How to Determine Empirical Formulas from Combustion Analysis

Understanding Empirical Formula Determination

To determine the empirical formula of a compound using combustion analysis, we measure the amounts of carbon dioxide (CO₂) and water (H₂O) produced when a sample of the compound is burned. By analyzing these products, we can deduce the number of moles of each element in the original compound.

Step-by-Step Process

1. Burn the Sample: When a known mass of the compound is combusted, it produces CO₂ and H₂O.
2. Collect the Data: Measure the mass of CO₂ and H₂O produced.
3. Convert Mass to Moles: Use molar masses to convert the masses of CO₂ and H₂O into moles of carbon (C) and hydrogen (H).
4. Calculate Moles of Other Elements: If the compound contains elements like oxygen, calculate their moles using the difference method.
5. Determine the Empirical Formula: Find the simplest ratio of moles of each element.

Example Calculation

Let’s say we combust a sample of a compound and collect the following data:

• Mass of the sample = 1.00 g
• Mass of CO₂ produced = 2.20 g
• Mass of H₂O produced = 0.90 g

Step 1: Convert Mass of Products to Moles

• Molar mass of CO₂ = 44.01 g/mol
• Molar mass of H₂O = 18.02 g/mol

Calculating moles of CO₂:
[
\text{Moles of CO₂} = \frac{\text{mass of CO₂}}{\text{molar mass of CO₂}} = \frac{2.20 g}{44.01 g/mol} = 0.0500 mol
]

Calculating moles of H₂O:
[
\text{Moles of H₂O} = \frac{\text{mass of H₂O}}{\text{molar mass of H₂O}} = \frac{0.90 g}{18.02 g/mol} = 0.0500 mol
]

Step 2: Determine Moles of Each Element

• From CO₂: Each mole of CO₂ contains 1 mole of C.
  [
  \text{Moles of C} = 0.0500 mol
  ]

• From H₂O: Each mole of H₂O contains 2 moles of H.
  [
  \text{Moles of H} = 0.0500 mol \times 2 = 0.1000 mol
  ]

Step 3: Assume No Other Elements (for simplicity)

For this example, we will assume there are no other elements (like O) in the original compound.

Step 4: Calculate the Empirical Formula

Now we have:

• Moles of C = 0.0500 mol
• Moles of H = 0.1000 mol

To find the simplest ratio:

• Divide each by the smallest number of moles (0.0500):
  [
  \text{C: } \frac{0.0500}{0.0500} = 1
  ]
  [
  \text{H: } \frac{0.1000}{0.0500} = 2
  ]

Final Empirical Formula

The empirical formula for the compound is CH₂.

Conclusion

By following the steps outlined in this example, you can effectively determine the empirical formula of a compound from combustion analysis. Understanding this process is essential for chemists and can be applied in various scientific fields.