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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?

a) 2.63$\cdot 10^{21} \mathrm{Catom}$
b) 1.39$\cdot 10^{20}$ molecule
c) 2.31$\cdot 10^{-4} \mathrm{mol}$
d) 66.6 $\mathrm{mg}$

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Video Transcript

So in this problem, we're given a sample off the district's turned, which has a monetary formal off C nineteen h twenty eight or two and which contains three point eight times when they were doing to on hydrogen atoms. It's in first part of this problem. We have to find out how many atoms off carbon does this sample contains. So so if we let that the number of Fatima's off carbon contained in this sample as X, then he can sit up a ratio off carbon and had risen Adam in the symbol and in one molecule off the, um, the compound. So if X is the number ofthe carbon present in the sample off testosterone and we have given and the number ofthe hydro's and present in the sample is three point eight times to the twenty one second right X over three point eight eight times ten to the port twenty one is equal to the ratio of carbon and hydrogen in one molecule off the testosterone, which is we have nineteen carbon and twenty eight had risen so he can write nineteen over printed. So from this ratio calm prison, we can easily find the Vela off X, which is the number off carbon atoms in the sample. So the veil off X will be equal to nineteen over twenty eight times, three point eight I am stirring. There were twenty one, and it will give us a fellow off two point six three times to the words twenty one. So this is the number off carbon atoms that is present in the sample. Now, in Barbie of this question, you have to find out how many molecules off Estes turned as it contained. So again, if we consider the number of molecules off testis journal which is contained in the sample is X. Then again, compare that with the number of hydrogen atoms present in the sample, which is again three point eight times to the twenty one. And we can compare it with the ratio off the testes, turn molecule and hydrogen atom in gets off one molecule. So in one molecule of the testes, John, we have one more nickel over the number of hydrogen, which is twenty eight. So on over twenty eight, and from here we can find the veil off X, which is the number of molecules off Mistress turn in the sample, say to everyone over twenty eight times three point eight eight Timestony, there were twenty one. And this will give us value off one point three eight times ten to the twenty. This is the number of molecules ofthe districts German, which is present in assemble. Then, in third part of this problem, we have to find out how many malls off Mistress turned as assemble contained. So he and we have celebrated how many molecules off distance journeys containing the same sample. And now we have to find out the number of most of the distrust urn containing assemble. So as you know, that one month off any substance contained six spent several times, sir. They were pointed him articles. So for American easily find out how many moles thiss much Mollica will contain. So six point zero two times ten to the part twenty three Molly Kills are contained in one mall. That means this much molecules which is one point three eight times tentative about twenty. So this much molecules are contained in one point three eight time. Stand over twenty over six point or two. I am stunned. The world twenty three no. R two point three zero times turn, the more miners formal. So this is the number of mall which is contained in a sample. Now, in less part of this problem, to find out what is the mass of the Semple and Grams. So to do, they're going to find out the molar mass off the testes churn and muller Mass means the mass contending one mall. That means from there we can find out what is the mass continous this much more, which is the number of malls for the sample. So let's find out the Moler mass off the commandment given. So the formula for testes journeys given a C nineteen h twenty eight or two so we can find out the more armas just he's really adding up the molar mass off. Um, individual Adam was the first to have carbon, which has the molar mass of twelve oh one, and we have nineteen carbon soil multiplies by nineteen. Then we have had risen, which has a more amounts of one point or eight, and I'd rather has enormous. We have twenty eight hundreds in here, so I multiplied by twenty eight. Then we have oxygen which the monuments off sixteen and we have to look see in here so multiplied by two. Well, give us a bell off. Created one for two Grandpa are more So this's the molar mass of the this compound. So this much mass is contained in one mole. That means how many mass is contained in this? Much more so. All right. One more of the districts Jerron contents twenty eight point four toe graham that men's two point three times to the minus formal Contain. This will contain, um, two point three zero times ten to the bar miners for more time's thiss Mass. Two eighty eight. Bland for tow Graham Barmal. And this will give us a value off zero point zero six Graham. So this is the mass of the sample. So we are asked in the final final part of this questioner has to find out the mass of the sample in grams, and this's the mess of the symbol in grams