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I was wondering, for this problem, I initially went in thinking that I would need to do an ICE box but I found the answer simply by using the equilibrium constant formula. How do you know when to do an ICE box? And also, why do the concentrations of N2 and O2 remain the same?
As far as the ICE table, sometimes they're helpful because they make a nice visual representation of what's happening in the reaction, but if you are given enough information to just use the K equation, that will work too (and it's faster).
The ICE box is just a great visual to see how the concentrations of the reactants and products change as the reaction reaches equilibrium. It's useful because it makes it easy to see the change in concentration based on the balanced chemical equation and gives you the expressions for the equilibrium concentrations so you can plug them into the equilibrium constant expression. You can use the quadratic formula to solve this problem, but since Kc is very small (1.00 x 10^-5), you can approximate that the change in the concentration of N2 and O2 is zero because x will be much smaller than 0.114M. This makes the equation a lot simpler to solve.
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