Second-Order Reaction: Pressure and Degree of Completion over Time

Question:
A second-order reaction 2A → B is taking place in a gas phase. The initial pressure in the system is P₀ (compound B is absent). Find the overall pressure as a function of time. After what time the total pressure will decrease 1.5 times with respect to the initial pressure? What is a degree of completion of the reaction at this time? Assume the ideal gas law behavior for all compounds.

Solution:
The reaction rate of this second-order reaction is given by,

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