Stoichiometry comes from Greek "stoikheion" meaning element and "metry" from "metron" meaning to measure. So stoichiometry is about measuring elements involved in a chemical reaction.

Because atoms are so small we must count them without counting them. We can also weigh them without weighing them.

Simple Combinations:

As said before, when atoms combine to make molecules, they combine in simple ratios, such as 1:1, 1:2, 2:2, 3:1, etc. There are no fractions. So this makes our job of counting much easier.

Chemical Equations are simple:  As shown in the tutorial on moles, atoms combine in simple ratios. That means the chemical equations that show and balance the starting "reactants" and ending "products" are fairly simple.

Here we see how hydrogen and oxygen (reactants) react and produce water. It's a simple rearrangement.
Roll mouse over image to see animation.

Need for Water:

I like to do problems that involve survival. That way you've got a good reason to learn how to do these calculations.

Let's say you are planning an expedition into a desert and water will be critical. They say that a person needs about 1 gallon or 4 liters of water a day to stay alive.

You don't mind carrying extra water, but liquid water has its drawbacks...

Liquid water drawbacks:

If water is spilled, it will quickly be lost as it soaks into the sand.

If the water gets contaminated with poison, bacteria, or mold, it would be unsuitable to drink.

If open to the hot, dry air, it will evaporate.

In some areas, the value of water is so high that you risk being robbed of your water.

Therefore depending only on liquid water has many drawbacks.

Salt Hydrates as an answer:

Many salts have water bound to the salt molecule. For example, Epsom salt has the formula of MgSO₄•7H₂O. This formula indicates that each magnesium sulfate molecule has 7 water molecules around it. The water that is bound to it will not evaporate in the sun nor get contaminated with microbes or poisons.

If spilled on the ground, it can be scooped up and salvaged.

Robbers won't recognize it as a water source.

Here's the magnesium sulfate heptahydrate molecule. "Hepta" means "7" and "hydrate" means water.

When heated to 250°C, the water molecules are driven off. In a distillation apparatus, the water will condense and can be collected.

Now that we have a safe way to store some extra water, let's get back to our expedition planning. We need 4 liters per day per person. (Remember "per" is set up as a fraction. If you hear "per" twice, then both are in the denominator and typically separated by a bullet "·".) Notice that "persons" and "days" cancel (shown in red).

We need 24 liters of water. How many pounds of Epsom salts do we need to take in order for us distill off 24 liters of water?

When you hear a question that you have no idea how to answer, don't panic. You don't need to know how to do the problem right away. Just take it a step at a time.

You begin these kind of problems with a balanced chemical equation. This one is easy. The magnesium sulfate heptahydrate decomposes into anhydrous magnesium sulfate and 7 water molecules. "Anhydrous" means no water.

MgSO₄•7H₂O -> MgSO₄ + 7H₂O

The problem would be easy if it asked "How many magnesium sulfate heptahydrate molecules do you need to make 14 water molecules?" From the balanced equation we see that there's one magnesium sulfate heptahydrate molecule for every 7 water molecules.

14 H₂O x 1MgSO₄•7H₂O = 2 MgSO₄•7H₂O (1 is not written but understood)
                          7H₂O
The thing to remember is that balanced equations are good at counting the various molecules and seeing the ratio of one to the other. So that means if we are given weight or volume, we must convert it to a number. Moles is the preferred way to count these large numbers and because the Periodic Table gives us weight per mole.

When dealing with water, it's easy to convert volume to weight. Once you have weight you can convert that to number (moles). Commit this to memory. A liter of water weighs 1,000 grams (1 kilogram).

We know we need 24 liters, so that's 24 kilograms or 24,000 grams.

The formula for water is of course, H₂O. We refer to these sections of the Periodic Table to find the weight of each mole of hydrogen and oxygen. One mole of hydrogen weighs 1.008 grams. One mole of oxygen weighs 16.00 grams. For a mole of H₂O, we need two moles of hydrogen atoms. So the total weight of a mole of H₂O molecules is 1.008 + 1.008 + 16.00 = 18.016 grams.

Now we have a conversion for weight to moles.

Now that we have moles of water we can use the equation to figure out the moles of the magnesium sulfate heptahydrate. Looking at the equation we see the number of water molecules is 7 times that as the molecules of magnesium sulfate heptahydrate.
MgSO₄•7H₂O -> MgSO₄ + 7H₂O

In the spreadsheet the math formula put into F2 (the answer) would be: =A2/C3
That will divide the 1332 by 7 giving us 190.3. You don't have to multiply by C2 because that's just a "1".

We know moles of Epsom salts, but the original question is how many pounds of Epsom salts. Now we work backwards to find weight (mass).
To do that we need to know what one mole of magnesium sulfate heptahydrate weighs. Just like water, we've got to go through the Periodic Table to find the weight of one mole of each element in that compound.

Here are the two sections of the Periodic Table that we can look up the mass of one mole of each of these atoms. Magnesium is 24.31 grams per mole. Sulfur is 32.07 grams per mole. Oxygen is 16.00 grams per mole, but since there are 4 oxygen atoms in sulfate and 7 in the 7 waters, that's 11 oxygen atoms. So 11x16.00g.=176g of oxygen in a mole of the compound. Hydrogen is 1.008 grams per mole, but there are 14 of them because there are 7 waters. Those all add up to 246 grams for each mole of magnesium sulfate heptahydrate.

