Chemistry Chemical Equilibrium: find concentration from 2 solutions (ICE table)

AI Thread Summary
The discussion focuses on understanding how to apply the ICE table to determine concentrations in a chemical equilibrium problem involving NO2 and N2O4. Participants express confusion about why values are plugged into (1-2x) instead of (1-2x)^2 in the equilibrium constant expression. It is clarified that while both approaches yield correct equations, using x=0.65 leads to a negative concentration for NO2, which is not physically viable. The correct method involves substituting values into the appropriate expressions to avoid unrealistic results. Ultimately, participants are encouraged to test their calculations to find the correct concentrations.
doridoridori
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Homework Statement
I've recently encountered this problem https://www.physicsforums.com/threads/need-major-help.117630/
In case the link doesn't open, here's the problem itself:
9. At a certain temperature, T, K for the reaction below is 7.5 liters/mole.

2NO2 <===> N2O4

If 2.0 moles of NO2 are placed in a 2.0-liter container and permitted to react at this temperature, what will be the concentration of N2O4 at equilibrium?

a) 0.39 moles/liter

b) 0.65 moles/liter

c) 0.82 moles/liter

d) 7.5 moles/liter

e) none of these
Relevant Equations
Super stuck on this. All of the deets are given in the question I linked. I'm still getting used to this forum so don't mind please if I accidentally mess something.
Also this is the equation itself:

7.5=x/(1-4x-4x^2)
30x^2-31x+7.5=0
x=0.39(approx.)
x=0.65(also approx.)
Hello! I've recently encountered this problem https://www.physicsforums.com/threads/need-major-help.117630/ and solved it and I'm stuck at choosing between 2 solutions. I don't understand why do we need to plug in 0.39 and 0.65 to (1-2x) and NOT to (1-2x)^2. I mean, we were given 2NO2, not just NO2. I see that in ICE table the result is [1-2x] but then why Keq=N2O4/(NO2)^2 and not just NO2?
 
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Those are both correct solutions to your equation, but x=0.65 corresponds to a negative concentration of NO2, which is physically impossible.
 
Chestermiller said:
Those are both correct solutions to your equation, but x=0.65 corresponds to a negative concentration of NO2, which is physically impossible.
Hello! Yes, that's essentially what I was asking. Sorry if I made it all unclear! So to know the right answer, we are plugging 0.65 and 0.39 into (1-2x). What I don't understand is why don't we plug it into K=x/(1-2x)^2 instead? I mean, we were given 2 moles of NO2, wouldn't it be reasonable then to calculate for 1-2x squared?
 
doridoridori said:
Hello! Yes, that's essentially what I was asking. Sorry if I made it all unclear! So to know the right answer, we are plugging 0.65 and 0.39 into (1-2x). What I don't understand is why don't we plug it into K=x/(1-2x)^2 instead? I mean, we were given 2 moles of NO2, wouldn't it be reasonable then to calculate for 1-2x squared?
That is what you do plug into. Try those values and see what you get.
 
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