Question

A pure sample of a hydrocarbon was analyzed and found to contain 12.00 g of carbon and 1.5 g of hydrogen.

a. Find the empirical formula of the compound. (Hint: as the masses are known, you do not need to assume you have a 100 g sample).

b. If the molar mass of the hydrocarbon is found to be 54.10 g/mol, what is its molecular formula?

Answer 1

• a. C₂H₃

• b. C₄H₆

Step-by-step explanation:

First question: a. Find the empirical formula of the compound

1) Calculate the number of moles of every element that is in the hydrocarbon

• number of moles = mass in grams / atomic mass

• Carbon: 12.00 g / 12.01 g/mol = 0.999 mol

• Hydrogen: 1.5 g / 1.008 g/mol = 1.488 mol

2) Divide by the least number of moles, to find the mol ratio:

• Carbon: 0.999 mol / 0.999 mol = 1

• Hydrogen: 1.488 mol / 0.999 mol = 1.5

3) Multiply by 2 to obtain whole numbers:

• Carbon: 1 × 2 = 2

• Hydrogen: 1.5 × 2 = 3

Thus, the mole ratio is 2 : 3, and the empirical formula is C₂ H₃

Second question: b. What is the molecular formula?

1) Find the mass of the empirical formula:

• C: 2 × 12.01 g/mol = 24.02 g/mol

• H: 3 × 1.008 g/mol = 3.024 g/mol

Molar mass of the empirical formula = 24.02 g/mol + 3.024 g/mol = 27.044 g/mol ≈ 27.04 g/mol

2) Find the number of times that the empirical mass is contained in the molar mass:

• 54.10 g/mol / 27.04 g / mol = 2

3) Multiply every atom in the empirical formula by the ratio 2:

• (C₂H₃)₂ = C₄H₆