Chapter 9: Reaction Mechanisms, Pathways, Bioreactions and Bioreactors
Derive: R1
\( \frac{dR_1}{d\theta} = \frac{k_o}{k_p} I_o e^{-\frac{k_o}{k_p} \theta} - R_1 \)
\( \frac{d(R_1 e^{\theta})}{d\theta} = \frac{I_o k_o}{k_p} e^{\left(1-\frac{k_o}{k_p}\right) \theta} \)
\( e^{\theta} R_1 = \left[ \frac{k_o/k_p}{1-k_o/k_p} I_o \right] e^{\left(1-\frac{k_o}{k_p}\right) \theta} \Bigg|_0^\theta \)
\( R_1 = \frac{I_o k_o/k_p}{1-k_o/k_p} e^{-\theta} \left[ e^{\left(1-\frac{k_o}{k_p}\right) \theta} -1 \right] \)
\( R_1 = \frac{I_o k_o}{k_o - k_p} \left[ e^{-\theta} - e^{-\frac{k_o}{k_p} \theta} \right] \)