Final answer:
The pressure in the vessel at 100 minutes cannot be determined without the necessary rate constant and initial concentration values.
Step-by-step explanation:
This question involves the decomposition of N₂O₅ to NO₂ and O₂, and follows first order kinetics. From the given information, we know that the pressure inside the vessel increased from 50 mm Hg to 87.5 mm Hg after 50 minutes. To find the pressure at 100 minutes, we can use the concept of first order kinetics and the given rate constant values at different temperatures.
The rate constant for the decomposition of N₂O₅ at the given temperature is not provided, so we cannot directly calculate the pressure at 100 minutes. We would need the rate constant at the given temperature to proceed with the calculations. It is also important to note that the pressure depends on the initial concentration of N₂O₅, which is not provided.
Therefore, without the necessary rate constant and initial concentration values, we cannot determine the pressure of the gaseous mixture at 100 minutes.