NaCl
0.00256 g C
6
H
8
O
7
Determine the mass of substance present.
1.58 mol Fe
2
O
3
0.710 mol Ne

Since chemical equations are actually “mole recipes” for a reaction, it is imperative that chemists have a way for determining the number of moles of a substance from its volume. This is easily done since the standard mole volume is
22.4 L/mole.
For example, how many moles of oxygen molecules are present in 5.0 liters?
Given
Unit wanted
5.0 Liters O
2
1 mole O
2
22.4 L O
2
Cancel out units
Cancel out unit
For example, what is the volume of 3.2 moles of carbon dioxide?
Mole ratio
Given
3.2 moles CO
2
22.4 L CO
2
1 mole CO
2
=
Unit wanted
Mole ratio
=0.22 moles O
2
71.68 L CO
2
Cancel out units
Determine the number of moles in the following amounts of substance.
0.45 L N
2
2.63 L CO
Determine the volume of substance present.
0.0025 moles H
2
O
7.82 moles SO
2
HINT: IF YOU CONVERT MOLES YOU CAN GET TO ANOTHER UNIT (AKA VOLUME OR GRAMS). THE MOLE IS THE
UNIVERSAL CONVERSION UNIT IN CHEMISTRY.