Coefficients from Balanced Equations
Dr. MJ Patterson
The coefficients in a balanced equation provide another set of conversion factors.
Let's start with the car analogy. If you take 4 wheels and 1 body you can make 1 car. As a chemical equation we would write:
4 wheels + 1 body => 1 car
From this equation, we can pull the following conversion factors:
4 wheels = 1 body = 1 car
This is not saying that 1 car and 4 wheels are identical. Instead, it is saying that 4 wheels and 1 body are required to make 1 car.
For a chemical process, let's look at the Haber process to produce ammonia from nitrogen and hydrogen.
N2 + 3H2 => 2NH3
We can write the following conversion factors:
1 mole N2 = 3 moles H2 = 2 moles NH3
and
1 molecule N2 = 3 molecules H2 = 2 molecules NH3
These conversion factors are saying that 1 mole (or molecule) of nitrogen and 3 moles (or molecules) of hydrogen are required to make 2 moles (or molecules) of ammonia.
Example 1:
In the Haber process, how many moles of ammonia can be made from 5.0 moles of
nitrogen?
Solution 1:
Start with the amount that is given in the problem. Use the appropriate
conversion factors to convert to ammonia, making sure that units cancel.
|
(5.0 moles N2) |
(2 moles NH3) |
= 10 moles NH3 |
|
(1) |
(1 mole N2) |
|
Example 2:
How many moles of both nitrogen and hydrogen are required to produce 7.6 moles
of ammonia?
Solution 2:
Start with the 7.6 moles of ammonia given in the problem, and use the
appropriate conversion factors to calculate both of these answers.
|
(7.6 moles NH3) |
(1 moles N2) |
= 3.8 moles N2 |
|
(1) |
(2 mole NH3) |
|
|
(7.6 moles NH3) |
(3 moles H2) |
= 11.4 moles H2 = 11 moles H2 |
|
(1) |
(2 mole NH3) |
|
Example 3:
How many grams of nitrogen and hydrogen are needed to produce 7.6 moles of
ammonia?
Solution 3:
We already calculated the number of moles of nitrogen and hydrogen
needed. Now we just need the molecular weights to convert to grams.
Note that nitrogen and hydrogen both are homonuclear
diatomic molecules, so the molecular weight of the molecules will be twice the
molar mass of the elements.
MW(N2) = 2(14.01) = 28.02 g/mol
MW(H2) = 2(1.01) = 2.02 g/mol
|
(3.8 moles N2) |
(28.02 g N2) |
= 106.476 g N2 = 110 g N2 |
|
(1) |
(1 mole N2) |
|
|
(11 moles H2) |
(2.02 g H2) |
= 22.22 g N2 = 22 g N2 |
|
(1) |
(1 mole H2) |
|