[sketch321]

A sample of nitrogen dioxide gas decomposes at 1000K according to the following equation:

2NO₂ (g) <-> 2NO (g) + O₂ (g) KP=158

The pressure of NO₂ initially is 0.42 atm, and the equilibrium pressure of NO₂ is 0.25 atm. Find the equilibrium pressures of O₂ and NO.

I have worked this problem as many different ways I can think of and for the life of me CANNOT get answers that satisfy all the requirements of the reaction.

[Cavillus]

Well, IMHO the data given in the problem aren't correct. So, assuming the final NO₂ pressure is mistaken, the solution is pretty simple:

                           2 NO_2(g)  2NO_(g) + O_2(g)
P_i (atm)                   0,42            0          0
P_f (atm)               0,42 - 2P         2P         P

So, substituting in the K_p formula:

K_p = ^{P2_NO P_O2} / _P²NO2 = ^4P3 / _{(0,42 - 2P)²}.

Solving the 3^rd degree equation resulting, you get the following results:
P₁ = 157 atm.
P₂ = 0,202 atm.
P₃ = 0,218 atm.

As it is pointed out by substitution in K_p, the latter is the correct one.