Is the reaction at equilibrium?

Question

Nitrogen dioxide dimerizes according to the following reaction: 

2NO₂​(g)⇌N₂​O4₄(g) Kp​ = 6.7 at 298 Kelvin  

A 2.25 - L container initially contains 0.055 mol of NO2​ and 0.082 mol of N2​O4​ at 298 Kelvin. If not, in what direction will the reaction proceed? 

Answer 1

2NO₂​(g)⇌N₂​O4₄(g) ... Kp​ = 6.7

Kp = Kc(RT)^∆n

Kp = 6.7

Kc = ?

R = 0.0821 Latm/Kmol

T = 298K

∆n = change in number of moles = 1 - 2 = -1

solve for Kp:

6.7 = Kp(0.0821x 298)^-1 = 0.0409Kp

Kp = 164

Q = [N2O4] / [NO2]² = (0.082/2.25) / (0.055/2.25)² = 0.0364 / 0.000598

Q = 609

Since Q is >> than K, the reaction is NOT at equilibrium and it will proceed toward the left, i.e. toward reactants.

NOTE: you can do this problem using the Kp value and then converting concentrations of NO2 ane N2O4 to pressures. Then compare Q to Kp.