[czmtzyddl]

There is an equilibrium in the reaction 2NO₂ N₂O₄.
Consider a constant-pressure system where such reaction has reached its equilibrium. How will the color change when adding extra NO₂ to the system? And why?

[billnotgatez]

read forum rules
We deleted your other copy of this question because you are not allowed to double post.
You should attempt to show some work before expecting help.

[czmtzyddl]

Well, from my perspective, when adding extra NO₂ to the system, the concentration of NO₂ increases. Therefore the color goes darker. However, according to Le Chatelier's principle, part of the NO₂ should turn into N₂O₄ and the color should turn lighter correspondingly. And that’s the problem, the extent to which the color changes.
My friends and I both agree that the color should be darker than the origin, while our teacher believes the color should stay the same. Since I don’t have the equipment to conduct the experiment, I tried to calculate the Δc during the process. It seems to be so complicated that it confuses me even more.
So what’s really happening in the system? How should I think about a problem like this the next time? I hope the answer could include some fundamental logics of chemistry rather than some conclusions I don’t even know where they are derived from. And this is also why I posted this high school chemistry problem here. Thanks!

[Borek]

There is a very important hint in the problem: system is kept at the constant pressure.

[czmtzyddl]

Hmm. So does it mean that although the reaction will consume more NO₂, the volume shall shrink at the same time, causing the reaction to keep on going till the concentration turns back to the origin?

[czmtzyddl]

Or is there an appropriate mathematical formula to explain this problem?

[Borek]

Hmm. So does it mean that although the reaction will consume more NO₂, the volume shall shrink at the same time, causing the reaction to keep on going till the concentration turns back to the origin?

Exactly.

And yes, there is a formula - just for the equilibrium constant. In this particular case (one reagent, one product, it doesn't have to be identical for other cases) no matter what the initial composition of the mixture is (you can start with just NO₂, just N₂O₄, or anything in between*) once the system gets to equilibrium partial pressures of both gases will have the same value - which also means identical concentrations and identical absorption of light (or the same color).

*technically preparing things like "pure NO₂" or "pure N₂O₄" is impossible, as they immediately start to interconvert.