The empirical and molecular formulas are two types of chemical formulas that tell you the ratios or proportions of elements in a compound. The empirical or simplest formula gives the smallest whole number ratio of elements in a compound, while the molecular formula gives the actual whole number ratio of elements. The molecular formula is a multiple of the empirical formula, although sometimes you multiply the empirical formula by “1”, so the two formulas are the same. Combustion and composition analysis always gives the empirical formula, but you can find the molecular formula if you know molecular weight. Here are examples of empirical and molecular formulas and worked problems showing how to find these formulas from mass percentages and molecular weight.

### Empirical Formula

The empirical formula is the simplest formula for a compound. You can get the empirical formula from the molecular formula by dividing all of the subscripts in the formula by the lowest common denominator. For example, if the molecular formula is H_{2}O_{2}, then the lowest common denominator is 2. Dividing both subscripts by 2 gives the simplest formula of HO. If the molecular formula is C_{6}H_{12}O_{6}, then the lowest common denominator is 6 and the simplest formula is CH_{2}O. If the molecular formula is CO_{2}, then the lowest common denominator is 1 and the empirical formula is the same as the molecular formula.

### Molecular Formula

The molecular formula is the actual formula for a compound. Like the empirical formula, the subscripts are always positive integers. The molecular formula is a multiple of the empirical formula. For example, the empirical formula of hexane is C_{3}H_{7}, while its molecular formula is C_{6}H_{14}. Both subscripts in the empirical formula were multiplied by 2 to get the molecular formula.

### Empirical vs Molecular Formula

Here is a simple comparison of the empirical versus molecular formula:

Empirical Formula | Molecular Formula |

Simplest elemental composition of compound | Actual elemental composition of compound |

Found from mass percentages of elements in compound | Found using the empirical formula and the molecular weight of the compound |

Simple whole number ratio of elements | Multiple of the empirical formula that remains a whole number ratio |

Found from combustion or composition analysis | Used to write chemical reactions and draw structural formulas |

### Steps to Find Molecular Formula From Empirical Formula

You can find the molecular formula from the empirical formula and molecular weight.

#### Example

For example, let’s find the molecular formula of hexane, knowing its empirical formula is C_{3}H_{7} and its molecular weight is 86.2 amu.

First calculate the formula weight of the molecule. To do this, look up the atomic weight of each element, multiply each by its subscript in the empirical formula, and then add up all the values to get the formula weight.

Carbon: 12.01 x 3 = 36.03

Hydrogen: 1.008 x 7 = 7.056

Formula weight = 36.03 + 7.056 = 43.09 amu

Now, you know the molecular formula must be a multiple of the empirical formula. Find the ratio between molecular and formula weight by dividing molecular weight by empirical weight:

molecular weight / empirical weight = 86.2 / 43.09 = 2

Often, you’ll get a decimal value, but it should be close to an integer. Finally, multiply each subscript in the empirical formula by this integer to get the molecular formula:

C_{3×2}H_{7×2} = C_{6}H_{14}

Sometimes you don’t know the empirical formula, but can determine it from other data and then use it to get the molecular formula. In this case, find the molecular formula of a compound from its molecular weight and the mass percentages of each atom. To do this, follow these steps:

- Assume you have a 100 gram sample of the compound. This way, the mass percent values all add up neatly to give you the number of grams of each element.
- Use the periodic table to look up the atomic weight for each element. Remember, the atomic weight is the numbers of grams per one mole of the element. Now you can convert the number of grams of each element into number of moles.
- Find the mole ratio between the elements by dividing each mole value by the smallest number of moles. Use this ratio to get the empirical formula.
- Calculate the formula weight of the compound using the empirical formula. To do this, multiply the atomic weight by the subscript for each element and then add up all the values.
- Find the ratio between the molecular formula and empirical formula by dividing the molecular weight by the formula weight. Round this number so it is an integer.
- Multiply all subscripts in the empirical formula by the integer to write the molecular formula.

#### Example

For example, find the empirical formula and molecular formula of ascorbic acid (Vitamin C) if the molecular mass is 176 amu and a sample is 40.92% C, 4.58% H, and 54.50% O by mass.

First assume you have a 100 gram sample, which makes the mass of each element:

- 40.92 g C
- 4.58 g H
- 54.50 g O

Next, look up the atomic weights of these elements to find out how many molecules you have of each element. If you’re uncertain about this step, review how to do a gram to mole conversion.

- mol C = 40.92 g x (1 mol/12.011 g) = 3.407 mol C
- mol H = 4.58 g x (1 mol/1.008 g) = 4.544 mol H
- mol O = 54.50 g x (1 mol/15.999 g) = 3.406 mol O

Find the simplest whole number ratio between the elements by dividing each mole value by the smallest one (3.406 in this example). Watch for decimal values like “1.5”, “1.333,” or “1.667” because they indicate fractions you can use to get integer values.

- C = 3.407 mol / 3.406 mol = 1.0
- H = 4.544 mol / 3.406 mol = 1.334
- O = 3.406 mol / 3.406 mol = 1.0

The subscripts in the empirical formula need to be whole numbers, but hydrogen is a fraction. You need to ask yourself what number would you need to multiply by to get a whole number. Since “.33” is the decimal value for 1/3, you can multiply all the numbers by 3 to get whole numbers.

- C = 1.0 x 3 = 3
- H = 1.333 x 3 = 4
- O = 1.0 x 3 = 3

Plugging in these values as subscripts, you get the empirical formula:

C_{3}H_{4}O_{3}

To find the molecular formula, first determine the empirical formula mass by multiplying each subscript by the atomic weight of its atom and adding up all the values:

(3 x 12.011) + (4 x 1.008) + (3 x 15.999) = 88.062 amu

If this value is about the same as the molecular weight of the sample, then the molecular formula is the same as the empirical formula. Since 88.062 is different from 176, you know the molecular formula is a multiple of the empirical formula. Find the multiplier by dividing the molecular weight by the empirical formula weight:

176 amu / 88.062 amu = 2.0

Finally, multiply each subscript in the empirical formula by this number to get the molecular formula:

molecular formula of ascorbic acid = C_{3×2}H_{4×2}O_{3×2} = C_{6}H_{8}O_{6}

### Structural Formulas

While the empirical and molecular formulas state the type and number of atoms in a compound, they don’t tell you how those atoms are arranged. Structural formulas indicate single, double, and triple bonds, rings, and sometimes three-dimensional conformation. Types of structural formulas include Lewis structures, skeletal formulas, Newman projections, sawhorse projections, Haworth projections, and Fischer projections.

### References

- Burrows, Andrew. (2013).
*Chemistry: Introducing Inorganic, Organic and Physical Chemistry*(2nd ed.). Oxford. ISBN 978-0-19-969185-2. - Petrucci, Ralph H.; Harwood, William S.; Herring, F. Geoffrey (2002).
*General Chemistry: Principles and Modern Applications*(8th ed.). Upper Saddle River, N.J: Prentice Hall. ISBN 978-0-13-014329-7.