Answer: C₃H₂
Explanation:
1) Since you are told naphthelene is a hydrocarbon, you know that its chemical formula only has atoms of C and H.
2) Since combustion adds O but not C nor H, you know that all the C and H present in the products come from the naphthelene sample.
3) Calculate the amount of C in 13.20 grams of CO₂:
Use atomic masses:
C: 12.01 g/mol
O: 16.00 g/mol
⇒ molar mass of CO₂ = 12.01 g/mol + 2×16.01 g/mol = 44.01 g/mol
Proportion of C in 13.20 g of CO₂
12.01 g C / 44.01 g CO₂ = x / 13.20 g CO₂ ⇒
x = 13.20 g CO₂ × 12.01 g C / 44.01 g CO₂ = 3.602 g C
3) Calculate the mass of H in 1.80 g of H₂O
Atomic masses:
H: 1.01 g/mol
O: 16.0 g/mol
Molar mass H₂O = 18.02 g/mol
Proportion of H in 1.80 g H₂O
2.02 g H / 18.02 g H₂O = x / 1.80 g H₂O
x = 1.80 gH₂O × 2.02 g H / 18.02 gH₂O = 0.202 g H.
4) Calculate the number of moles of C and H in the masses calculated above
Number of moles of C = 3.602 g C / 12.01 g/mol = 0.3 mol
Number of moles of H = 0.202 g / 1.01 g/mol = 0.2 mol
5) Divide both amounts by the smallest one to calculate the proportion in moles:
C: 0.3 / 0.2 = 1.5 mol
H = 0.2 / 0.2 = 1 mol
Multiply by 2 to obtain integers:
C: 3
H: 2
6) Then the proportion leads to the empirical formula C₃H₂
