15. What is the molecular formula of a compound that has a molar mass of 54g and the empirical formula C_(2)H_(3) C_(4)H_(6) C_(2)H_(3) C_(6)H_(9) C_(8)H_(12)

To determine the molecular formula of a compound from its empirical formula and molar mass, follow these steps:<br /><br />1. **Calculate the molar mass of the empirical formula**: <br /> The empirical formula given is \( \mathrm{C}_{2} \mathrm{H}_{3} \). <br /> - Carbon (C) has an atomic mass of approximately 12 g/mol. <br /> - Hydrogen (H) has an atomic mass of approximately 1 g/mol. <br /><br /> Therefore, the molar mass of \( \mathrm{C}_{2} \mathrm{H}_{3} \) is: <br /> \[<br /> (2 \times 12) + (3 \times 1) = 24 + 3 = 27 \text{ g/mol}<br /> \]<br /><br />2. **Determine the ratio of the molar mass of the compound to the molar mass of the empirical formula**: <br /> The molar mass of the compound is given as 54 g/mol. <br /> \[<br /> \text{Ratio} = \frac{\text{Molar mass of compound}}{\text{Molar mass of empirical formula}} = \frac{54}{27} = 2<br /> \]<br /><br />3. **Multiply the subscripts in the empirical formula by this ratio to find the molecular formula**: <br /> Since the ratio is 2, multiply each subscript in \( \mathrm{C}_{2} \mathrm{H}_{3} \) by 2: <br /> \[<br /> \mathrm{C}_{2 \times 2} \mathrm{H}_{3 \times 2} = \mathrm{C}_{4} \mathrm{H}_{6}<br /> \]<br /><br />Therefore, the molecular formula of the compound is \( \mathrm{C}_{4} \mathrm{H}_{6} \).