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An exothermic, aqueous phase, irreversible, first order reaction, $Y \rightarrow Z$ is carried out in an ideal continuous stirred tank reactor (CSTR) operated adiabatically at steady state. Rate of consumption of $Y$ (in $\text{ mol litre}^{-1} \text{ minute}^{-1}$) is given by $$-r_Y=10^9 e^{-\frac{6500}{T}}C_Y$$ where $C_Y$ is the concentration of $Y$ (in $\text{ mol litre}^{-1}$), and $T$ is the temperature of the reaction mixture (in $K$). Reactant $Y$ is fed at $50^{\circ} C$. Its inlet concentration is $1.0 \text{ mol litre}^{-1}$, and its volumetric flow rate is $1.0 \text{ litre minute}^{-1}$.

In addition, use the following data and assumptions

  • Heat of the reaction $=-42000 \: J \text{ mol}^{-1}$
  • Specific heat capacity of the reaction mixture $=4.2 \: J g^{-1} K^{-1}$
  • Density of the reaction mixture $=1000 \text{ g litre}^{-1}$
  • Heat of the reaction, specific heat capacity and density of the reaction mixture do not vary with temperature
  • shaft work is negligible

If the conversion of $Y$ at the exit of the reactor is $90 \%$, the volume of the CSTR (in $\text{litre}$) is ______ (round off to $2$ decimal places)

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