Respuesta :
There are [tex]2.63\times 10^{21}[/tex] atoms of carbon.
It contains [tex]1.38\times 10^{20}[/tex] molecules of testosterone.
It contains 0.0000229 moles of testosterones.
0.0661 grams is the mass of this sample of testosterone.
Explanation:
Given:
The molecular formula of testosterone, [tex]C_{19}H_{28}O_2[/tex]
The [tex]3.88\times 10^{21}[/tex]atoms of hydrogen.
To find:
The number of carbon atoms
The number of molecules of testosterone
The moles of testosterone
Mass of testosterone in grams
Solution
The molecular formula of testosterone=[tex]C_{19}H_{28}O_2[/tex]
The number of hydrogen atoms =[tex]3.88\times 10^{21} atoms[/tex]
The carbon to hydrogen atom ratio:
[tex]C:H=\frac{19}{28}[/tex]
The carbon atoms associated with testosterone's molecules hydrogen atom =x
[tex]\frac{x}{ 3.88\times 10^{21} atoms }=\frac{19}{28}\\x=\frac{19}{28}\times 3.88\times 10^{21} atoms =2.63\times 10^{21} atoms[/tex]
There are [tex]2.63\times 10^{21}[/tex] atoms of carbon.
The molecular formula of testosterone= [tex]C_{19}H_{28}O_2[/tex]
The number of hydrogen atoms = [tex]3.88\times 10^{21} atoms[/tex]
The number of testosterone molecules = N
In one molecule of testosterone, there are 28 atoms of hydrogen. Then in N number of testosterone molecules, there will be:
[tex]3.88\times 10^{21} atoms=N \times 28\\N=\frac{ 3.88\times 10^{21} atoms }{28}=1.38\times 10^{20} molecules[/tex]
It contains [tex]1.38\times 10^{20}[/tex] molecules of testosterone.
The number of testosterone molecules = [tex]N = 1.38\times 10^{20} molecules[/tex]
The moles of testosterone = n
According to the mole concept:
[tex]N=n\times N_A\\1.38\times 10^{20} molecule=n\times 6.022\times 10^{23} molecules\\n=\frac{1.38\times 10^{20} molecule}{6.022\times 10^{23} molecule}\\n=0.000229 mol[/tex]
It contains 0.0000229 moles of testosterones.
The moles of testosterone = 0.000229 mol
The molar mass of testosterone:
[tex]=12.01 g/mol\times 19+1.008g/mol\times 28+16.00\times g/mol\times 2\\=288.414 g/mol[/tex]
The mass of 0.000229 moles of testosterone:
[tex]=0.000229 mol\times 288.414 g/mol=0.0661 g[/tex]
0.0661 grams is the mass of this sample of testosterone.
Learn more about the mole concept here:
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