The document explains the concepts and calculations of empirical and molecular formulas in chemistry, detailing how to derive one from the other and their unique coefficients. It provides a variety of practice problems for finding empirical and molecular formulas based on percent composition and molecular weights. Key points include the role of whole number coefficients, different problem types, and the importance of proper calculations using atomic masses.

1. Empirical and Molecular Formulas
Dr. Renuka Rajasekaran
Chemist and Chemistry Educator
Progressive Learning Series in Chemistry

2. Empirical and Molecular Formulas
Usually obtained by
Experimental
Methods
Usually obtained by
Calculations
So, the Empirical Formula is the simplified or condensed or reduced form of the Molecular Formula
In other words, you can get the molecular formula by multiplying the empirical formula by a whole
number coefficient or you can get the Empirical Formula by Dividing the Molecular Formula by the
Whole Number Coefficient. The whole number coefficient is also called the Magic Number, which is
unique of the particular set of empirical and molecular formulas.
Molecular Formula = Empirical Formula x Whole Number Coefficient
Empirical formula is the shortened molecular formula of
a substance. It gives the simplest ratio of atoms in the
formula of the substance. Empirical formula is generally
obtained by Experimental Methods. It can also be
derived from known molecular formula of any substance.
Molecular formula is the actual molecular formula of a
substance. It gives the exact number of atoms in the
formula of the substance. Molecular formula is generally
derived from the Assays and Empirical Formula by
calculations
Molecular Formula/
Whole Number Coefficient
Empirical Formula x
Whole Number Coefficient

4. Check Your Findings
1. The Whole Number Coefficient can be different for
different compounds.
2. The Whole Number Coefficient can be 1, which
means: for some compounds, the Molecular and
Empirical Formulas can be the same.
3. Different Molecular Formulas can have the Same
Empirical Formula.

5. Math Problems with Empirical and Molecular Formulas
Types of Problems
(1) Finding the Whole Number
Coefficient (Magic Number)
(2) Finding the Empirical Formula
from Percent Composition
(3) Finding the Molecular Formula
from Percent Composition and
Molecular Weight (aka Molar
Mass or Molecular Formula
Mass)
Note: Problem Type 3 is a
combination of Type 1 and Type 2
problems.
You need: Periodic Table and a Calculator
Recall the following before proceeding with calculations
Number of Moles of a substance = Mass/Molecular Formula Mass
Number of Moles of atoms in a substance = Percent Composition/Average Atomic Mass
Molecular Formula Mass is also often interchangeably referred to as
Molar Mass, Molecular Weight, Formula Weight, or Formula Mass. Note
that unless and until the prefix empirical has been used, the phrase,
“formula mass’ refers only to the molecular formula mass.
Remember
(1) mol when used as a unit is number of moles
(2) Number of atoms need to be a whole number; in your calculations, if
you get number of atoms in fractions in the empirical formula,
multiply the entire empirical formula by an integer to get a whole
number ratio of atoms.
(3) Remember: We are dealing with the mass of one mole of atoms;
therefore, the average atomic mass of atoms should be expressed in
gram and not in atomic mass unit.

6. TYPE 1 Problems

7. 1. Finding the Magic Number or the Whole
Number Coefficient
By Comparisons of the
Empirical and Molecular
Formulas
Or
Ratio of the Molecular
Weight to the Empirical
Formula Mass
Empirical Formula
H2O
HO
O
O
18
17
16
16
Molecular Formula
H2O
H2O2
O2
O3
18
34
32
48
Magic Number
H2O
H2O2
O2
O3
1 (18/18 = 1)
2 (34/17 = 2)
2 (32/16 = 2)
3 (48/16 = 3)

8. TYPE 2 Problems

9. 2. Empirical Formula from Percent composition
Independent Practice
A compound is 75.46% carbon, 4.43% hydrogen, and 20.10% oxygen by
mass. What is the empirical formula for this compound?
1. Treat percent as mass (grams) and thus
convert grams to moles by using the formula
Number of Moles = Percent Composition/Average Atomic Mass
Carbon: 49.32/12.01 = 4.107 mol
Hydrogen: 6.85/1.01 = 6.78 mol
Oxygen: 43.84/16.00 = 2.74 mol
2. Divide each of the above three values of
moles by the smallest of the value found
amongst them
Carbon: 4.107 mol/2.74 mol = 1.5
Hydrogen: 6.78 mol/2.74 mol = 2.47
Oxygen: 2.74 mol/2.74 mol = 1
3. Multiply each number by a suitable integer to
obtain whole number for all the atoms. In this
case, 2 is the suitable integer.
Carbon: 1.5 x 2 = 3
Hydrogen: 2.5 x 2 = 5
Oxygen: 1 x 2 = 2
So the Empirical Formula for Adipic acid is: C3H5O2.
Guided Practice
Adipic acid contains 49.32? C, 43.84% O, and 6.85% H by
mass. What is the Empirical Formula for Adipic acid?

10. TYPE 3 Problems

11. 3. Molecular Formula from Empirical Formula
Independent Practice
A compound with an empirical formula of C10H7O2 has a formula mass of
318.31 g/mol, find its molecular formula
Guided Practice
The empirical formula for adipic acid is C3H5O2. The
molecular weight of adipic acid is 146 g/mol. What is the
molecular formula of adipic acid?
1. Find the Mass of the Empirical Formula of C3H5O2
2. Divide the Molecular Weight by the mass of the
Empirical Formula to get the Whole Number Coefficient
3. Multiply the Empirical Formula by the Whole Number
Coefficient
The Molecular Formula for Adipic Acid is C6H10O4
146/73 = 2
3(12.01 g) + 5(1.01 g) + 2(16.00 g) = 73.08 g
[C3H5O2] x 2 = C6H10O4

12. Home Work: Show Detailed Work
Find the empirical formula for the following
molecular compositions:
1. 88.8% copper; 11.2% oxygen
2. 40% carbon; 6.7% hydrogen; 53.3% oxygen
3. 92.3% carbon; 7.7% hydrogen 4. 70.0% iron;
30.0% oxygen
4. 5.88% hydrogen; 94.12% oxygen
5. 38.7% chlorine; 61.3% fluorine
6. 7.19% phosphorus; 92.81% bromine
7. 30.4% nitrogen; 69.6% oxygen
Find the molecular formula for the following:
1. If the compound in question 7 has a molar
mass of 431g/mol, what is the molecular
formula?
2. If the compound in question 8 has a molar
mass of 92g/mol, what is the molecular
formula?
3. Naphthalene is a carbon and hydrogen
containing compound often used in moth
balls. Its empirical formula is C5H4 and its
molar mass is 128.16g/mol. Find the
molecular formula.
4. A compound with the following
composition has a molar mass of
60.10g/mol: 39.97% carbon; 13.41%
hydrogen; 46.62% nitrogen. Find the
molecular formula.
Answers
Empirical Formula
Answers:
1. Cu2O
2. CH2O
3. CH
4. Fe2O3
5. HO
6. ClF3
7. PBr5
8. NO2
Molecular Formula
Answers:
1.PBr5
2. N2O4
3. C10H8
4. C2H8N2