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The following isothermal autocatalytic reaction $$ A +B \longrightarrow 2B \quad\quad\quad(-r_A)=0.1C_AC_B(\text{mol } L^{-1} s^{-1})$$is carried out in an ideal continuous stirred tank reactor ($\text{CSTR}$) operating at steady state. Pure $A$ at $1 \text{ mol }L^{-1}$ is fed, and $90 \%$ of $A$ is converted in the $\text{CSTR}$. The spare time of the $\text{CSTR}$ is _________ seconds.
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