Final answer:
To find the empirical formula of the hydrocarbon, we need to determine the moles of carbon and hydrogen in the given quantities of CO₂ and H₂O produced. The empirical formula for the hydrocarbon is C₁H₂. Option a
Step-by-step explanation:
To find the empirical formula of the hydrocarbon, we need to determine the moles of carbon and hydrogen in the given quantities of CO₂ and H₂O produced. First, convert the mass of CO₂ and H₂O to moles using their molar masses. Then, determine the moles of carbon and hydrogen in each compound by dividing the moles of CO₂ and H₂O by their respective coefficients in the balanced equation for combustion.
Finally, divide the moles of carbon and hydrogen by the smallest number of moles to get the empirical formula.
In this case, the moles of carbon and hydrogen in CO₂ are:
Moles of CO₂ = 8.94 g CO₂ x (1 mol CO₂ / 44.01 g CO₂) = 0.203 mol CO₂
Moles of C in CO₂ = 0.203 mol CO₂ x (1 mol C / 1 mol CO₂) = 0.203 mol C
Moles of H in CO₂ = 0.203 mol CO₂ x (0 mol H / 1 mol CO₂) = 0 mol H
Similarly, the moles of carbon and hydrogen in H₂O are:
Moles of H₂O = 4.12 g H₂O x (1 mol H₂O / 18.02 g H₂O) = 0.229 mol H₂O
Moles of C in H₂O = 0.229 mol H₂O x (0 mol C / 1 mol H₂O) = 0 mol C
Moles of H in H₂O = 0.229 mol H₂O x (2 mol H / 1 mol H₂O) = 0.458 mol H
Since the moles of carbon and hydrogen are both very low, the empirical formula must have a 1:2 ratio of carbon to hydrogen. Therefore, the empirical formula of the hydrocarbon is C₁H₂. Option a