To find the empirical formula of the organic compound containing carbon (C), hydrogen (H), and oxygen (O) based on the combustion data provided, we can follow these steps:
### Step 1: Calculate the moles of carbon from CO₂ produced
The mass of CO₂ produced is 25.56 g. The molar mass of CO₂ is 44 g/mol (12 g/mol for C and 32 g/mol for O).
\[
\text{Moles of } CO₂ = \frac{\text{mass of } CO₂}{\text{molar mass of } CO₂} = \frac{25.56 \, \text{g}}{44 \, \text{g/mol}} = 0.581 \, \text{mol}
\]
Since each mole of CO₂ contains 1 mole of carbon, the moles of carbon are also 0.581 mol.
### Step 2: Calculate the moles of hydrogen from H₂O produced
The mass of H₂O produced is 10.46 g. The molar mass of H₂O is 18 g/mol (2 g/mol for H and 16 g/mol for O).
\[
\text{Moles of } H₂O = \frac{\text{mass of } H₂O}{\text{molar mass of } H₂O} = \frac{10.46 \, \text{g}}{18 \, \text{g/mol}} = 0.581 \, \text{mol}
\]
Since each mole of H₂O contains 2 moles of hydrogen, the moles of hydrogen are:
\[
\text{Moles of H} = 2 \times 0.581 = 1.162 \, \text{mol}
\]
### Step 3: Calculate the mass of carbon and hydrogen
Now, we can calculate the mass of carbon and hydrogen in the original compound.
\[
\text{Mass of C} = \text{moles of C} \times \text{molar mass of C} = 0.581 \, \text{mol} \times 12 \, \text{g/mol} = 6.97 \, \text{g}
\]
\[
\text{Mass of H} = \text{moles of H} \times \text{molar mass of H} = 1.162 \, \text{mol} \times 1 \, \text{g/mol} = 1.162 \, \text{g}
\]
### Step 4: Calculate the mass of oxygen in the compound
The total mass of the compound is given as 12.8 g. We can find the mass of oxygen by subtracting the mass of carbon and hydrogen from the total mass.
\[
\text{Mass of O} = \text{Total mass} - (\text{Mass of C} + \text{Mass of H}) = 12.8 \, \text{g} - (6.97 \, \text{g} + 1.162 \, \text{g}) = 4.678 \, \text{g}
\]
### Step 5: Calculate the moles of oxygen
The molar mass of oxygen is 16 g/mol.
\[
\text{Moles of O} = \frac{\text{mass of O}}{\text{molar mass of O}} = \frac{4.678 \, \text{g}}{16 \, \text{g/mol}} = 0.292 \, \text{mol}
\]
### Step 6: Determine the ratio of moles of C, H, and O
Now we have:
- Moles of C = 0.581
- Moles of H = 1.162
- Moles of O = 0.292
To find the simplest whole number ratio, we divide each by the smallest number of moles (0.292):
\[
\text{Ratio of C} = \frac{0.581}{0.292} \approx 1.99 \approx 2
\]
\[
\text{Ratio of H} = \frac{1.162}{0.292} \approx 3.98 \approx 4
\]
\[
\text{Ratio of O} = \frac{0.292}{0.292} = 1
\]
### Step 7: Write the empirical formula
The simplest whole number ratio of C:H:O is approximately 2:4:1. Therefore, the empirical formula of the compound is:
\[
\text{Empirical Formula} = C_2H_4O
\]
