HW 11.41

[Pauline Tze 3B]

I understand how the solution manual answers this question (though is the first step where it converts 25.0g of the reactant to moles seems irrelevant), but I'm not understanding why my approach didn't work.
I tried to find the concentration of CO₂ and NH₃ separately, then plug that back into the K_c equation.
For CO₂, the concentration was correct, but for NH₃, I ended up with a much larger concentration than the answer.
Why doesn't it work to subtract 17.4 mg from 25.0g, convert that to moles of NH₃ then divide by 0.250 L?

Is it that in decomposition chemical equations, the mass isn't preserved on both sides of the equation?

Thank you in advance!

[Hao 1I]

Subtracting 17.4g of CO2 from 25.0g of ammonium carbonate does not work. 25.0g of ammonium carbonate is present initially (before any reaction happened) but only 17.4g CO2 are present in equilibrium. Because 17.4g of CO2 are present in equilibrium, there are still still some amount of ammonium carbonate left from the left hand side of the equation but not all of 25.0g.