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The liquid phase irreversible reactions, $P \xrightarrow[]{k_1} Q$ and $P \xrightarrow[]{k_2} R$, are carried out in an ideal continuous stirred tank reactor (CSTR) operating isothermally at steady state. The space time of the CSTR is $1$ minute. Both the reactions are first order with respect to the reactant $P$, and $K_1$ and $K_2$ denote the rate constants of the two reactions. At the exit of the reactor, the conversion of reactant $P$ is $60\%$, and the selectivity of $Q$ with respect to $R$ is $50 \%$. The value of the first order rate constant $k_1$ (in minute$^{-1}$) is ______ (correct up to one decimal place)
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