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Problem 62

The reaction between potassium superoxide, $\mathrm{KO}_{2},$ and $\mathrm{CO}_{2}$
$$4 \mathrm{KO}_{2}+2 \mathrm{CO}_{2} \longrightarrow 2 \mathrm{K}_{2} \mathrm{CO}_{3}+3 \mathrm{O}_{2}$$
is used as a source of $\mathrm{O}_{2}$ and absorber of $\mathrm{CO}_{2}$ in self-contained breathing equipment used by rescue workers.
(a) How many moles of $\mathrm{O}_{2}$ are produced when 0.400 $\mathrm{mol}$ of $\mathrm{KO}_{2}$ reacts in this fashion?
(b) How many grams of $\mathrm{KO}_{2}$ are needed to form 7.50 $\mathrm{g}$ of $\mathrm{O}_{2} ?$
(c) How many grams of $\mathrm{CO}_{2}$ are used when 7.50 $\mathrm{g}$ of $\mathrm{O}_{2}$ are produced?

a) 0.300 $\mathrm{mol} \mathrm{O} 2$
b) 22.2 $\mathrm{g} \mathrm{KO} 2$
c) 6.88 $\mathrm{g} \mathrm{CO} 2$

## Discussion

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## Video Transcript

So in this problem, we're given this rationing question between Kyoto and Soto Marcato CEO three and order where oxygen is produced. So the first question here is how many moles off or two are produced when born formal, off kilter reacts initiation. So from the balanced chemical equation, we can see that Ah, for more g o to it will produce three matloff oxygen. That means from here, um, we can find out how many more off or two will be produced from point formal of Kyoto. That means, um, point formal kill two will proposed three or four times point for mall, which is equal to point three mole or two. That means one formal off you go to will produce one tree. Matloff Auto. Now, in the second part of this problem, we're asked to find out how many grams off killed or needed to form seven point five gram off auto. So what we have to do is we just have to onboard this graham into number of malls, and again we could just find out how many most ofthe killed will be required. He couldn't produce that much more for two. And from there we can find out how many grams off Kyoto will be needed to form seven point five. Promoter sagging here we can see that so far. So let's find out the number of malls of or do for seven point five grandma, too. So, um, as you know that the number of most is basically the math of our molar mass. That means seven point five gram Ordway, seven point five over thirty two, which is the molar mass off auto since for one oxygen, it is sixteen. The more mass off a single oxygen atoms sixteen's that meant for auto molecule is thirty two. So if we divide seven point five by thirty two, um, we'LL get value off zero one, two three four Wait. So this is the number of more off seven point five gram oto. Now we have to find out how many months off killed we need to produce point to formal a photo. So since three more or two is produced from formal Kyoto exporters from formal killed, too, that means zero point two three more or two will it produce from four by three times zero point two three four more, which is equal to zero point two on two. Five, um, three, one two more Kyoto. That means our country want to mull. Kyoto will produce point three formal or two, which is the number of most of seven points. Five grand moto now from this number of mosaic and find out the massive still too, which is required. So just simply multiply this number of malls off Kyoto by the more massive skilled, which is seventy one point one. So massive killed, too. Which is record is when three, one, two more times the molar mass of killed, which is so into one point one gram per mall. And this will give us the value ofthe, um, twenty two point two. So this's the mass ofthe Kyoto, which is required are needed to form seven point five grandma photo. Now, in the last part of this problem, we have to find out how many grams off suit were used when seven point five grand motor produced, Um, same as before. We have to find out the number of most ofthe seven point five promoter, which we have already calculated. So for seven point five grand moto, the number of Moses point too formal. So we have to find out to produce point with your formal orto How many more off Soto we require So we can see that to produce three months or tow we have to use to maul Toto. That means Trimmel or two is produce from tumult Here too. That means point two three formal or two will be produced from to over three times point two three four more which is equal to point one five six mall's CEO too. So this is the number of Mall of Seo too which is required to produce point two three formal oto r seven point five gram Otto. Now we have to convert this number of most ofthe Sciutto grams and we can do that by simply multiplying this number of malls by the more massive Soto. So mass off too which is required is equal to, um the number of malls of cierto which is your opponent one five six mole and the molar mass of surgeries forty four plant or one Grandpa our mole It'LL give us a fellow off six point eight six gram Theo So this is the massive cierto um which is required are used to produce seven point five gram oto