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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.
N_{2} + 3H_{2} => 2NH_{3}
We can write the following conversion factors:
1 mole N_{2} = 3 moles H_{2} = 2 moles NH_{3}
and
1 molecule N_{2} = 3 molecules H_{2} = 2 molecules NH_{3}
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 N_{2})  (2 moles NH_{3})  = 10 moles NH_{3} 
(1)  (1 mole N_{2}) 

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 NH_{3})  (1 moles N_{2})  = 3.8 moles N_{2} 
(1)  (2 mole NH_{3}) 

(7.6 moles NH_{3})  (3 moles H_{2})  = 11.4 moles H_{2} = 11 moles H_{2} 
(1)  (2 mole NH_{3}) 

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(N_{2}) = 2(14.01) = 28.02 g/mol
MW(H_{2}) = 2(1.01) = 2.02 g/mol
(3.8 moles N_{2})  (28.02 g N_{2})  = 106.476 g N_{2} = 110 g N_{2} 
(1)  (1 mole N_{2}) 

(11 moles H_{2})  (2.02 g H_{2})  = 22.22 g N_{2} = 22 g N_{2} 
(1)  (1 mole H_{2}) 
