How to solve an empirical formula problem

academics chemistry

In this blog post, we will review how to determine the empirical formula of a compound using the mass percentages of the elements from which it is formed.

First, we will review the definition of an empirical formula. An empirical formula represents the simplest ratio of elements in a compound. It does not tell you about the total number of atoms in the molecule. You can determine whether a formula is empirical by looking at the subscripts on each element. Do the subscripts have a common factor? If yes (e.g. C2H6), then it is not an empirical formula. If no (e.g. CH3), then it is an empirical formula. Consider the following problem:

Which of the following could be an empirical formula?

  1. N2O4
  2. H2O
  3. N3O6
  4. Na2(PO3)2

Remember how in math class, you were asked to simplify your fractions? You can do the same thing here.

Choice A is wrong because 2:4 can be simplified to 1:2. Choice B is correct because you cannot further simplify 2:1. Choice C is wrong because 3:6 can be simplified to 1:2. Choice D is wrong because 2:2 can be simplified to 1:1.

Next, we will review how to calculate the empirical formula of a molecule based on the mass percent of the elements from which it is formed.

Consider the following problem:

What is the empirical formula of a compound with the following mass percentages? 71% Cl, 24.27% C, 4.07% H.

To solve this problem, we will use four steps.

Step 1: Change each percentage to an expression of the mass of each element in grams.

 

71% Cl becomes 71 g
24.27% C becomes 24.27 g
4.07% H becomes 4.07 g H

Step 2: Convert the amount of each element in grams to its amount in moles.

 

The molar mass of Cl = 35.45 g/mol
71 g / (35.45 g/mol) = 2 mol 

The molar mass of C = 12.01 g/mol
24.37 g / (12.01 g/mol) = 2.02 mol

The molar mass of H = 1.01 g/mol
4.07 g / (1.01 g/mol) = 4.03 mol

Step 3: Divide each of the resulting values by the smallest of these values.

 

The smallest value is 2.

Thus,

For Cl, 2 / 2 = 1
For C, 2.02 / 2 = 1.01
For H, 4.03 / 2 = 2.01

Step 4: If necessary, convert these values to whole numbers. 

 

In this problem, we can round each value to the nearest whole number.

For Cl, 1 --> 1
For C, 1.01 --> 1
For H, 2.01 --> 2

Thus our empirical formula is ClCH2, or CH2Cl.

Note that you may need to multiply the values by an integer to obtain a whole number (e.g. 3.5 can be multiplied by 2 to get 7). If you perform an operation on one value, you must do it to all of them.

To summarize, you can use these four steps to solve any problem of this type.

Step 1: Change each percentage to an expression of the mass of each element in grams.

Step 2: Convert the amount of each element in grams to its amount in moles.

Step 3: Divide each of the resulting values by the smallest of these values.

Step 4: If necessary, multiply these numbers by integers to get whole numbers. If you perform an operation on one of these numbers, you need to do it to all of them.

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