(Smith and Vukovich, Chapter 12)

**examples**

7.20 moles of methane CH_{4} (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 × 10^{23} CH_{4} molecues/~~mol~~
= 1.30 × 10^{25} CH_{4}
molecules

(which contains 1.30 ×
10^{25} C atoms and 4 × 1.30
× 10^{25} 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/cm^{3}; 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 cm^{3}
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

2H_{2} + O_{2}
® 2 H2O

Formation of ammonia

3H_{2} + N_{2}
® 2NH_{3}

If you want to prepare 9 pancakes (or 2H_{2}O
or 2NH_{3} molecules), you need 1 cup flour (or 2 H_{2}
or 3 H_{2} molecules, respectively).

If you want to prepare 27 pancakes (or 6H_{2}O
or 6NH_{3} molecules), you need 3 cup flour (6 H_{2} or
9 H_{2} 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 H_{2} and 10 moles
of O_{2}, how many moles of water can be prepared? Which gas is
in excess and how much?

10 mol H_{2} ´
2 mol H_{2}O/2 mol H_{2} = 10 mol H2O

10 mol O_{2} ´
2 mol H_{2}O/1 mol O_{2} = 20 mol H2O

However, after 10 mol H2O is formed, there is no
more H_{2} left. In the mean time, 10 mol H2O requires 10 mol H2O
´ 1 O_{2}
mol/2 mol H2O = 5 mol O_{2}. Thus, there is still 5 mol O_{2}
left.

**HOMEWORK**: What about you have 5 mol H_{2}
and 20 mol O_{2}? How about you have 5 H_{2} and
2 mol O_{2}?

3) If you have 15 moles of H_{2} and 10 moles
of N_{2}, how many moles of ammonia can be produced? Which gas
is in excess and how much?

15 mol H_{2} ´
2 mol NH_{3}/3 mol H_{2} = 10 mol NH_{3}

10 mol N_{2} ´
2 mol NH_{3}/1 mol N_{2} = 20 mol H2O

However, after 10 mol NH_{3} is formed,
there is no more H_{2} left. In the mean time, 10 mol NH_{3}
requires 10 mol NH_{3} ´
1 N_{2} mol/2 mol NH_{3} = 5 mol N_{2}. Thus, there
is still 5 mol N_{2} left.

**HOMEWORK**: What about you have 10 mol H_{2}
and 2 mol N_{2}? 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!