April 16th-17th

 

Empirical and Molecular Formula 

 

What is an Empirical and Molecular Formula? Calculations Involving Empirical and Molecular Formula Calculating Empirical Formula Step 1: Percent to Mass Step 2: Mass to Moles Step 3: Divide By Small  Step 4: Multiply Til Whole Calculating Molecular Formula Step 1: Calculate the Empirical Formula Step 2: Compare the empirical and molecular formula and find the factor. Step 3: Multiply the subscript in the empirical formula by the factor. In Summary

What is an Empirical and Molecular Formula?

 

An empirical formula is the simplest ratio of elements in a compound.  For example, the empirical formula for ethane is CH₃. This formula cannot be reduced any further, since it is already in its simplest ratio.

 

A molecular formula is the actual number of each atom in the molecule in a compound.  For example, the molecular formula for ethane is C₂H₆. This formula tells us the actual number of each atom (which in this case is 2 carbon atoms and 6 hydrogen atoms in each molecule). 

 

What is the Difference?

 

Many compounds have the same empirical formulas, but different molecular formulas. For example, benzene (C₆H₆) and acetylene (C₂H₂) both have an empirical formula of CH, but their properties are very different:

 

	Benzene	Acetylene
Formula	C6H6	C2H2
State	Liquid at room temp.	Gas at room temp.
Chemical Property	Flammable	Highly combustible
Uses	Used in gasoline	Used in welding torches

 

 Even though they have the same empirical formula, it is their molecular formula that tells us how many atoms of each element there are and determines the properties of each compound. Here is a video that helps show the difference between empirical and molecular formula.

 

---

Calculations Involving Empirical and Molecular Formula

 

Calculating Empirical Formula

You can calculate the empirical formula for a compound using this song:

 

Empirical Formula Song (to the tune of “Happy Birthday”)

1.       Percent to Mass
2.       Mass to Moles
3.       Divide By Small
4.       Multiply Til Whole

 

---

Example #1:  What is the empirical formula for a compound that contains 80.04% carbon and the remainder is hydrogen?

 

Step 1: Percent to Mass

To convert from percent to mass, we assume that there is 100 grams. The ratios would not change no matter how many grams we assumed there was, but 100 is an easy number to use.  By doing this, the mass will equal the same number as the percent, but in grams.

 

_mc= 80.04 g

_mH= 19.96 g (100 g- 80.04 g)

 

Step 2: Mass to Moles

To convert from the mass to moles, you use the formula n=m/MM, where n=moles in mol, m=mass in g and MM=molar mass in g/mol. The mass is the number calculated in the previous step and the molar mass is found on the periodic table. You only need to write the formula once in your answer.

 

n_c= m_c                                                                                                                n_H= 19.96g

     MM_c                                                                                                                       1.01g/mol    

    = 80.04g                                                                                   =19.76238 mol

       12.01g/mol                                           

    = 6.66445 mol

 

Step 3: Divide By Small

To determine the ratio of the elements, you set the moles you calculated in a ratio and divide all the numbers by the smallest number.

 

          n_c: n_H= 6.66445 mol: 19.76238 mol                     

                    ÷ 6.66445= 1: 2.97

 

 Step 4: Multiply Til Whole

 When elements form compounds, the atoms combine in simple whole number ratios. This means that the subscript of the formula must be whole numbers and not decimals. For example, you cannot have C_3.5H₇ because you cannot have half of an atom. So, if you don’t get all whole numbers in step 3, you will need to multiply by a co-efficient to get a whole number using this chart:

 

If it ends in...	Multiply by...
0.33	3
0.5	2
0.25	4
0.75	4

 

If none of these work, simply try multiplying by 2, then 3, then 4, then 5, etc until you get a whole number.

 

****NOTE: If you are within 0.05 of a whole number (the decimal value is between 0.01 and 0.05 or 0.95 and 0.99) then you can round to the nearest integer.**** 

 

In this example, 2.97 is within 0.05 of 3.00, since it is only 0.03 away, so you can round to 3.00 and you do not have to do this step.

