Step 1

When the elements of a compound are given as percentages such as

assume that there is a 100.0-g sample of the compound. Therefore, we have:

Step 2

Convert grams of each element to moles.

molar mass
grams <==> moles

ElementConversion to MolesMoles of each Element
C:(39.10 g C) / 12.011 g C = 3.258 mole C
H:(8.77 g H) / 1.008 g H = 8.683 mole H
O:(52.13 g O) / 15.999 g O= 3.258 mole O

The last column gives the mole ratios of the elements.

Step 3

Divide the number of moles of each element by the smallest of the mole ratios calculated.

Here, we will divide by 3.258 moles.

C:3.528 mole / 3.258 mole = 1.00
H:8.683 mole / 3.258 mole = 2.66
O:3.528 mole / 3.258 mole = 1.00

Change the mole ratios in Step 3 to the smallest set of whole numbers.

C:1.00 x 3 =3
H:2.66 x 3 =8
O:1.00 x 3 =3

The empirical formula is C3H8O3