The design equation for a CSTR is:
$V = \frac{F_{A0}X_A}{-r_A}$
For a first-order reaction, $-r_A = kC_A$.
Also, $C_A = C_{A0}(1-X_A)$.
So, $V = \frac{F_{A0}X_A}{kC_A} = \frac{F_{A0}X_A}{kC_{A0}(1-X_A)}$.
$V = \frac{Q_0 C_{A0} X_A}{k C_{A0}(1-X_A)} = \frac{Q_0
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