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Problem 44

At least 25$\mu \mathrm{g}$ of tetrahydrocannabinol $(\mathrm{THC}),$ the active ingredient in marijuana, is required to produce intoxication. The molecular formula of THC is $\mathrm{C}_{21} \mathrm{H}_{30} \mathrm{O}_{2} .$ How many moles of THC does this 25$\mu \mathrm{g}$ represent? How many molecules?

Answer

See work and explanation.

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## Discussion

## Video Transcript

So in this problem, we're given that we have a twenty five microgram off Tetra Hydro Can a banal are being C, which is an active ingredient in marijuana, and this is recorded produce intoxication. So this is the mass ofthe DSC, which is required to produce intoxication, and the molecule or formal off its has given us citrine too on his thirty or two. In first part of the question, you have to find out how many malls off T. H. C does this trait of five microgram represent and then we have to find out how many molecules subject etc. Does. This, Trent, if I'm acronym represents so what we have to do first is simply since we have to find out the number of malls off this mass off, etc. First you have to find out the Moler, massive t etc. That means the molar misses the mass contained in one mall. That means from there we can find out how many months is contained in strange if I microgram mess. So from this formula, we can find out on the Moler mass off the sea. My children, since we have carbon carbon, has a more mass of twelve point Oh Won, and we have twenty one carbon here when multiplied by twenty one. Then we have Metro's on which has more elements of one point or eat, and we have her t I'd risen sun multiplied by eight thirty, and then we have to walk season. That means sixteen is the monuments of oxygen and we have to oxygen multiplied by two. And this will give us a value off three one four point four five I, um So this is the two and four point four five gram per mall, and this is the molar mass off. Let's see, That means one more lofty is he will contain through one four point four five gram and then so we can write three one four point four five gram is contained in one multi it. See, that means twenty five microgram, or twenty five times ten to the minus six gram is contained in, um, twenty five times ten to the four minus six over two on four point four five Graham this a gram per mole and it will give us value off seven point nine five times intended to par minus eight more so This is the number of malls that going to find microgram off dates represent. And then we have to find out how many molecules is contained in twenty five macron. And since we have calculated the number of morals, so twenty five microgram TOC, then we know that one mole off any substance contains six point or co times ten to the twenty three molecules. That means from there we can find out how many molecules is contending this much more are twenty five micrograms of hearsay, so one more it's sea contains six point or two times ten to the port twenty three molecules, therefore seven point nine five times during the one minus eight. Here's the contents. Six point oto time stint Report twenty three Time's thiss and this will give us value off for planned seven nine I'm standing. There were sixteen molecules, so this is the number of molecules containing twenty five microgram off, etc.

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