Questions: The molecular weight of a compound is 140 g/mol. If the empirical formula is C4H6O, what is the molecular formula? Provide your answer below: C square H square O square

The molecular weight of a compound is 140 g/mol. If the empirical formula is C4H6O, what is the molecular formula? Provide your answer below: C square H square O square
Transcript text: The molecular weight of a compound is $140 \frac{\mathrm{~g}}{\mathrm{~mol}}$. If the empirical formula is $\mathrm{C}_{4} \mathrm{H}_{6} \mathrm{O}$, what is the molecular formula? Provide your answer below: \[ { }^{\mathrm{C}} \square^{\mathrm{H}} \square^{\mathrm{O}} \square \]
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Solution

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Solution Steps

Step 1: Calculate the Empirical Formula Weight

First, calculate the empirical formula weight of \(\mathrm{C}_4\mathrm{H}_6\mathrm{O}\).

  • Carbon (C): \(4 \times 12.01 = 48.04 \, \text{g/mol}\)
  • Hydrogen (H): \(6 \times 1.008 = 6.048 \, \text{g/mol}\)
  • Oxygen (O): \(1 \times 16.00 = 16.00 \, \text{g/mol}\)

Add these together to find the empirical formula weight:

\[ 48.04 + 6.048 + 16.00 = 70.088 \, \text{g/mol} \]

Step 2: Determine the Multiplication Factor

Divide the molecular weight by the empirical formula weight to find the multiplication factor:

\[ \frac{140 \, \text{g/mol}}{70.088 \, \text{g/mol}} \approx 2 \]

Step 3: Calculate the Molecular Formula

Multiply the subscripts in the empirical formula by the multiplication factor:

  • Carbon: \(4 \times 2 = 8\)
  • Hydrogen: \(6 \times 2 = 12\)
  • Oxygen: \(1 \times 2 = 2\)

Thus, the molecular formula is \(\mathrm{C}_8\mathrm{H}_{12}\mathrm{O}_2\).

Final Answer

\[ \boxed{\mathrm{C}_8\mathrm{H}_{12}\mathrm{O}_2} \]

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