Exercise $4\mathrm{.}2$: Irreversible reactions at variable volume

A reaction $A2R+S$ is carried out in a tubular reactor, and the reactant $A$ is introduced with $30\%$ of inert. The reaction is irreversible and of second order. The reactor of $0\mathrm{.}2L$ is isothermal, and the reaction occurs at $800K$ and pressure of $10$atm. It is known that the outflow of the product $R$ is $0\mathrm{.}034mo\frac{l}{s}$ and the conversion was $10\%.$

a$)$ Calculate the reaction rate constant. $[$Ans: $k=10\mathrm{.}75\frac{L}{m}ol.s]$

b$)$ If this reaction would be further carried out in a batch reactor, calculate the reaction time based on the previous condition. $[$Ans: $t=0\mathrm{.}1s]$