Problem

A blue powdered substance is found to be made of 25.3% copper, 12.9% sulfur, 25.7% oxygen, and 36.1% water. Determine the empirical formula of this substance.

Solution

Consider only 100 grams of this mystery compound. Its contents would be 25.3 grams of copper , 12.9 grams of sulfur, 25.7 grams of oxygen, and 36.1 grams of water. With this information, construct a table including the molar masses of each component, and the number of moles (to be calculated).

Compound Cu S O H2O
Mass (g) 25.3 12.9 25.7 36.1
Molar mass (g/mol) 63.55 32.06 16.00 18.02
Moles (mol)

To calculate the moles, simply divide the masses of each component by its respective molar mass.

Compound Cu S O H2O
Mass (g) 25.3 12.9 25.7 36.1
Molar mass (g/mol) 63.55 32.06 16.00 18.02
Moles (mol) 0.398 0.402 1.61 2.00

There is approximately 0.400 moles of copper, 0.400 moles of sulfur, 1.6 moles of oxygen, and 2 moles of water. Look at the lowest number of moles, in this case copper and sulfur, and determine the multiplier.

To calculate the multiplier, simply divide 1 by the lowest number of moles. Use this multiplier to determine the ratio of each component of this mystery compound.

Cu:S:O:H2O = 1:1:4:5

Since this compound is not dissolved in water, it should be a hydrate. Hence the empirical formula is .

This is copper (II) sulfate pentahydrate!