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Numerade Educator



Problem 77 Hard Difficulty

Lead can be prepared from galena [lead(II) sulfide] by first roasting the galena in oxygen gas to form lead(II) oxide and sulfur dioxide. Heating the metal oxide with more galena forms the molten metal and more sulfur dioxide.
(a) Write a balanced equation for each step.
(b) Write an overall balanced equation for the process.
(c) How many metric tons of sulfur dioxide form for every metric
ton of lead obtained?


a) $2 \mathrm{PbS}(\mathrm{s})+3 \mathrm{O}_{2}(\mathrm{g}) \longrightarrow 2 \mathrm{PbO}(\mathrm{s})+2 \mathrm{SO}_{2}(\mathrm{g})$
$2 \mathrm{PbO}(\mathrm{s})+\mathrm{PbS}(\mathrm{s}) \longrightarrow 2 \mathrm{Pb}(\mathrm{s})+\mathrm{SO}_{2}(\mathrm{g})$
b) $\mathrm{PbS}(\mathrm{s})+\mathrm{O}_{2} \rightarrow \mathrm{Pb}(\mathrm{s})+\mathrm{SO}_{2}(\mathrm{g})$
c) $\mathrm{m}\left(\mathrm{SO}_{2}\right)=309169,88 \mathrm{g}=0,309 \mathrm{t}$


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Video Transcript

all right for problem 77. Ah, this is a two step reaction. Um emigrated to balance both of them. So that's where we will start. Okay, so we start with, um he led to sulfide, which reacts with oxygen gas. And this is stuff one, and that gives us the lead oxide, the lead to oxide and sulfur dioxide. So we want to balance this one first. Uh, the first thing you want to do here is count your Adam's on each side and see if you have the same. We don't have the same. We have two oxygen here and three oxygen here. So what I want to do is I first want to, um but it to here because that will give me an even amount of oxygen. So now I have four here and to hear, but now we have to lead here. So I'm gonna add another two here, and that's going to give me two leads to the leads now balance. But the sulphur isn't so I need a to hear perfect. And that now leaves me with four oxygen plus two. Oxygen equals six oxygen s o. If I put a three here Now I have six auction on this side and step one of the reaction has been bounced. So for step two of the reaction, we have the lead oxide, which with which is what reacts with more, um, lead sulfide or the Galina, as they say in the problem. And this gives me the elemental lead. And finally, the sulfur dioxide or more of the sulfur dioxide. So the balance, this one, I can already see that there's two lead on the side and only one lead on this side. There's also to oxygen on the side and only one on this side. So I'm gonna balance my oxygen first just because this lead is alone. So I can like at as many as I want, even or odd at the end. So to lead three lead down on this side. And now the oxygen's balanced and the soul first balanced. So if I put it three here Now I have 123123 It's about perfect. Okay, So for part B, we're going to add these equations together, uh, to give us our final kind of like our reaction that takes away like all the intermediate steps, and I'll show you that in a second how they cancel out. So if I look here, I have three of the lead. So find and I have two let oxides and three moles of the oxygen gas. And that gives me three sulfur dioxides, three moles of elemental lead and two moles of lead oxide. So right here I can see that I have this on the lead oxide on one side and on the other side so I can cancel these ones out because they they balance each other out kind of thing. And same with, um same with this year. If I right this hopefully you can see that we have three moles of each compound. And basically, that means that I You can cancel that three oat, and it can just turn to one. So get rid of this three because we have an equivalent amount of each on both sides, and this leaves me with one more of each thing. Hear of each compound should say Okay, so this is my final reaction here. Oh, I didn't mean to put a three there, okay? And now, for part C, all they want to do for it asks how many metric tons of sulfur dioxide form for every metric ton off lead taint. So if you look here, that's a 1 to 1 molar ratio. But I'm going to a racist doctor. Okay. So wonder one mole ratio of the oh. Oops. Okay. Yeah. Wonder one mullah ratio of these sulfur dioxide in the lead. So for every one Moeller or one bowl of lead, I get one mole of the S 04 I didn't mean to say that. So for S 02 Okay. Yeah, That is the problem. Perfect.