The forms obtained from general mole balances for batch and plug flow reactors are

identical if there is no volume change. Then, what happens to these expressions with volume change?

You can consider an isothermal and isobaric first$-$order gas$-$phase reaction. Derive integrated rate

expressions for a batch reactor $($time to reach a certain level of conversion, t versus X$)$ with volume

change $[7$ points$]$ and a plug flow reactor $($Volume or $\backslash$tau to reach a certain level of conversion, $\backslash$tau

versus X$)$ with volume change $[10$ points$].$ Are these expressions the same? Explain your answer

briefly $[3$ points$].$