7.20 moles of methane CH4 (molar mass = 12 + 4 ´ 1 g) is
16.0 g/ mol = 115 g
345 g methane is
16.0 g/mol = 21.6 mol, which contains
6.02 × 1023 CH4 molecues/ mol
= 1.30 × 1025 CH4
(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
÷ 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".
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!