Consider a homogeneous gas phase reaction, $\mathrm{A}+2 \mathrm{~B} \rightarrow 2 \mathrm{C}+3 \mathrm{D}$, occurring at constant temperature and pressure in a varying volume batch reactor. The vessel is initially charged with $50$ moles of $\text{A}$ and $150$ moles of $\text{B}$. The gases behave ideally. For complete conversion of $\text{A}$, the ratio of the final volume to the initial volume is $\_\_\_\_$ (rounded off to one decimal place).
