Question

The elemental composition of a compound is 54.2%C, 9.2%H, and 36.6%O. If the molar mass of the compound is 132 g/mol, the molecular formula of the compound is:

• A. \( \text{C}_6 \text{H}_{12} \text{O}_6 \)
• B. \( \text{C}_6 \text{H}_{12} \text{O}_3 \)
• C. \( \text{C}_4 \text{H}_9 \text{O}_3 \)
• D. \( \text{C}_4 \text{H}_8 \text{O}_2 \)

Hint:

The empirical formula can help determine the molecular formula by using the molar mass.

Answer 1

The Correct Option is A

The elemental composition of a compound is 54.2%C, 9.2%H, and 36.6%O. If the molar mass of the compound is 132 g/mol, the molecular formula of the compound is:

Step 1: Calculate the Empirical Formula

Given the percentage composition, we can assume we have 100 g of the compound. This makes the mass of each element in the compound directly equal to the percentage values:

• C: 54.2 g
• H: 9.2 g
• O: 36.6 g

Step 2: Calculate the Moles of Each Element

To find the moles of each element, divide the mass of each element by its atomic mass:

• For Carbon (C): \[ \frac{54.2 \, \text{g}}{12.01 \, \text{g/mol}} = 4.51 \, \text{mol} \]
• For Hydrogen (H): \[ \frac{9.2 \, \text{g}}{1.008 \, \text{g/mol}} = 9.13 \, \text{mol} \]
• For Oxygen (O): \[ \frac{36.6 \, \text{g}}{16.00 \, \text{g/mol}} = 2.29 \, \text{mol} \]

Step 3: Find the Mole Ratio

Next, divide the moles of each element by the smallest number of moles (which is 2.29 in this case, corresponding to Oxygen):

• C: \[ \frac{4.51}{2.29} = 1.97 \approx 2 \]
• H: \[ \frac{9.13}{2.29} = 3.98 \approx 4 \]
• O: \[ \frac{2.29}{2.29} = 1 \]

Step 4: Write the Empirical Formula

The mole ratio of the elements is approximately C₂H₄O₁, so the empirical formula is:

CH₂O

Step 5: Find the Molecular Formula

The empirical formula mass is:

CH₂O: 12 + 2 + 16 = 30 g/mol

The molecular formula mass is given as 132 g/mol. To find the ratio of the molecular mass to the empirical formula mass, divide the molar mass by the empirical formula mass:

\[ \frac{132 \, \text{g/mol}}{30 \, \text{g/mol}} = 4.4 \approx 4 \]

So, multiply the empirical formula by 4 to get the molecular formula:

The molecular formula is C₆H₁₂O₆.