 

Final Answer: To determine the empirical formula, you use the numbers you calculated in step 3 or 4 and use them as the subscript for the elements in the formula. So, for this question, the empirical formula is CH₃. 

---

Example #2:  What is the empirical formula for a compound that contains 82.6% carbon and 17.4% hydrogen?

 

          1)  Percent to Mass

_mc= 82.6 g

_mH= 17.4 g

 

2)  Mass to Moles

            n_c= m_c                                                                                         n_H= 17.4 g

            MM_c                                                                                             1.01 g/mol    

         = 82.6 g                                                                    =17.22776 mol

         12.01 g/mol                                           

         = 6.87760 mol

 

3)   Divide By Small

          n_c: n_H= 6.87760 mol: 17.22776 mol               

                    = 1: 2.5

 

4)  Multiply til Whole

   n_c: n_H = 1: 2.5

                        = 2 : 5

 

Therefore, the empirical formula is C₂H₅. 

---

Calculating Molecular Formula

 

Ionic compounds are always in their empirical formula, since you reduce them to their simplest ratios when doing nomenclature. For example, if you get Mg₂O₂, you reduce it to MgO, which is its empirical formula. However, most covalent compounds have different empirical and molecular formulas, so you must know how to calculate the molecular formula.

 

There is a factor that exists between a compound’s empirical and molecular formula. For example, between C₅H₄O (the empirical formula) and C₁₅H₁₂O₃ (the molecular formula), there is a factor of 3. When you compare their molar masses, the same factor exists. For example, the molar mass of C₅H₄O is 80.09 g/mol, which is 3 times less than the molar mass of C₁₅H₁₂O₃, which is 240.28 g/mol. You can use this relationship to calculate the molecular formula. 

 

 

---

Example #3:  What is the molecular formula for a compound that contains 82.6% carbon and 17.4% hydrogen? The molar mass of the compound is 116.28 g/mol.

 

Step 1: Calculate the Empirical Formula

Although it does not ask for the empirical formula, you must calculate it to determine the molecular formula. Remember- percent to mass, mass to moles, divide by small and multiply til whole.

 Since we already calculated the empirical formula in the previous question, we can skip this step.

 

Step 2: Compare the empirical and molecular formula and find the factor.

Using the empirical formula you calculated, find the molar mass. Then compare it to the molar mass of the molecular formula given in the question and divide the molecular molar mass by the empirical molar mass.

 

MM_emp. = 2 (12.01g/mol) + 5 (1.01g/mol)

=29.07 g/mol

 

MM_emp. = 29.07 g/mol    <---------- x 4 ------------>    MM_mol. = 116.28 g/mol (from the question)

 

So, the molecular formula is 4 times greater than the empirical.

 

Step 3: Multiply the subscript in the empirical formula by the factor.

Therefore, the molecular formula of this compound is C₈H₂₀.

---

Here are a video with more examples of empirical and molecular formula calculations. 

 

 

If that isn't working for you, try watching this video. It is a song about empirical and molecular formula. 

 

 

Here is the link for another video that summarizes everything discussed on this wiki page. By request of the video owner, embedding is disabled, but you can click on the link below to access the video.

 

http://youtu.be/eHR9saDmeYk 

---

 

In Summary

 

•  The  empirical formula is the simplest ratio of elements in a compound and the molecular formula is the actual number of each atom in the molecule.

 

• Compounds can have the same empirical formula, but different molecular formulas and very different properties.

 

• To calculate the empirical formula, use the song- percent to mass, mass to moles, divide by small and multiply til whole.

 

• To calculate molecular formula, find the factor between the molar masses of the empirical and molecular formula and multiply the subscript by that factor. 

 

Practice

 

For some practice on calculating the empirical and molecular formula, try these online quizzes by clicking on the pictures below:

 

                       

 

If you have any questions about empirical and molecular formula, just leave a comment.