Final answer:
The molecular formula of the original hydrocarbon is C₄H₉, determined by analyzing the molar ratios of CO₂ and H₂O produced from the combustion of 0.40 mol of the hydrocarbon, which indicated there were 4 moles of carbon and 9 moles of hydrogen in the hydrocarbon.
Step-by-step explanation:
The question asked is to determine the molecular formula of the hydrocarbon from the products of its complete combustion. It is given that 0.40 mol of a hydrocarbon CxHy produces 1.60 mol of CO₂ and 1.80 mol of H₂O. To solve this, we use the stoichiometric relationships that 1 mol of CO₂ comes from 1 mol of carbon (C), and 1 mol of H₂O comes from 2 mol of hydrogen (H).
Since 1.60 mol of CO₂ is produced, there must have been 1.60 mol of carbon in the original hydrocarbon. Similarly, since 1.80 mol of H₂O is produced, there must have been 1.80 mol * 2 = 3.60 mol of hydrogen in the original hydrocarbon. Given that the original sample is 0.40 mol, the molecular formula can be deduced by dividing the mols of each element in the product by the mols of the original sample to find the subscripts in the molecular formula. Therefore, for carbon, we have 1.60 mol / 0.40 mol = 4, and for hydrogen, we have 3.60 mol / 0.40 mol = 9. Thus, the molecular formula is C₄H₉.