The reaction given below was performed in a batch reactor and in the gas phase. $10\%$

$N_2$ was introduced in the reactor at $2$atm and $450C.$ After $50$min, the pressure was $3\mathrm{.}3$

atm. The reaction is irreversible and of first order.

a$)$ Calculate the specific reaction rate constant.

b$)$ If the same reaction would be performed in a piston system with variable volume,

what will be the final volume of the system keeping pressure constant at $2$atm and

considering the same conversion as before.

c$)$ Calculate the initial concentration of Ethylene Oxide.