A catalytic gas phase reaction $P \rightarrow Q$ is conducted in an isothermal packed bed reactor operated at steady state. The reaction is irreversible and second order with respect to the reactant $P$. The feed is pure $P$ with a volumetric flow rate of $1.0$ litre minute $^{-1}$ and concentration of $2.0$ mol litre $^{-1}$.

In addition, use the following assumptions

• The reactant and product are ideal gases
• There is no volume change associated with the reaction
• Ideal plug flow conditions prevail in the packed bed

When the mass of catalyst in the reactor is $4$ g, the concentration of $P$ measured at the exit is $0.4$ mol litre $^{-1}$. The second order rate constant (in litre$^2 g_{\text{catalyst}}^{-1}$ mol$^{-1}$ minute$^{-1}$) is _______ (correct up to one decimal place).

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