The molecular formula for the compound is therefore (CH1.4)₁₃, which simplifies to C₁₃H₁₈.
To determine the molecular formula for the hydrocarbon, we need to follow these steps:
1. Convert the percentages of carbon and hydrogen into moles:
- The mass of carbon in 94.34% of the compound is calculated as:
(94.34 / 100) * 178.23 g/mol = 168.22 g/mol
- The mass of hydrogen in 5.66% of the compound is calculated as:
(5.66 / 100) * 178.23 g/mol = 10.10 g/mol
To convert these masses into moles, we use the molar mass of each element:
- The molar mass of carbon (C) is 12.01 g/mol, so the number of moles of carbon is:
168.22 g/mol / 12.01 g/mol = 14.00 mol
- The molar mass of hydrogen (H) is 1.01 g/mol, so the number of moles of hydrogen is:
10.10 g/mol / 1.01 g/mol = 10.00 mol
2. Determine the empirical formula:
The empirical formula represents the simplest ratio of atoms in a compound.
To find it, divide the number of moles of each element by the smallest number of moles. In this case, hydrogen has the smallest number of moles (10.00 mol).
- Carbon: 14.00 mol / 10.00 mol = 1.40
- Hydrogen: 10.00 mol / 10.00 mol = 1.00
The empirical formula is therefore CH1.4 (rounded to CH1).
3. Determine the molecular formula:
The molecular formula represents the actual number of atoms of each element in a compound.
To find it, we need to know the molar mass of the compound.
- The molar mass of the empirical formula CH1.4 is:
(12.01 g/mol * 1) + (1.01 g/mol * 1.4) = 13.41 g/mol
Now, divide the molar mass of the compound (178.23 g/mol) by the molar mass of the empirical formula (13.41 g/mol) to find the whole number multiple.
- 178.23 g/mol / 13.41 g/mol = 13.30
Since we need a whole number multiple, we round 13.30 to the nearest whole number, which is 13.
The molecular formula for the compound is therefore (CH1.4)₁₃, which simplifies to C₁₃H₁₈.
In summary, the molecular formula for the hydrocarbon is C₁₃H₁₈
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