A compound is 54.5% carbon, 9.1% hydrogen and 36.4% oxygen. Its molar mass is 88.0 g/mol. What is its molecular formula?
The correct answer and explanation is :
To determine the molecular formula of the compound, we follow these steps:
Step 1: Determine the empirical formula
Assume a 100 g sample of the compound. This allows us to treat the percentages as grams:
- Carbon (C): 54.5 g
- Hydrogen (H): 9.1 g
- Oxygen (O): 36.4 g
Convert grams to moles:
- Moles of C = 54.5 g ÷ 12.01 g/mol = 4.54 mol
- Moles of H = 9.1 g ÷ 1.008 g/mol = 9.03 mol
- Moles of O = 36.4 g ÷ 16.00 g/mol = 2.28 mol
Next, divide each mole value by the smallest number of moles to find the simplest whole number ratio:
- C: 4.54 ÷ 2.28 ≈ 1.99 ≈ 2
- H: 9.03 ÷ 2.28 ≈ 3.96 ≈ 4
- O: 2.28 ÷ 2.28 = 1
So, the empirical formula is C₂H₄O.
Step 2: Determine the molecular formula
Calculate the empirical formula mass of C₂H₄O:
- (2 × 12.01) + (4 × 1.008) + (1 × 16.00) = 24.02 + 4.032 + 16.00 = 44.05 g/mol
Now, divide the given molar mass by the empirical formula mass:
- 88.0 g/mol ÷ 44.05 g/mol ≈ 2.00
This means the molecular formula is 2 times the empirical formula:
Final Answer: C₄H₈O₂
Explanation (300 words):
The process of determining a molecular formula begins with analyzing the compound’s percent composition by mass. These percentages indicate the relative amount of each element present in a compound. By assuming a 100 g sample, we simplify the math so that the mass percentages become actual gram values, which are then converted into moles using the atomic masses from the periodic table.
After obtaining the moles of each element, we find the simplest whole-number mole ratio by dividing each by the smallest mole quantity among the elements. These ratios give the empirical formula, representing the simplest integer ratio of atoms in the compound. In our case, the empirical formula is C₂H₄O.
However, the empirical formula does not necessarily reflect the true number of atoms in a molecule. The molecular formula is a multiple of the empirical formula and is determined using the compound’s given molar mass. By dividing the molar mass (88.0 g/mol) by the empirical formula mass (44.05 g/mol), we find the multiple to be 2. Multiplying the subscripts in the empirical formula by this multiple gives the molecular formula: C₄H₈O₂.
This molecular formula provides the actual number of carbon, hydrogen, and oxygen atoms in a molecule of the compound and is essential for understanding the compound’s structure, properties, and reactivity.