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Problem 64

An iron ore sample contains $\mathrm{Fe}_{2} \mathrm{O}_{3}$ together with other substances. Reaction of the ore with CO produces iron metal:

$$

\mathrm{Fe}_{2} \mathrm{O}_{3}(s)+\mathrm{CO}(g) \longrightarrow \mathrm{Fe}(s)+\mathrm{CO}_{2}(g)

$$

(a) Balance this equation.

(b) Calculate the number of grams of CO that can react with 0.350 $\mathrm{kg}$ of $\mathrm{Fe}_{2} \mathrm{O}_{3}$ .

(c) Calculate the number of grams of Fe and the number of grams of $\mathrm{CO}_{2}$ formed when 0.350 $\mathrm{kg}$ of $\mathrm{Fe}_{2} \mathrm{O}_{3}$ reacts.

(d) Show that your calculations in parts (b) and (c) are consistent with the law of conservation of mass.

Answer

a) See explanation for solution.

b) 184.16$g$

c) $F e=244.80 g, C O_{2}=289.36 g$

d) See explanation for solution.

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## Discussion

## Video Transcript

So in this problem we're given or with the reaction off on Iran or which has a formal off if it two or three and that is reacting with carbon monoxide on to produce Iran and Syria, it's in first part of this problem. We have to balance this reaction for balancing what we'LL do. Well, first, right down each specific. I just present in both side of the reaction aggression. Send reactor inside. We have a facey and all, and we have also iffy See an oil in the product side. Now we have two f e in the reactor side, we have one Kurban and we have three plus one total for oxygen. The product side, we have one. Byron, we have one, Carbone, and we have to oxygen. No first real balance or metal, which is iron. So we have to hire on in reactor inside. But one I don't in the product side, so we'LL place it to hear tohave Tyrone in the in this side also on the upside. Now we have acquired on in both side and we have one car. One in both sides now will balance our oxygen. So we have four oxygen in the reactor inside. But we have talks in the production side. That means we need two more oxygen in the in this sort of a parasite. So what we'LL do we'LL multiply this hero two by two tohave for OCS isn't in the product site Now we have four four oxen in the reactors side and for oxygen the product side But at the same time, we have Jane the number of carbon in the product side. Now we have two carbon in the production side, but we have one covering the reactor's side. That means we have tto place A to here. You have to carbon in the reactor side also. But again, we have changed a number of oxygen in the reactor site. Now we have to treat them three plus two. That means five oxygen in the reaction sign. Now we need more oxygen in the product side, but we cannot have five boxes in the product sign since the number of boxes and we can have here is the multiple off too. So what we can have here is six oxygen. So you can Our place is three here to have two times two will give us six oxygen. So now we have six oxygen in the peroxide. But we have five in the reactor site that men's we'LL have to place three here also, which will give us six oxygen in the perfect site. Also in the reactor inside also. And we have three carbon now in the reaction sign and we have tree carbon in the product sign. That means now we have two irony in his sight. We have three carbon inside and we have six oxygen inside. That means this is our balance creation in question. Now, in a second part, we have to find out, um, the number of grams off seal that can react with point three five Casey off every two or three. So what we will do is, um, first, we have to find out the number of most for point three fifty gives you off every two or three. It's a point three fifty. Cus Siemens three five zero Graham three five zero grams. Every two or three is in number of malls off three five zero over the Moler massage. Every two or three, which is one fifty nine point six nine cramp Our Mall, The state fifty Graham doing give us a bell off two point one nine Tamal. So this is the number of most for point three five zero. Get you off every two or three. Now we have to find out how many more off CEO Ah will react. Wait this much mall off every two or three. And from there we can find out Ah, the grams of seal that would react with this much Graham off every two or three. So from the reaction equation, we can see that one mall of reputable she will react with three mile of CEO and men's one more if Ito tree when reactivated Trimmel seal That means this much more off every two or three more every two or three will react to it. Um, three times to plant one nine two mall See all which is equal to six point five seven five months seal. And if we just multiply this by the molar mass of carbon monoxide, we confined the mass off this much more of carbon monoxide. So the mole Irma's of Criminal Studies twenty eight point zero one grandpa are more so you didn't give us a bad off one. Eighty four point one seven gram Feel that means this is the gram of seo which will react with ah two point one nine two more or three. Fifty Graham or point three five zero Get you off every two or three. Now, in the hard part of this problem, we have to find out how many grams off if he and how many grams are see. Oto can be formed from twenty five zero kids. You off every two or three second, we have find out the number of malls off four point five zero gives you off every two or three which is two point one nine two more So we have to find out how many more off Effie and feel toe can reform from this much mall off if it were three and from there we can find out how many grams off each of them were reproduced. The first we'Ll find out how many? Most of if he would be produced. So from one matloff individual tree we can find out what we conform to Melo. Fifty. Let me in One more every toe tree can propose two more if he that means two point one nine to mollify. Two or three. Well, adios. Two times two point one nine two Mall which is equal to four point Create six small if he And if we want to find the massif ifI which is simply, multiply this number of malls by the molar mass of a fee which is fifty five point eight four. Grandpa Armel, which is equal to two. Forty four point nine one gram Effie. So this is the mass off a fee which will be produced from point three fifteen Get you off every two or three. Now we'LL find out how many grams off ex seal to really produced. So from here you can see Ah, one more left two or three can produce three moles Photo That means one more effort to a tree can give us Trimmel Soto that man's two point one nine tamal effort or tree will give us three times two point one nine two more is equal to six Planned five, seven five mole Soto And if we just want to find the massive Soto, we just multiply this number of moles by the molar mass of Soto which is forty four grams and you'LL give us two eighty nine point three Graham cierto So this is the grams of Theodore Massive Theater two eighteen and Burnt Program which will separate us from point three five zero k Z off on every two or three. Now, in the last part of this problem, we have to show the calculations in part B and C are consistent with the love conservation off mess Salov conservation of masses the mass of the reactant reacting will be called to the mass of the products produced, So the massive, reactant subjecting here is ah three five zero Graham off every two or three is reacting with wanted to four point one seven gram of seal So the total reactant here is one eighty four point So the total is five. Thirty four point one seven thirty four point one seven gram and the products produced her. We're having two forty four point nine one gram off Effie and two eighty nine point tree Graham off Soto. So the total Parexel five. Thirty four point two on ground so we can see that the mass of react Ince's almost similar to the mass of the products which is produced. That means the calculations in Part B and C are consistent with their love conservation of mass.

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