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The elementary irreversible gas-phase reaction $A\rightarrow B+C$ is carried out adiabatically in an ideal $CSTR$ (Continuous-Stirred Tank Reactor) operating at 10 $atm$. Pure $A$ enters the $CSTR$ at a flow rate of 10 mol/$s$ and a temperature of $450$ $K$. Assume $A, B$ and $C$ to be ideal gases. The specific heat capacity at constant pressure $\left ( C_{Pi} \right )$ and heat of formation  $\left ( H_{i}^{0} \right )$, of component  $i\left ( i=A,B,C \right )$,are :

$\begin{array}{cc}\
&\text{$C_{PA}=30$ $J$/(mol $K$)} & \text{$C_{PB}=10$ $J$/(mol $K$)} & \text{$C_{PC}=20$ $J$/(mol $K$)} \\
&\text{ $H_{A}^{0}=-90$ $kJ$/mol} & \text{$H_{B}^{0}=-54$ $kJ$/mol} & \text{$H_{C}^{0}=-45$ $kJ$/mol} \\
 \\  \end{array}$

The reaction rate constant $k$ (per second)=$0.133exp$ $\left \{ \frac{E}{R}\left ( \frac{1}{450} -\frac{1}{T}\right ) \right \}$, where $E = 31.4$ $kJ$/mol and universal gas constant $R=0.082\: L$ $atm$/(mol $K$)=$8.314$ $J$/(mol $K$). The shaft work may be neglected in the analysis, and specific heat capacities do not vary with temperature. All heats of formation are referenced to $273 \:K$. The reactor volume (in Liters) for $75\%$conversion is __________________ (rounded off to the nearest integer).
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