Determination of Empirical Formula

Example:

An analysis of a substance shows that it is made up of carbon, hydrogen, and oxygen. The percentage composition of the elements in the compound are determined to be:

39.10 % carbon,
8.77 % hydrogen, and
52.13 % oxygen.

Determine its empirical formula, C_xH_yO_z. What is x, y, and z?

Answer:

Step 1: Understand what the percentages mean.

When the elements of a compound are given as percent composition of the compound, it is always mass percentages. Then you can assume that if there is a 100.0 g sample of the compound:

39.10 g of the 100.0 g is contributed by the mass of carbon,
8.77 g of the 100.0 g is contributed by the mass of hydrogen,
52.13 g of the 100.0 g is contributed by the mass of oxygen.

We learned that in chemistry we count by weighing.

39.10 g of carbon is equivalent to x' moles of carbon.
8.77 g of hydrogen is equivalent to y' moles of hydrogen.
52.13 g of oxygen is equivalent to z' moles of oxygen.

Step 2: Convert grams of each element to moles.

IWe learned how to convert the mass of atoms in grams to moles of atoms.

To convert
you need to divide by the atomic mass of the atom.

Element	Conversion to Moles	Moles of each Element
C:	(39.10 g C) / 12.011 g/mole C	x' = 3.258 mole C
H:	(8.77 g H) / 1.008 g/mole H	y' = 8.683 mole H
O:	(52.13 g O) / 15.999 g/mole O	z' = 3.258 mole O

The last column,
x' (pronounced x prime), y' (pronounced y prime) and z' (pronounced z prime)

gives the mole ratios of the elements.

Step 3: Find the simplest mole ratio of C, H and O.

To derive the empirical formula of the substance, we need to find the smallest whole number mole ratio of C, H and O. This is carried out by dividing the number of moles of each element by the smallest of the mole ratios calculated.

Here, we will divide through by 3.258 moles.

C:	3.528 mole / 3.528 mole = 1.00
H:	8.683 mole / 3.528 mole = 2.66 (or 2²/₃)
O:	3.528 mole / 3.528 mole = 1.00

At this point, we manage to find the simplest mole ratio of C, H and O. If the ratio is in whole-numbers, then our job is complete. But we notice that the number ratio at this point is not whole-number, so we need to proceed to step 4.

Step 4: Convert the mole ratio obtained in Step 3 to the simplest whole-number mole ratio.

To remove the fraction, we need to multiply through by 3.

C:	1.00 x 3 = 3
H:	2 ²/₃ = ⁸/₃ x 3 = 8
O:	1.00 x 3 = 3

The empirical formula, which has the form C_xH_yO_z, has x=3, y=8, and z=3.

The empirical formula is C₃H₈O₃