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# Coefficients in Balanced Equations

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)