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Chapter 3: Problem 42

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?

Short Answer

Expert verified
\(= 2.62 \times 10^{21}\) carbon atoms

Step by step solution

01

Identify Components in the Molecule

The testosterone molecule has a molecular formula of \(\mathrm{C}_{19}\mathrm{H}_{28}\mathrm{O}_{2}\). This means that the molecule consists of 19 carbon atoms, 28 hydrogen atoms, and 2 oxygen atoms. In this problem, we are given information about the number of hydrogen atoms in the sample.
02

Calculate Number of Carbon Atoms

We can find the number of carbon atoms by using the ratio of carbon to hydrogen atoms in the molecule. Since there are 19 carbon atoms for every 28 hydrogen atoms, we can write the proportion as: $$\frac{\text{Number of Carbon Atoms}}{\text{Number of Hydrogen Atoms}} = \frac{19}{28}$$ Given that there are \(3.88 \times 10^{21}\) hydrogen atoms, let's solve for the number of carbon atoms: $$\text{Number of Carbon Atoms} = \frac{19}{28} \times (3.88 \times 10^{21})$$

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Most popular questions from this chapter

Viridicatumtoxin B, \(\mathrm{C}_{30} \mathrm{H}_{31} \mathrm{NO}_{10},\) is a natural antibiotic compound. It requires a synthesis of 12 steps in the laboratory. Assuming all steps have equivalent yields of \(85 \%\), which is the final percent yield of the total synthesis?

Propenoic acid, \(\mathrm{C}_{3} \mathrm{H}_{4} \mathrm{O}_{2},\) is a reactive organic liquid that is used in the manufacturing of plastics, coatings, and adhesives. An unlabeled container is thought to contain this liquid. A \(0.275-g\) sample of the liquid is combusted to produce \(0.102 \mathrm{~g}\) of water and \(0.374 \mathrm{~g}\) carbon dioxide. Is the unknown liquid propenoic acid? Support your reasoning with calculations.

Hydrofluoric acid, HF \((a q)\), cannot be stored in glass bottles because compounds called silicates in the glass are attacked by the $\mathrm{HF}(a q)\(. Sodium silicate \)\left(\mathrm{Na}_{2} \mathrm{SiO}_{3}\right),$ for example, reacts as follows: $$ \mathrm{Na}_{2} \mathrm{SiO}_{3}(s)+8 \mathrm{HF}(a q) \longrightarrow \mathrm{H}_{2} \mathrm{SiF}_{6}(a q)+2 \mathrm{NaF}(a q)+3 \mathrm{H}_{2} \mathrm{O}(l) $$ (a) How many moles of HF are needed to react with 0.300 mol of \(\mathrm{Na}_{2} \mathrm{SiO}_{3} ?\) (b) How many grams of NaF form when \(0.500 \mathrm{~mol}\) of HF reacts with excess \(\mathrm{Na}_{2} \mathrm{SiO}_{3} ?\) (c) How many grams of \(\mathrm{Na}_{2} \mathrm{SiO}_{3}\) can react with $0.800 \mathrm{~g}$ of HF?

Write a balanced chemical equation for the reaction that occurs when (a) \(\mathrm{Mg}(s)\) reacts with \(\mathrm{Cl}_{2}(g) ;(\mathbf{b})\) barium carbonate decomposes into barium oxide and carbon dioxide gas when heated; \((\mathbf{c})\) the hydrocarbon styrene, \(\mathrm{C}_{8} \mathrm{H}_{8}(l),\) is combusted in air; \((\mathbf{d})\) dimethylether, $\mathrm{CH}_{3} \mathrm{OCH}_{3}(g),$ is combusted in air.

Balance the following equations and indicate whether they are combination, decomposition, or combustion reactions: (a) \(\mathrm{NaClO}_{3}(s) \longrightarrow \mathrm{NaCl}(s)+\mathrm{O}_{2}(g)\) (b) $\mathrm{NH}_{4} \mathrm{OH}(a q) \longrightarrow \mathrm{H}_{2} \mathrm{O}(l)+\mathrm{NH}_{3}(g)$ (c) \(\mathrm{K}(s)+\mathrm{Cl}_{2}(g) \longrightarrow \mathrm{KCl}(s)\) (d) $\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(l)+\mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(\mathrm{~g})+\mathrm{H}_{2} \mathrm{O}(l)$
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