Calculating the empirical formula of a hydrocarbon involves determining the simplest whole-number ratio of carbon and hydrogen atoms present in the compound. Here's a step-by-step guide:
1. Obtain Experimental Data:
- You'll typically be given the percentage composition by mass of carbon and hydrogen in the hydrocarbon. If you are given the mass of CO2 and H2O produced from combustion, you will need to convert to the mass of C and H using stoichiometry. Remember that a hydrocarbon is a compound solely made of carbon and hydrogen.
2. Convert Percentage to Mass (if necessary):
- Assume you have 100g of the compound. This makes the percentages directly equivalent to masses in grams. For example, if a hydrocarbon is 80% carbon and 20% hydrogen, you have 80g of carbon and 20g of hydrogen.
3. Convert Mass to Moles:
- Divide the mass of each element by its atomic mass (found on the periodic table).
- Moles of Carbon = (Mass of Carbon) / (Atomic Mass of Carbon)
- Moles of Hydrogen = (Mass of Hydrogen) / (Atomic Mass of Hydrogen)
- Example: If you have 80g of Carbon (Atomic Mass ~12.01 g/mol) and 20g of Hydrogen (Atomic Mass ~1.01 g/mol):
- Moles of Carbon ≈ 80g / 12.01 g/mol ≈ 6.66 moles
- Moles of Hydrogen ≈ 20g / 1.01 g/mol ≈ 19.80 moles
4. Determine the Simplest Whole Number Ratio:
- Divide the number of moles of each element by the smallest number of moles calculated in the previous step. This will give you a ratio.
- In the example above, the smallest number of moles is 6.66 (Carbon).
- Carbon Ratio ≈ 6.66 / 6.66 ≈ 1
- Hydrogen Ratio ≈ 19.80 / 6.66 ≈ 2.97 ≈ 3 (Rounding to the nearest whole number is acceptable if the number is close to a whole number)
- In the example above, the smallest number of moles is 6.66 (Carbon).
5. Write the Empirical Formula:
- Use the whole-number ratio as subscripts for the elements in the empirical formula.
- In our example, the ratio is approximately 1:3 (Carbon:Hydrogen), so the empirical formula is CH3.
Example Table:
| Element | Percentage | Mass (g) | Atomic Mass (g/mol) | Moles | Mole Ratio (Divide by smallest) | Simplest Whole Number Ratio |
|---|---|---|---|---|---|---|
| Carbon | 80% | 80 | 12.01 | 6.66 | 6.66 / 6.66 = 1 | 1 |
| Hydrogen | 20% | 20 | 1.01 | 19.80 | 19.80 / 6.66 ≈ 3 | 3 |
Important Considerations:
- Rounding: If the ratios are not close to whole numbers, you might need to multiply all the ratios by a common factor to obtain whole numbers. For example, if you get a ratio of 1:1.5, multiply both by 2 to get 2:3.
- Experimental Error: Experimental data can have errors, leading to slightly inaccurate ratios. Consider the potential for error when rounding.
- Combustion Analysis: When deriving the empirical formula from combustion analysis (measuring CO2 and H2O produced), you will need to use stoichiometry to determine the mass of carbon and hydrogen initially present in the hydrocarbon.
In summary, calculating the empirical formula of a hydrocarbon involves converting mass percentages to moles, finding the simplest mole ratio, and expressing that ratio as subscripts in the formula.
