How Does the Concentration of a Gas Vary over Time on a Reaction of Order n>1?

Question:


Consider a gas-phase reaction of order n (n>1), nA → B with a rate constant k. The reaction is taking place at temperature T. At initial time there is no compound B in the system, and the pressure is equal to P0 . Assume that all compounds can be described by ideal gas law.
a) Find an explicit dependence of [A] as a function of time.
b) At what time the reaction is 80% completed?
c) Express the rate of production of B in terms of the total pressure P of the system.

Solution:
a) Time rate of concentrations are given by,

Integration yields to:

……………………………………………………………………………………………………………………………………………………………………………………………………………………

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