Chapter 6: Isothermal Reactor Design: Molar Flow Rates
Derivation for Constant Density:
\( C_A = \frac{N_A}{V} = \frac{N_{A0}(1 - X)}{V_0 + v_0 t} \)
\( C_B = \frac{N_B}{V} = \frac{N_{B0}}{V_0 + v_0 t} \)
\( N_s = \text{[B initially] + B added + B reacted} \)
\( N_s = [N_{Bi} + F_{Bo} t - N_{A0} X] \)
\( C_B = \frac{N_{Bi} + F_{Bo} t - N_{A0} X}{V_0 + v_0 t} \)
\( \frac{dX}{dt} = -r_A V_0 = \frac{1}{N_{A0}} k \left( \frac{N_A}{V} \right) V = \frac{k N_{A0} (1 - X) \left( N_{Bi} + F_{Bo} t - N_{A0} X \right)}{V_0 + v_0 t} \)
\( \frac{dX}{dt} = k(1 - X) \left( N_{Bi} + F_{Bo} t - N_{A0} X \right) \)