A sample of the male sex hormone testosterone, \(\mathrm{C}_{19} \mathrm{H}_{28} \mathrm{O}_{2}\) , contains \(3.88 \times 10^{21}\) hydrogen atoms. (a) How many atoms of carbon does it contain? (b) How many molecules of testosterone does it contain? (c) How many moles of testosterone does it contain? (d) What is the mass of this sample in grams?

First, we need to find the number of carbon atoms in the given sample. Since the ratio of hydrogen to carbon atoms in testosterone is 28:19, we can use this to find the number of carbon atoms: Number of carbon atoms = \((\frac{19}{28}) \times (3.88 \times 10^{21})\) Now, calculate the answer: Number of carbon atoms = \((\frac{19}{28}) \times (3.88 \times 10^{21}) \approx 2.61 \times 10^{21}\) carbon atoms

Now we need to find the number of testosterone molecules in the sample. Since there are 28 hydrogen atoms in one molecule of testosterone, we can use the provided hydrogen atom count to find the number of molecules: Number of testosterone molecules = \(\frac{3.88 \times 10^{21}}{28}\) Now, calculate the answer: Number of testosterone molecules = \(\frac{3.88 \times 10^{21}}{28} \approx 1.39 \times 10^{20}\) testosterone molecules

To find the number of moles of testosterone, we will use Avogadro's number, which states that there are \(6.022 \times 10^{23}\) molecules in one mole of any substance: Number of moles = \(\frac{1.39 \times 10^{20}}{6.022 \times 10^{23}}\) Now, calculate the answer:function Find-theValueGiven (){ Number of moles = \(\frac{1.39 \times 10^{20}}{6.022 \times 10^{23}} \approx 2.31 \times 10^{-4}\) moles of testosterone

To find the mass of the sample, we need to find the molar mass of testosterone first. Using the periodic table, we can see that the molar mass of carbon (C) is approximately 12.01 g/mol, hydrogen (H) is approximately 1.01 g/mol, and oxygen (O) is approximately 16.00 g/mol. The chemical formula for testosterone is \(\mathrm{C}_{19}\mathrm{H}_{28}\mathrm{O}_{2}\), so its molar mass can be found as follows: Molar mass of testosterone = \((19 \times 12.01) + (28 \times 1.01) + (2 \times 16.00)\) Now, calculate the molar mass: Molar mass of testosterone = \((19 \times 12.01) + (28 \times 1.01) + (2 \times 16.00) \approx 288.45\) g/mol Now, we can find the mass of the sample by multiplying the number of moles by the molar mass: Mass = \((2.31 \times 10^{-4}) \times 288.45\) Now, calculate the answer: Mass = \((2.31 \times 10^{-4}) \times 288.45 \approx 0.0666\) grams The mass of the testosterone sample is approximately 0.0666 grams.