In chemistry, the **simplest formula** is a chemical formula for a compound that shows the smallest whole number ratio of elements. A formula consists of element symbols, followed by subscripts that indicate the number of atoms. If there is a single atom of an element, omit the subscript. Another name for the simplest formula is the empirical formula. In contrast, the molecular formula is a multiple of the simplest or empirical formula and gives the actual whole number ratio of elements in a compound.

### Simplest Formula Examples

For example, the simplest formula for water is H_{2}O. There are two moles of hydrogen for every mole of oxygen in water. In this case, the simplest formula and molecular formula are the same.

In contrast, the simplest and molecular formula for glucose are different from each other. The simplest formula is CH_{2}O, while the molecular formula is C_{6}H_{12}O_{6}. Note that the molecular formula is a multiple of the simplest formula, where you multiply each subscript by 6.

### Example Problem: Simplest Formula From Mass Percent Composition

#### Problem

One common application of the concept is finding the simplest formula of a compound from its mass percent composition. For example, find the simplest formula for vitamin C given the mass percentages of element are:

- C = 40.9
- H = 4.58
- O = 54.5

#### Solution

The easiest method of solving this problem is assuming you have 100 grams of the sample. This way, the mass percent values add up to the same number (100%) as the sample mass (100 grams).

Next, use a periodic table and look up the atomic masses of the elements:

- H is 1.01
- C is 12.01
- O is 16.00

Knowing the atomic masses, you have a moles-to-grams conversion factor. Calculate the number of moles of each element:

- C = 40.9 g C x 1 mol C / 12.01 g C = 3.41 mol C
- H = 4.58 g H x 1 mol H / 1.01 g H = 4.53 mol H
- O = 54.5 g O x 1 mol O / 16.00 g O = 3.41 mol O

All that remains is finding the smallest whole number ratio of the elements. Do this by dividing the number of moles of each element by the small number. In this case, the smallest number is 3.41 moles (for both C and O).

- C: 3.41 / 3.41 = 1.00
- H: 4.53 / 3.41 = 1.33
- O: 3.41 / 3.41 = 1.00

A ratio of 1:1.33:1 is not a whole number ratio. Hopefully, you recognize 1.33 is about the same as the fraction 4/3. If not, you’ll recognize common fractions with a bit of practice. Write the element ratio is 1 C: 4/3 H: 1 O. Finally, multiply each number by the fraction denominator (3) to clear the fraction and get whole numbers. This gives you 3 C: 4 H: 3 O. Turn this into a chemical formula turning the ratio numbers into subscripts.

The simplest formula for vitamin C is C_{3}H_{4}O_{3}.

### References

- Burrows, Andrew. (2013).
*Chemistry: Introducing Inorganic, Organic and Physical Chemistry*(2nd ed.). Oxford. ISBN 978-0-19-969185-2. - Hill, Edwin A. (1900). “On a system of indexing chemical literature; Adopted by the Classification Division of the U.S. Patent Office”. J. Am. Chem. Soc. 22 (8): 478–494. doi:10.1021/ja02046a005
- 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.