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The fuel in the buster rockets of the Space Shuttle is constituted of a mixture of ammonium perchlorate, $\ce{NH4ClO4}$, and aluminum powder. One of the reactions taking place during taking off is given by $$\ce{6 NH4ClO4(s) + 10 Al(s) -> 5 Al2O3(s) + 3 N2(g) + 6 HCl(g) + 9 H2O(g)}$$ The indication (s) and (g) signify solid and gaseous phase. Suppose that these rockets are loaded with $\pu{11.75 ton}$ of ammonium perchlorate and $\pu{2.70 ton}$ of aluminum.

Calculate the volume of nitrogen gas produced during taking off under normal conditions ($\pu{0^\circ C}$ and atmospheric pressure, so that $\pu{1 mol}$ corresponds to $\pu{22.4 L}$ of gas).

I got to the point where it's $\pu{10^5 mol}$ for each of the compounds. How do you get to the answer $\pu{6.72e5 L}$?

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    $\begingroup$ LOL - Had to run through calculations twice. I used English tons rather than metric tons. $\endgroup$
    – MaxW
    Dec 24, 2017 at 16:34
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    $\begingroup$ I ran right over this reading the problem statement but the statement (0 ∘C and atmospheric pressure, so that 1 L corresponds to 22.4 mol of gas). is backwards. 1 mole of gas is 22.4 liters. $\endgroup$
    – MaxW
    Dec 24, 2017 at 16:46
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    $\begingroup$ chemistry.stackexchange.com/questions/80780/… $\endgroup$
    – Mithoron
    Dec 24, 2017 at 18:32
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    $\begingroup$ @MaxW I have no idea how I missed it. Those sneaky 22.4 liters. $\endgroup$
    – andselisk ♦
    Dec 24, 2017 at 21:08

1 Answer 1

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Your next step is to identify the limiting reagent.

Observe that six moles of ammonium perchlorate react with ten moles of aluminum. So by taking ratios you find that:

1) The $10^5$ moles of ammonium perchlorate you started with react with approximately $1.7×10^5$ moles of aluminum.

2) The $10^5$ moles of aluminum you started with react with $6×10^4$ moles of ammonium perchlorate.

Now there is a problem with (1) -- you have only $1.0×10^5$ moles of aluminum available so not all of the ammonium perchlorate can react as indicated in (1). So we now look at (2) -- it indicates that all of the aluminum can react and you still have $4×10^4$ moles of ammonium perchlorate remaining.

Thus we can realize condition (2) rather than (1) because the amount of reaction is limited by the aluminum you have available. Thus aluminum is the limiting reagent.

Now that you know the limiting reagent you can infer how much product is formed. With $10^5$ moles of aluminum all being consumed, you should be able to see that $3×10^4$ moles of nitrogen molecules are formed as gas. The volume under normal conditions should then follow.

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