Nitrogen dioxide dimerizes according to the reaction: 2 NO2(g) ⇌ N2O4(g) Kp = 6.7 at 298 K. A 2.25-L container contains 0.055 mol of NO2 and 0.082 mol of N2O4 at 298 K. Is the reaction at equilibrium? If not, in which direction will the reaction proceed?

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1. Calculate the initial partial pressures of NO2 and N2O4 using the ideal gas law: P = (nRT)/V, where n is the number of moles, R is the ideal gas constant (0.0821 L·atm/mol·K), T is the temperature in Kelvin, and V is the volume of the container.
2. Determine the reaction quotient, Qp, using the expression Qp = (P_{N2O4}) / (P_{NO2})^2, where P_{N2O4} and P_{NO2} are the partial pressures of N2O4 and NO2, respectively.
3. Compare the calculated Qp to the given equilibrium constant Kp. If Qp < Kp, the reaction will proceed in the forward direction to reach equilibrium. If Qp > Kp, the reaction will proceed in the reverse direction. If Qp = Kp, the reaction is at equilibrium.
4. Analyze the direction of the reaction based on the comparison of Qp and Kp to determine if the reaction will shift towards the formation of more products (N2O4) or reactants (NO2).
5. Conclude whether the reaction is at equilibrium or predict the direction in which the reaction will proceed to reach equilibrium.