Final answer:
The Correct option is 2). To cause the equilibrium between N₂O₄ and NO₂ to become darker brown, increasing the concentration of NO₂, decreasing the temperature, or increasing the pressure would be effective, due to the reaction's endothermic nature.
Step-by-step explanation:
The student is asking about the effects of different changes on the equilibrium between colorless dinitrogen tetroxide (N₂O₄) and brown nitrogen dioxide (NO₂). Since the reaction is endothermic, adding heat shifts the equilibrium towards more NO₂. Therefore, the equilibrium would become darker brown by (1) increasing the concentration of NO₂, (3) decreasing the temperature (which would shift the equilibrium to the exothermic reaction to restore heat, thus decreasing NO₂), or (4) increasing the pressure (since there are more moles of gas on the NO₂ side and the system would favor the formation of additional NO₂ to counteract the pressure increase).