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Problem 88 Hard Difficulty

Ozone is depleted in the stratosphere by chlorine from $\mathrm{CF}_{3} \mathrm{Cl}$ according to this set of equations:
$$\begin{array}{c}{\mathrm{CF}_{3} \mathrm{Cl}+\mathrm{UV} \text { light } \longrightarrow \mathrm{CF}_{3}+\mathrm{Cl}} \\ {\mathrm{Cl}+\mathrm{O}_{3} \longrightarrow \mathrm{ClO}+\mathrm{O}_{2}} \\ {\mathrm{O}_{3}+\mathrm{UV} \operatorname{light} \longrightarrow \mathrm{O}_{2}+\mathrm{O}} \\ {\mathrm{ClO}+\mathrm{O} \longrightarrow \mathrm{Cl}+\mathrm{O}_{2}}\end{array}$$
What total volume of ozone at a pressure of 25.0 $\mathrm{mm} \mathrm{Hg}$ and a tem-
perature of 225 $\mathrm{K}$ is destroyed when all of the chlorine from 15.0 $\mathrm{g}$ of
$\mathrm{CF}_{3} \mathrm{Cl}$ goes through ten cycles of the above reactions?


$1.61 \times 10^{3} \mathrm{L} \mathrm{O}_{3}$


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Video Transcript

So this question were given, um, a series of reactions that causes those in depletion by chlorofluorocarbons. Um, and were given that we have 15 grams of CF three CEO i things going through 10 cycles of this reaction. So we're doing this first thing we're gonna do is we're gonna want to calculate how many moles of that chlorofluorocarbon we have, starting with just 15 grams of, uh see if three c l and I'm gonna convert two moles, so I'm gonna do that is using the more massive this which is one of 4.46 grams per mole, and then go to convert to malls which, if I look at that, gives me 0.14 malls. Now, if you look at the first direction, you'll see that there's a oneto one molar concentration of ah cf three clt, Jesse L. So I can say this is Mel's off. Corinne. All right, so now we're gonna look at this, um, reaction. And the first step of this reaction is that chlorine combines with ozone to create ah cielo and oxygen gas. Um, and then that same Cielo product is later used in the reaction. So If you look at this, every one mole of chlorine leads to two moles of ozone depleted. All right, eso What we can do is weaken, and also we're going through 10 cycles. So 10 cycles of this reaction means 20 moles of 03 depleted. Now, that's assuming that we're using one mole of chlorine, though, and that's not sure. So what we're gonna do is 20 times 200.14 That's going to give us the moles of over three that we deplete, which is going to be 2.8 on that We could do this is you could Alm you could double the 0.14 number, give us point to a and then times that by 10 to get the same two point number. And that is, um, moles of 03 are So now we can just use the ideal gas law where I can say the equals and r t overpay. I consult from there so I can save E is equal to 2.8 malls. Ah, and then our since I'm using. Since the problem gives everything in millimeters of mercury, where is gonna continue to use that? It's like 62.36 uh, millimeters of Mercury Times leaders over mole times. Calvin, the problem gives us a temperature of, um, 225 Children and a pressure of 25.0 millimeters of mercury. All right. So I won't go through and check our units. Ah, we have moles that cancels their and their Kelvin cancels their and their militarism record cancels there, and they're leaving us with only leaders. Ah, and that works very, very well, because the question is asking us how many leaders of ozone depleting or it's the volume of those, Um, all right, so if you do this and you run through this calculation, you under with a very large number of 1571.5 leaders of both three