14. A complete combustion of a hydrocarbon forms 1.10 g of CO2 and 0.45 g of H2O. The molar mass is 84.00 g mol-1. Determine the empirical formula and molecular formula of the hydrocarbon.
Answer (1)
To determine the empirical and molecular formula of the hydrocarbon, we must follow a series of steps involving mass conversion and mole calculations.
Step 1: Calculate the moles of each combustion product.
The given masses are:
1.10 g of CO2
0.45 g of H2O
To find the moles, we need the molar masses:
Molar mass of CO2 = 44.01 g/mol
Molar mass of H2O = 18.02 g/mol
Moles of CO2 = 44.01 g/mol 1.10 g = 0.025 mol
Moles of H2O = 18.02 g/mol 0.45 g = 0.025 mol
Step 2: Determine the moles of carbon and hydrogen in the hydrocarbon.
Since each molecule of CO2 has 1 carbon atom, the moles of carbon is equal to the moles of CO2:
Moles of C = 0.025 mol
Since each molecule of H2O has 2 hydrogen atoms, we multiply the moles of H2O by 2 to find the moles of hydrogen:
Moles of H = 0.025 mol × 2 = 0.050 mol
Step 3: Establish the empirical formula.
The ratio of moles of carbon to hydrogen in the empirical formula is 0.025:0.050, which simplifies to 1:2.
Thus, the empirical formula of the hydrocarbon is CH 2 .
Step 4: Determine the molecular formula using the molar mass.
The empirical formula molar mass of CH 2 is:
Carbon: 12.01 g/mol
Hydrogen: 2.02 g/mol ( 1.01 g/mol × 2 )
Total: 14.03 g/mol
To find the molecular formula, divide the given molar mass by the empirical formula molar mass:
14.03 g/mol 84.00 g/mol ≈ 6
Multiply the subscripts in CH 2 by 6:
Molecular formula: C 6 H 12
Therefore, the empirical formula is CH 2 , and the molecular formula is C 6 H 12 .
