[mirox]

The problem goes: For the reaction N₂(g) + 3H₂(g) 2NH₃(g) at T=473 K, equilibrium constant Kp equals to 4.2*10^-8 1/kPa². At this temperature, nitrogen and hydrogen of partial pressures of 87.3 and 37.8 kPa, respectively, have been placed in a reaction vessel of the constant volume. Calculate partial pressures of both reactants and ammonia as well, and the total pressure of gaseous mixture after the equilibrium is reached.

Attempt on solving this: I write the Kp expression, but I am then stuck with  something I can't solve: Kp=(3x)²/(87.3-x)*(37.8-2x)³; where x, 2x represent reduction of partial pressures of N₂ and H₂ and 3x is equilibrium partial pressure of ammonia. I am stuck, so I would really, really appreciate some advice and guidance in solving this! Thanks a lot!

[Borek]

Equilibrium constant is so low you can as a first approximation assume partial pressures of nitrogen and hydrogen didn't change.

[mirox]

Dear Borek,

that's what my initial answer was (my prof. asked me the question), however he said that I should precisely calculate everything. I am really frustrated, I have spent the whole day yesterday trying to solve it, but the prof. won't give me any guidance, so I am kind of in a deep problem over here... Maybe there is a different, more elegant approach than mine that I'm not aware of?

[mirox]

I have found out that the answers should be:
P_N2=87.1 kPa;
P_H2=37.1 kPa
P_NH3=0.460 kPa

Which is what you also get when you assume what you mentioned, but they just won't accept my answer. I am really, really confused right now. Don't know what I'm doing wrong.

[Borek]

You can always try the iterative approach, or some other kind of numeric solution.

http://www.wolframalpha.com/input/?i=(3x)^2/((87.3-x)*(37.8-2x)^3)=4.2e-8

[mjc123]

3x and 2x are the wrong way round. Ammonia pressure is 2x; hydrogen is 37.8 - 3x.

[Borek]

Good point. I have read the part

I have found out that the answers should be

as meaning "these are answers that were listed as correct ones in the key", but apparently it is not what it means. Oh, well.