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Chapter 3: Problem 39

Combustion analysis of \(1.00 \mathrm{~g}\) of the male sex hormone, testosterone, yields \(2.90 \mathrm{~g}\) of \(\mathrm{CO}_{2}\) and \(0.875 \mathrm{~g} \mathrm{H}_{2} \mathrm{O}\). What are the mass percents of carbon, hydrogen, and oxygen in testosterone?

Short Answer

Expert verified
Answer: The mass percentages of carbon, hydrogen, and oxygen in testosterone are approximately 79.1%, 9.80%, and 11.1%, respectively.

Step by step solution

01

Calculate the moles of CO₂ produced

Divide the mass of CO₂ (2.90 g) by the molar mass of CO₂ (44.01 g/mol) to find the moles of CO₂ produced: \(\frac{2.90\ \mathrm{g}}{44.01\ \mathrm{g/mol}} \approx 0.0659\) moles of CO₂ Since each CO₂ molecule has one carbon atom, there are 0.0659 moles of carbon in the testosterone sample.
02

Calculate the moles of H₂O produced

Divide the mass of H₂O (0.875 g) by the molar mass of H₂O (18.02 g/mol) to find the moles of H₂O produced: \(\frac{0.875\ \mathrm{g}}{18.02\ \mathrm{g/mol}} \approx 0.0486\) moles of H₂O Since each H₂O molecule has two hydrogen atoms, there are \(2 \times 0.0486 \approx 0.0972\) moles of hydrogen in the testosterone sample.
03

Convert moles of carbon and hydrogen to masses

To find the mass of carbon, multiply the moles of carbon by the molar mass of carbon (12.01 g/mol): \(0.0659\ \mathrm{mol} \times 12.01\ \mathrm{g/mol} \approx 0.791\ \mathrm{g}\) of carbon To find the mass of hydrogen, multiply the moles of hydrogen by the molar mass of hydrogen (1.008 g/mol): \(0.0972\ \mathrm{mol} \times 1.008\ \mathrm{g/mol} \approx 0.0980\ \mathrm{g}\) of hydrogen
04

Calculate the mass of oxygen

Since the total mass of testosterone is 1.00 g and the masses of carbon and hydrogen have been found, the mass of oxygen can be calculated by subtracting the masses of carbon and hydrogen from the total mass: \(1.00\ \mathrm{g} - (0.791\ \mathrm{g} + 0.0980\ \mathrm{g}) = 0.111\ \mathrm{g}\) of oxygen
05

Determine the mass percentages of carbon, hydrogen, and oxygen

For each element, divide its mass by the total mass of testosterone (1.00 g) and multiply by 100%: Percent carbon: \(\frac{0.791\ \mathrm{g}}{1.00\ \mathrm{g}} \times 100\% \approx 79.1\%\) Percent hydrogen: \(\frac{0.0980 \mathrm{g}}{1.00\ \mathrm{g}} \times 100\% \approx 9.80\%\) Percent oxygen: \(\frac{0.111\ \mathrm{g}}{1.00\ \mathrm{g}} \times 100\% \approx 11.1\%\) Therefore, the mass percentages of carbon, hydrogen, and oxygen in testosterone are approximately 79.1%, 9.80%, and 11.1%, respectively.

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