Combustion analysis of a hydrocarbon produced 33.01 g {\rm CO}_2 and 27.04 g {\rm H}_2{\rm O}. Calculate the empirical formula of the hydrocarbon.

Express your answer as a chemical formula.

33.01 g CO2

27.04 g H2O

mols CO2 = 33.01/44 = ? = mols C.
mols H2O = 27.04/18 = ? and that x 2 = mols H.
Now find the ratio of C to H with C being no larger than 1.0

To determine the empirical formula of the hydrocarbon, we need to first calculate the number of moles of carbon and hydrogen in the given amounts of carbon dioxide (CO2) and water (H2O).

1. Calculate the moles of CO2:
The molar mass of CO2 is 44.01 g/mol (12.01 g/mol for carbon + 2 * 16.00 g/mol for oxygen). We can use the formula: moles = mass / molar mass.
So, the number of moles of CO2 = 33.01 g / 44.01 g/mol = 0.750 mol.

2. Calculate the moles of H2O:
The molar mass of H2O is 18.02 g/mol (2 * 1.01 g/mol for hydrogen + 16.00 g/mol for oxygen). Again, using the formula: moles = mass / molar mass.
So, the number of moles of H2O = 27.04 g / 18.02 g/mol = 1.499 mol.

3. Determine the empirical formula:
Now, we need to find the simplest whole number ratio between the moles of carbon and hydrogen. We divide the number of moles of each element by the smallest number of moles.
In this case, the smaller value is 0.750 mol of C. Dividing both values by 0.750 mol, we find:
Carbon: 0.750 mol / 0.750 mol = 1
Hydrogen: 1.499 mol / 0.750 mol = 1.998 ≈ 2

Therefore, the empirical formula of the hydrocarbon is CH2.

To determine the empirical formula of the hydrocarbon, we need to calculate the mole ratio of carbon to hydrogen in the given data.

1. First, let's convert the given masses of CO2 and H2O into moles.

Moles of CO2 = mass / molar mass
Molar mass of CO2 = 12.01 g/mol (C) + 2(16.00 g/mol) (O) = 44.01 g/mol

Moles of CO2 = 33.01 g / 44.01 g/mol = 0.750 mol

Moles of H2O = mass / molar mass
Molar mass of H2O = 2(1.01 g/mol) (H) + 16.00 g/mol (O) = 18.02 g/mol

Moles of H2O = 27.04 g / 18.02 g/mol = 1.50 mol

2. Next, determine the mole ratio of carbon to hydrogen.

Mole ratio of C to H = (moles of CO2) / (moles of H2O)
Mole ratio of C to H = 0.750 mol / 1.50 mol = 0.50

This means there is 0.50 moles of carbon for every 1 mole of hydrogen.

3. Finally, we convert the mole ratio into a whole number ratio by multiplying by the appropriate factor. In this case, we multiply by 2 to get whole number values.

C: 0.50 * 2 = 1
H: 1 * 2 = 2

Therefore, the empirical formula of the hydrocarbon is CH2.

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