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While doing questions on percentage yield, this one took my attention

As a result of the reaction of 20 grams of hematite with a purity of 60% with a sufficient amount of pure aluminum, how much impure iron with a purity of 70% will we get? (The percentage yield of this reaction is 40%)

$$\ce{2 Al + Fe2O3 -> 2 Fe + Al2O3}$$

My question is that why does it say "How much impure iron will we get " aren't all products of a reaction pure ?

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  • $\begingroup$ They are not pure if mixed with something else. $\endgroup$
    – Poutnik
    Commented Jul 21, 2023 at 19:40
  • $\begingroup$ For the body of questions, answers, and comments, chemistry.se offers you to use mhchem. Don't apply it to the titles of questions, though (because it is an extension not every web browser processes equally well). $\endgroup$
    – Buttonwood
    Commented Jul 21, 2023 at 19:44
  • $\begingroup$ @Poutnik So do you mean when the reaction is taking place some molecules or atoms are forming their own reactions with our products ? $\endgroup$
    – Shadow sparkle
    Commented Jul 21, 2023 at 19:45
  • $\begingroup$ @Poutnik Wikipedia reports a density of solid $\ce{Al2O3}$ (though not sure which polymorph) of $\pu{3.987 g/cm³}$ (ref and for molten Fe of $\pu{6.98 g/cm³}$ (ref). While I don't know if the two easily mix into each other during a thermite reaction (welding of train rails), maybe the lower part of the «bucket» the workers use to join rails to join is at least enriched in Fe, while portions richer in $\ce{Al2O3}$ yield a protective blanket to prevent Fe to oxidize again at these high temperatures. $\endgroup$
    – Buttonwood
    Commented Jul 21, 2023 at 19:53
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    $\begingroup$ @Buttonwood If one mixes e.g. 7 g of pure iron with 3 g of mixture of original hematite impurities, remaining Al, Al2O3 and not reacted hematite, one can easily get heterogenous mixture with 70% iron purity.(. Not sure if Al and Fe makes alloy). Anyway, the task gives vibes of made up task for computation exercise, so I would not worry so much about how much it reflects reality. $\endgroup$
    – Poutnik
    Commented Jul 23, 2023 at 7:49

1 Answer 1

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To start let's assume that you're using some reaction to make some compound in the lab. There are two "products." First the products as given in the the chemical formula for the reaction and second there are the products that you collect. The products that you collect are never absolutely pure. 99.99% pure would be essentially pure since working to 4 significant figures in a typical chemistry lab is very good work. But that isn't absolutely pure.

Now to discuss the problem you posed. This is just a made up problem and to worry to much about the details will send you down the rabbit hole.

But let's think about the problem this way. Suppose you are going to do the reaction in a crucible and after the reaction is complete you crack the crucible with a hammer to get the "button" of metal as the "collected product."

Now the stated problem throws in some wrinkles to see if you understand chemistry and are not just solving a math problem.

  • First the problem states "the reaction of 20 grams of hematite" but then the problem backpedals and states that the hematite is only 60% pure. Who knows what the other 40% is. Make the assumption that the 40% is inert. (The problem would have been better stated as the reaction of 20 grams of hematite ore which is 60% pure.)

  • The problem states that there is "a sufficient amount of pure aluminum" which means that there is at least enough aluminum to react with all the hematite.

  • Now, as in my contrived experiment, the problem states that the button of metal produced is only 70% iron. Let's assume that 12.0 grams of hematite should yield x grams of pure iron. Then the button would weigh x/0.70 grams since it is impure.

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  • $\begingroup$ Thank you so much for your explanation 🍂 So when we say our product has percentage purity, we are not talking about the products given in the the chemical formula but the products that we collect ?! $\endgroup$
    – Shadow sparkle
    Commented Jul 22, 2023 at 13:28
  • $\begingroup$ And can this be another reason or not " when the reaction is taking place some molecules or atoms are forming their own reactions with our products " $\endgroup$
    – Shadow sparkle
    Commented Jul 22, 2023 at 13:32
  • $\begingroup$ @Shadowsparkle - Yes the chemical formula implies absolute purity, but the actual product collected will never be absolutely pure. // The problem statement doesn't give any indication as to what the impurity in the "hematite" is, nor what the 30% of the product that is not iron. This was just a "problem" not a lab exercise. Don't go down a rabbit hole trying to figure out either of those. $\endgroup$
    – MaxW
    Commented Jul 22, 2023 at 19:16

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