Dinitrogen tetroxide decomposes according to the equilibrium
N₂O₄(g) ⇌ 2 NO₂(g)
At 298 K, K_p = 0.15. A rigid 1.0 L container initially holds 1.0 atm of N₂O₄(g) and 1.0 atm of NO₂(g) at this temperature.
The system subsequently undergoes two rapid disturbances in succession, each occurring before the mixture can re-establish equilibrium:
(1) The volume of the container is suddenly reduced to 0.50 L while the temperature remains at 298 K.
(2) Immediately afterward, the temperature is raised until K_p increases to 0.40; the total pressure has not yet changed appreciably since the temperature rise is instantaneous.
a. Using the initial partial pressures, calculate the reaction quotient Q_p at 1.0 L and predict the spontaneous direction of the net reaction. State the sign of ΔG for the forward reaction.
b. Determine the new value of Q_p immediately after the volume is halved to 0.50 L (assume ideal-gas behavior and instantaneous pressure change). Predict the favored direction at this moment and the corresponding sign of ΔG for the forward reaction.
c. With the mixture still at 0.50 L, the equilibrium constant becomes 0.40 because of the temperature increase. Using the Q_p value from part (b), decide again which direction is favored and give the sign of ΔG for the forward reaction.
d. Discuss how each disturbance (volume change versus temperature change) affects Q_p, K_p, and thereby the thermodynamic driving force of the reaction. Include an explanation of why ΔG changes sign or remains the same in each step.