examples
7.20 moles of methane CH₄ (molar mass = 12 + 4 ´ 1 g) is
    7.20 mol ´ 16.0 g/mol = 115 g

345 g methane is
    345 g ÷ 16.0 g/mol = 21.6 mol, which contains
    21.6 mol × 6.02 × 10²³ CH₄ molecues/mol = 1.30 × 10²⁵ CH₄ molecules
    (which contains 1.30 × 10²⁵ C atoms and 4 × 1.30 × 10²⁵ H atoms.)

The volume of 1 mole methane gas is 22.4 L at standard temperature and pressure (STP). What is the volume of 345 g methane?
    From above question, 345 g methane is 21.6 mol, which is 21.6 mol × 22.4 L/mol = 484 L

How many times does water expand when it is completely changed into gaseous form (not the visible "moisture" or "steam")?
(Seemingly there is no number for you to do any calculation!  However, here are the numbers you can easily obtain: water density, 1.00 g/cm³; gaseous water occupies 22.4 L at STP; molar mass; and compare a fixed amount of water and its gaseous form)
    1.00 g water is 1.00 cm³ or 0.01 L
    1.00 g water is 1.00 g ÷ 18.0 g/mol = 0.0556 mol
    0.0556 mol water is changed into 0.0556 mol of gaseous water, which is
    0.0556 mol × 22.4 L/mol = 1.25 L
    0.01 L water expands to 1.25 L gaseous form, which is 1.25/0.01 = 125 times expansion (at STP)

When the temperature is higher, the expansion will be larger (this will be discussed in a later chapter). This is the theoretical foundation of the "steam engine".
 

Stoichiometry

recipe for pancakes
    1 cup flour + 3 eggs + 2 cups milk = 9 pancakes (4×1/4 inch)

Formation of water
    2H₂ + O₂ ® 2 H2O

Formation of ammonia
    3H₂ + N₂ ® 2NH₃

If you want to prepare 9 pancakes (or 2H₂O or 2NH₃ molecules), you need 1 cup flour (or 2 H₂ or 3 H₂ molecules, respectively).
If you want to prepare 27 pancakes (or 6H₂O or 6NH₃ molecules), you need 3 cup flour (6 H₂ or 9 H₂ molecules, respectively).

How about the following situations?
1) You have 10 cups of flour, 8 cups of milk, and 6 eggs, how many pancakes can you prepare?
Having stoichiometric amount of every thing (i.e., with the correct ratios of the ingredients), you can prepare
    10 cups flour ´ 9 pancakes/1 cup flour = 90 pancakes
    6 eggs ´ 9 pancakes/3 eggs = 18 pancakes
    8 cups milk ´ 9 pancakes/2 cups milk = 36 pancakes

This suggests that after you have prepared 18 pancakes you will run out of eggs, despite the large amount of other ingredients!
    How much of the other ingredients are left after you have prepared 18 pancakes?
(Out of the 90 pancakes from 10 cups of flour, you can prepare only 18 pancakes because of the limited number of eggs you have. That means you'll have the amount of flour which can prepare 90 – 18 = 72 pancakes, which is equivalent to 72 cups flour ÷ 9 pancakes/1 cup flour = 8 cups flour left.)

It is very obvious that if you do not have one of the ingredients, you cannot make the kind of pancake describe here.

If you know how to prepare any number of pancakes with correct amount of each ingredient and also know different situations like the one described above, you should have no problem working out the following "chemical calculations".  This is just like that if you know how to do grocery calculations, you should be able to work out the calculations about moles, mass, and molar mass.

2) If you have 10 moles of H₂ and 10 moles of O₂, how many moles of water can be prepared? Which gas is in excess and how much?
    10 mol H₂ ´ 2 mol H₂O/2 mol H₂ = 10 mol H2O
    10 mol O₂ ´ 2 mol H₂O/1 mol O₂ = 20 mol H2O
However, after 10 mol H2O is formed, there is no more H₂ left. In the mean time, 10 mol H2O requires 10 mol H2O ´ 1 O₂ mol/2 mol H2O = 5 mol O₂. Thus, there is still 5 mol O₂ left.

HOMEWORK: What about you have 5 mol H₂ and 20 mol O₂?  How about you have 5 H₂ and 2 mol O₂?

3) If you have 15 moles of H₂ and 10 moles of N₂, how many moles of ammonia can be produced? Which gas is in excess and how much?
    15 mol H₂ ´ 2 mol NH₃/3 mol H₂ = 10 mol NH₃
    10 mol N₂ ´ 2 mol NH₃/1 mol N₂ = 20 mol H2O
However, after 10 mol NH₃ is formed, there is no more H₂ left. In the mean time, 10 mol NH₃ requires 10 mol NH₃ ´ 1 N₂ mol/2 mol NH₃ = 5 mol N₂. Thus, there is still 5 mol N₂ left.

HOMEWORK: What about you have 10 mol H₂ and 2 mol N₂?  and other situations?

All this means that if you know how to follow a recipe to prepare a dish and do some calculations to determine how much of each ingredient you need and how much of some ingredients will be left, you can also follow the stoichiometry of a chemical reaction to do similar kinds of calculations!