To derive the empirical formula of a compound, you need to determine the simplest whole number ratio of the elements present in the compound.
Step 1: Convert the percentage by mass to grams.
- If you have 100 g of the compound, then you would have 85.63 g of carbon (C) and 14.37 g of hydrogen (H).
Step 2: Determine the number of moles of each element.
- To find the number of moles, divide the mass of each element by its molar mass, which is the atomic mass found on the periodic table.
- The molar mass of carbon (C) is approximately 12 g/mol.
- The molar mass of hydrogen (H) is approximately 1 g/mol.
- Therefore, the number of moles of carbon (nC) can be calculated by dividing the mass of carbon by its molar mass: nC = 85.63 g / 12 g/mol = 7.14 mol.
- Similarly, the number of moles of hydrogen (nH) can be calculated as: nH = 14.37 g / 1 g/mol = 14.37 mol.
Step 3: Find the simplest whole number ratio.
- Divide each of the moles by the smaller number of moles.
- In this case, the number of moles of carbon is smaller, so we divide each of the moles by 7.14 mol.
- nC / 7.14 mol = 1
- nH / 7.14 mol = 2
Step 4: Round the ratios to the nearest whole number.
- The simplest whole number ratio is C1H2.
Now, let's move on to determining the molecular formula.
Step 5: Calculate the empirical formula mass.
- The empirical formula mass is the sum of the atomic masses in the empirical formula.
- In this case, the empirical formula mass is: 1(12 g/mol) + 2(1 g/mol) = 14 g/mol.
Step 6: Calculate the ratio of the molecular mass to the empirical formula mass.
- The ratio is calculated as: molecular mass / empirical formula mass = 56 g/mol / 14 g/mol = 4.
Step 7: Multiply the subscripts in the empirical formula by the ratio obtained in Step 6.
- The molecular formula is obtained by multiplying the subscripts in the empirical formula by the ratio.
- In this case, the molecular formula is: C1H2(4) = C4H8.
Therefore, the empirical formula for the hydrocarbon is C1H2, and the molecular formula is C4H8.