Valeric acid, an organic acid, contains only C, H, and O. If 0.471 g of the acid burns completely in O2 it gives 1.01 g CO2 and 0.415 g H2O. Determine the empirical formula of the acid.

The empirical formula is C5H10O2

Explanation:

Step 1: Data given

Mass of the acid = 0.471 grams

Mass of O2 produced = 1.01 grams

Mass of H2O produced = 0.415 grams

Molar mass CO2 = 44.01 g/mol

Molar mass C = 12.01 g/mol

Molar mass O = 16.00 g/mol

Molar mass H2O = 18.02 g/mol

Molar mass of H = 2.02 g/mol

Step 2: Calculate moles CO2

Moles CO2 = mass CO2 / molar mass CO2

Moles CO2 = 1.01 grams / 44.01 g/mol

Moles CO2 = 0.0229 moles

Step 3: Calculate moles C

In 1 mol CO2 we have 1 mol C

In 0.0229 moles CO2 we have 0.0229 moles C

Step 4: Calculate mass C

Mass C = moles C * molar mass C

Mass C  = 0.0229 moles * 12.01 g/mol

Mass C = 0.275 grams

Step 5: Calculate moles H2O

Moles H2O = 0.415 grams / 18.02 g/mol

Moles H2O = 0.0230 moles

Step 6: Calculate moles H

In 1 mol H2O we have 2 moles of H

In 0.0230 moles we have 2*0.0230 = 0.0460 moles H

Step 7: Calculate mass H

Mass H = 0.0460 * 1.01 g/mol

Mass H = 0.04646 grams

Step 8: Calculate mass O

Mass O = 0.471 grams - 0.275 grams - 0.04646

Mass O = 0.14954 grams

Step 9: Calculate moles O

Moles O = 0.14954 grams / 16.00 g/mol

Moles O = 0.009346 moles

Step 10: Calculate mol ration

We divide the smallest amount of moles

C: 0.0229 moles /  0.009346 moles =2.5

H: 0.0460 moles/  0.009346 moles = 5

O:  0.009346 moles /  0.009346 moles = 1

The empirical formula is C5H10O2