Incomplete combustion of a hydrogen carbon 3.52 g of carbon IV oxide gas and 1.44 g of water were formed determine the molecular formula of the hydrocarbon
To determine the molecular formula of the hydrocarbon, we first need to write out the balanced equation for its combustion:
CₓHᵧ + (x + y/4)O₂ → xCO₂ + (y/2)H₂O
We know that 3.52 g of CO₂ and 1.44 g of H₂O were formed. We can use this information to calculate the moles of each product using their molar masses:
moles of CO₂ = 3.52 g ÷ 44.01 g/mol = 0.08 mol
moles of H₂O = 1.44 g ÷ 18.02 g/mol = 0.08 mol
Since the coefficients in the balanced equation are in a ratio of 1:1, we can see that the moles of carbon dioxide and water are equal, and therefore, the moles of carbon and hydrogen in the original hydrocarbon must also be equal.
We can use the mass of carbon in the CO₂ (0.08 mol × 12.01 g/mol = 0.96 g) to find the mass of carbon in the original hydrocarbon:
mass of carbon in hydrocarbon = 0.96 g
Similarly, we can use the mass of hydrogen in the H₂O (0.08 mol × 2.02 g/mol = 0.16 g) to find the mass of hydrogen in the original hydrocarbon:
mass of hydrogen in hydrocarbon = 0.16 g
Now we can use these masses to find the empirical formula of the hydrocarbon:
mass percent of carbon = (0.96 g / 3.52 g) × 100% ≈ 27.3%
mass percent of hydrogen = (0.16 g / 1.44 g) × 100% ≈ 11.1%
We can assume a 100 g sample of the hydrocarbon, which would mean 27.3 g carbon and 11.1 g hydrogen. Next, we can convert these masses to moles using the molar masses of carbon and hydrogen:
moles of carbon = 27.3 g / 12.01 g/mol ≈ 2.28 mol
moles of hydrogen = 11.1 g / 1.01 g/mol ≈ 11.0 mol
Dividing these values by the smaller value (2.28 mol in this case) and rounding to the nearest whole number gives us the empirical formula of the hydrocarbon:
C₂H₅
To find the molecular formula, we need to know the molecular mass of the empirical formula. The empirical formula mass is:
(2 × 12.01 g/mol) + (5 × 1.01 g/mol) = 29.07 g/mol
The ratio of the molecular mass to the empirical formula mass gives us the factor by which we need to multiply the empirical formula:
molecular mass / empirical formula mass = n
molecular mass / 29.07 g/mol = n
We don't have the molecular mass yet, but we can find it by adding up the molar masses of the atoms in the empirical formula:
molecular mass = (2 × 12.01 g/mol) + (5 × 1.01 g/mol) = 31.07 g/mol
So now we can solve for n:
31.07 g/mol / 29.07 g/mol ≈ 1.07
This means that the molecular formula is:
C₂H₅ × 1.07 ≈ C₃H₇
Therefore, the molecular formula of the hydrocarbon is C₃H₇.