"1 L"1 L of "CO"_2CO2 is passed through red hot coke. The volume becomes "1.4 L"1.4 L at the same temperature and pressure. What is the composition of the products?

1 Answer
Stefan V.
Aug 19, 2017

Here's what I got.

Explanation:

Start by writing the balanced chemical equation that describes this reaction

"CO"_ (2(g)) + "C"_ ((s)) -> 2"CO"_ ((g))CO2(g)+C(s)→2CO(g)

Now, notice that every mole of carbon dioxide that takes part in the reaction produces 22 moles of carbon monoxide.

This implies that if the sample of carbon dioxide would react completely, you would end up with "2 L"2 L of carbon monoxide--keep in mind that when working with gases kept under the same conditions for pressure and temperature, their mole ratio is equivalent to a volume ratio.

In your case, the resulting gaseous mixture has a volume of "1.4 L"1.4 L, so you know for a fact that the carbon dioxide was not completely consumed.

If you take xx "L"L to be the volume of carbon dioxide consumed by the reaction, you can say that 2x2x "L"L will be the volume of carbon dioxide produced by the reaction.

This means that after the reaction is complete, you will be left with

overbrace((1 - x)color(white)(.)color(red)(cancel(color(black)("L"))))^(color(blue)("volume of unreacted CO"_2)) + overbrace((2x)color(white)(.)color(red)(cancel(color(black)("L"))))^(color(blue)("volume of CO produced")) = 1.4color(red)(cancel(color(black)("L")))

This will get you

1 + x =1.4 implies x= 0.4

Therefore, you can say that the resulting mixture will contain

(1 - 0.4)color(white)(.)"L" = "0.6 L " -> " CO"_2

(2 * 0.4)color(white)(.)"L" = "0.8 L " -> " CO"

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