This is how we changed grams to moles for water:
24,000 grams x  1 mole H₂O  = 1332 moles
                          18.016 grams
Above we show the the Epsom salt is 1/7 the number of water molecules (1/7 of 1332moles=190.3moles) Now we need to do the reverse. Change moles to grams for Epsom salt
190.3 moles x  246.5 grams MgSO₄·7H₂O  = 46909 grams of Epsom salt
                            1 mole
Notice that to cancel the moles, gram is on top and mole is on the bottom.

In the USA we don't normally buy things in grams but in pounds. So let's do one final conversion (grams to lbs).

Commit this number to memory. One pound is 454 grams. If you look at the bottom of the box, you will see that they say 1 lb. = 453 grams. It is actually 453.6 grams. So 454 is rounded up and 453 is rounded down. I remember 454 because my old Corvette had a 454 cubic inch engine.

46909 g. x   1 lb. = 103 lbs.
                  454 g.

So we have our answer. 103 lbs of Epsom salt will release 24 liters of water ( about 53 lbs of water).

Epsom Salt costs about $1 per pound, so for $103 we can help guarantee our survival.

Here are the 3 steps that we followed. (1) We started with the 24,000 grams of water and converted that into the number of water molecules (1332 moles). (2) Using the 1 to 7 ratio in the balanced equation, we changed 1332 moles to 190.3 moles of magnesium sulfate heptahydrate. (3) That was converted to grams, and then to pounds.

With all of these calculations to do, you might prefer to just take your chances with the desert.

These kind of problems can be summarized by this graph. Typically the mass of a reactant or product is given, and the mass of something else is asked for. In this example on the left, the mass of the first reactant is given and the mass of the first product is asked for. The first step is to go from the grams given to its number of moles. One consults the Periodic Table to find the grams per mole of each element. From the moles of the given compound, you calculate the moles of the compound asked about. You use the balanced equation to see the ratio. Here it is "n₁" and "n₃". If "n₁" is 1 and "n₃" is 2, we know the moles of the product is two times larger. Finally, we convert these moles to grams again using the Periodic Table to lookup the grams per mole of each element in the compound.

FACT:  If the mass or moles of any compound is given, the mass or moles of any other compound in the balanced chemical equation can be found.

Let's do the math.

Na (sodium) is 22.99 grams per mole. Oxygen is 16.00, and hydrogen is 1.008. Those add up to 40.00 grams per mole for NaOH

5.00 g. x 1 mole = 0.125 moles NaOH
               40.00 g

(1) is finished. Now for (2). Note: "mol" is abbreviation for "mole".
0.125 mol NaOH x 1 Na₂SO₄  = 0.0625 moles Na₂SO₄
                                 2 NaOH

Normally the 1 in front of compounds is not shown. So if you don't see a number, just assume it is 1.
(3) The last step is to convert the 0.0625 moles of Na₂SO₄ to grams. Consulting the Periodic Table above, we get 32.07 g/mol for sulfur. 16.00 g/mol for oxygen (times 4) and 22.99 for Na (times 2). That all adds up to 142 grams per mole of Na₂SO₄
0.0625 mol x 142 g. = 8.88 g. Na₂SO₄
                      1 mol
Notice "moles" are placed so that they cancel. So 8.88 grams is the final answer.

Problem 1: What is the math formula put into cell H2?

Problem 2: What is the math formula put into cell J2? (Note: the math formula does not need to include any cells that just contain a "1")

Problem 3: What is the math formula put into cell R2? (Note: the math formula does not need to include any cells that just contain a "1" because multiplying or dividing by "1" does not change the answer)

Instead of Epsom salts to obtain water, another common hydrated salt can be used. It is alum, which is found in the spice section of a grocery store. Alum is used in pickling of pickles and olives. The chemical equation for the dehydration of alum is:
KAl(SO₄)₂·12H₂O --> KAl(SO₄)₂ + 12H₂O

Problem 9:

The image on the left shows the balanced equation for sodium hydroxide neutralizing sulfuric acid. For the starting grams, use the atomic number of your element code name. For example, if your code name was sulfur, you would use 16 grams as the starting grams of NaOH because the atomic number of sulfur is 16. How many grams of water is produced starting with the grams of NaOH that match your atomic number? (Hint: Notice that the number of NaOH molecules match those of H₂O molecules).

If locked in a room that was sealed from any air coming in, this jar of potassium chlorate (KClO₃) could save your life. When heated, it decomposes into KCl and O₂.

Problem 10: If this jar contained 445 grams of KClO₃, how many moles of O₂ is produced?

Problem 11: Let's say the room oxygen plus the oxygen from the KClO₃ totals 223 liters of oxygen. How many minutes will the oxygen last if you consume 2 grams of oxygen per minute? (Note 22.4 liters of oxygen equals one mole of oxygen)

Problem 12: After an explosion on the Apollo 13 moon mission, the astronauts aboard the module had to make an emergency return trip to Earth. They had enough O₂ to make it back to Earth but the CO₂ build up from their breath would kill them first. So they had to create a make-shift CO₂ scrubber to remove the excess CO₂ in the air. The chemical in the scrubber that captures CO2 is Lithium hydroxide (LiOH). Here's the equation:
2LiOH + CO₂ --> Li₂CO₃+ H₂O

If there were 3.0 pounds of lithium hydroxide in the scrubber, how many grams of CO₂ could be captured?