Textbook Question 5I.33

[Sophia_Venegas_3F]

Hi! I was having a bit of trouble on how to get the values to set up this equation. How do I calculate the concentration of the NH3 with what I was given. I know that the NH4(NH2CO2) is not included in calculating Kc, but do I need it to find other elements. Here is the question:
A sample of ammonium carbonate, NH4(NH2CO2), of mass 25.0 g was placed in an evacuated flask of volume 0.250 L and kept at 25 degrees C. At equilibrium, 17.4 mg of Co2 was present. What is the value of Kc for the decomposition of ammonium carbamate into ammonia and carbon dioxide? The reaction is :
NH4(NH2CO2)(s) ← → 2NH3(g) + CO2(g)

Any help would be much appreciated! Thank you!

[005754640]

First you want to know how Kc is calculated, which would be [NH3]^2 * [CO2] in this case (since solids don't count). At equilibrium, we have 17.4mg of CO2. We can convert this to moles of CO2 using its molecular mass (44g/mol). After obtaining the moles of CO2, we divide this number by 0.25 to get the molarity of CO2. This molarity is essentially [CO2] in the Kc equation. According to the reaction, 1 mole of CO2 corresponds to 2 moles of NH3. Therefore at equilibrium, [NH3] would just be [CO2] times two. You plug in the two concentrations into the Kc expression and you should get the correct answer.