on complete combustion a gaseous hydrocarbon produces3.38g of CO2 and 0.690g of H2O and no other products. find the empirical formula of hydrocarbon
We can use the products of combustion to determine the number of moles of carbon and hydrogen in the hydrocarbon, and from there find the empirical formula.
First, let's convert the masses of CO2 and H2O to moles using their molar masses:
moles of CO2 = 3.38 g / 44.01 g/mol = 0.0768 moles
moles of H2O = 0.690 g / 18.02 g/mol = 0.0383 moles
Next, let's use the coefficients from the balanced equation for combustion to relate these moles to the number of moles of carbon and hydrogen in the hydrocarbon:
1 mole of hydrocarbon produces 1 mole of CO2 and 0.5 moles of H2O
So for the given amounts of CO2 and H2O, we have:
moles of carbon = 0.0768 moles
moles of hydrogen = 2 x 0.0383 moles = 0.0766 moles
Now we can use these mole ratios to find the empirical formula. The ratio of carbon atoms to hydrogen atoms is roughly 1:2, so we can start by assuming a hydrocarbon with one carbon atom and two hydrogen atoms:
C1H2
The molar mass of this formula is:
1 x 12.01 g/mol + 2 x 1.01 g/mol = 14.03 g/mol
The actual molar mass of the hydrocarbon in the problem is:
12.08 g/mol / 0.0768 moles = 157.29 g/mol
This is about 11 times the molar mass of C1H2, so we need to multiply the subscripts by 11 to get the correct molar mass:
C11H22
This is the empirical formula of the hydrocarbon.
molecular formula=
To find the molecular formula, we need the molecular mass of the compound. The empirical formula mass of C11H22 is:
11 x 12.01 g/mol + 22 x 1.01 g/mol = 142.32 g/mol
We can divide the actual molar mass of the compound (157.29 g/mol) by the empirical formula mass to find the factor by which we need to multiply the subscripts in the empirical formula:
157.29 g/mol / 142.32 g/mol ≈ 1.106
Rounding to the nearest whole number, we get a factor of 1. Therefore, the molecular formula of the hydrocarbon is the same as the empirical formula:
C11H22
To find the empirical formula of the hydrocarbon, we need to determine the ratios of carbon and hydrogen in the compound.
Step 1: Calculate the moles of CO2 produced:
Molar mass of CO2 = 12.01 g/mol + 2 * 16.00 g/mol = 44.01 g/mol
Moles of CO2 = mass of CO2 / molar mass of CO2
Moles of CO2 = 3.38 g / 44.01 g/mol = 0.0766 mol
Step 2: Calculate the moles of H2O produced:
Molar mass of H2O = 2 * 1.01 g/mol + 16.00 g/mol = 18.02 g/mol
Moles of H2O = mass of H2O / molar mass of H2O
Moles of H2O = 0.690 g / 18.02 g/mol = 0.0383 mol
Step 3: Calculate the mole ratio of carbon to hydrogen:
Mole ratio = moles of carbon / moles of hydrogen
Mole ratio = (moles of CO2 / moles of CO2) / (moles of H2O / moles of CO2)
Mole ratio = (0.0766 mol / 0.0766 mol) / (0.0383 mol / 0.0766 mol)
Mole ratio = (1 / 1) / (0.5 / 1)
Mole ratio = 1 / 0.5 = 2
Step 4: Write the empirical formula using the mole ratio:
The empirical formula of the hydrocarbon is CH2.