[Kromede]

I solved this exercise but I doubt something is wrong...  There is no result at the end of it.

"A volume of 4.60 lt SPT of a mixture composed of NO₂ and Cl₂ react with the following reaction:

NO₂ + Cl₂  NO₂Cl

We know that NO₂ is the limiting reagent. The final volume of all the gas is 4.14 lt SPT. Please calculate the starting composition of the mixture".

First of all, I balanced the reaction: 2NO₂ + Cl₂  2NO₂Cl

Than I wrote: V(mixture) = V(NO₂) + V(Cl₂)

V(final) = final V(NO₂) + final V(Cl₂) + final V(NO₂Cl) (at the end)

So I called the final V(NO₂) = x - 2 (2 lt is the volume it should lose after the reaction because of the coefficients) and then I called the final V(Cl₂) = y - 1 (2 lt is the volume it should lose after the reaction because of the coefficients).

So now I have a linear system with two equations:

x + y = 4.60

and

x - 2 + y - 1 + x = 4.14

I solved it and I found that V(NO₂)= 2.54 lt and V(Cl₂)= 2.06 lt so the composition of the starting mixture is:

55.2% of NO₂ and 44,8 % of Cl₂.

I'm really not sure of what I did... especially because of the fact that I didn't use the SPT information about the volumes.

Sorry for my english which is not perfect 

Thanks!!!

[Borek]

So I called the final V(NO₂) = x - 2 (2 lt is the volume it should lose after the reaction because of the coefficients)

Idea of using x, y and writing set of equations is definitely one of the correct approaches to the problem, but no, it is not that 2 liters of the gas reacted.

Assume x (initial NO₂), y (initial Cl₂) and z (final NO₂Cl) to be your unknowns. You have the first equation already. The second is the one describing the final mixture - however, you need to represent amount of NO₂ and Cl₂ in the final mixture using x, y and z. And you also know that all NO₂ reacted, so it is easy to write the third equation, combining initial amount of NO₂ and the final amount of NO₂Cl (just use the stoichiometry).

I'm really not sure of what I did... especially because of the fact that I didn't use the SPT information about the volumes.

STP doesn't matter, all that matters is the assumption the ratio of volumes is identical to the ratio of number of moles. This is so called Avogadro's hypothesis.

[Kromede]

Hi, thanks for your answer. I kept an eye on the problem more accurately and I wrote:

x (initial NO₂), y (initial Cl₂) and z (final NO₂Cl)

But z = x if we see the reaction's stoichiometry and we remember that NO₂ is the limiting reagent. So I can write the system made by the two equations:

x + y = 4.6

and now the volume of the final mixture is the sum of x and (y - 1/2*x) because the volume of Cl2 I'm considering at the end is a remaining part.

x + (y - 1/2*x) = 4.14

Solutions are x=3.68 lt and y=0.92 lt. In conclusion % NO₂ = 20% and % Cl₂ = 80%

What do you think about that?

P.S: I accidentally sent another message below but I don't know how to delete it.

[Borek]

I haven't checked numbers, but the logic looks sound.