[Traume]

I have a question about calculating the equilibrium constant for a particular generic reaction.  I am attempting to prove that for the generic reaction:

A  2B + C

for an ideal gas, the equilibrium constant K=(4/27)P³ assuming you start with N moles of A and 0 moles of B and C and then proceed to equilibrium. 

Starting with the equation:
K=((X_CP)(X_BP)²)/(X_AP)

and using extents of reaction (E), and setting the mole fractions at equilibrium in terms of E, I was able to reduce the equation down to the following form:

K=[(4(E³))/{(N-E)((N+(2E))²)}]P². 

However from here I can't find any way to simplify it further or to go from P² to P³.  I tried using the relation ln(K)=-G/(RT) and substituting in other relations for G (and RT using ideal gas law) but I couldn't manage to get anywhere with that either.  I also tried relating K in terms of the dissociation constant rather than extent of reaction but again I ended up with alot of mess similar to above that I was unable to reduce any further.  Does anyone have any suggestions for ways that I might further reduce this equation down to the form shown above?  I get the feeling that I am greatly over complicating this problem, but after a few hours of trying to manipulate it I'm still having trouble.  Thanks a bunch in advance for any suggestions provided!

[Borek]

Won't hurt if you will explain what P is. Total pressure?

What is A - solid? Gas? If the latter, does the question make sense? Hint: check K units.

[Traume]

Oh sorry, yes P is total pressure.  A is a solid that dissociates to B and C which are both gases.  I did check to make sure that the units work out and they appear to be fine (N, E in my equation above are both in moles which cancel out, P is actually total pressure over standard state pressure, but since the pressure at standard state is 1 bar I just write it as total pressure for simplicity (this means that the pressure units also cancel out to leave K unitless)

[Borek]

If A is a solid, it doesn't appear in the K.

Use stoichiometry (molar ratio of products) to express partial pressures of B and C in terms of total pressure. Then just plug into K.