A complete combustion of a hydrocarbon forms 1.10 g of CO2 and 0.45 g of H2O. The molar mass of the hydrocarbon is 84.0 g mol⁻¹. Determine its empirical and molecular formula.
Answer (1)
To determine the empirical and molecular formula of a hydrocarbon from the given information, we can follow these steps:
Identify the Masses Given:
The mass of CO₂ produced is 1.10 g.
The mass of H₂O produced is 0.45 g.
Determine Moles of Carbon and Hydrogen:
The combustion of a hydrocarbon yields CO₂ and H₂O, allowing us to find the number of moles of C and H in the original hydrocarbon.
Moles of CO₂:
The molar mass of CO₂ is approximately 44.01 g/mol. Therefore, moles of CO₂ can be calculated using:
Moles of C O 2 = 44.01 g/mol 1.10 g ≈ 0.0250 moles
Each mole of CO₂ contains one mole of C, so there are 0.0250 moles of C.
Moles of H₂O:
The molar mass of H₂O is approximately 18.02 g/mol. Therefore, moles of H₂O can be calculated using:
Moles of H 2 O = 18.02 g/mol 0.45 g ≈ 0.0250 moles
Each mole of H₂O contains two moles of H, so there are 2 × 0.0250 = 0.0500 moles of H.
Determine the Empirical Formula:
Convert the moles of C and H into whole-number ratios to find the empirical formula.
The ratio of C:H is 0.0250:0.0500, which simplifies to 1:2.
Thus, the empirical formula is CH₂.
Determine the Molecular Formula:
To find the molecular formula, we utilize the molar mass of the hydrocarbon (given as 84.0 g/mol) and compare it to the molar mass of the empirical formula.
Molar mass of CH₂ (empirical formula) = 12.01 + 2 ( 1.01 ) = 14.03 g/mol
To find the number of empirical units in the molecular formula:
n = 14.03 g/mol 84.0 g/mol ≈ 6
Thus, the molecular formula is C₆H₁₂.
Therefore, the empirical formula of the hydrocarbon is CH₂, and its molecular formula is C₆H₁₂.
