Chapter 9: Reaction Mechanisms, Pathways, Bioreactions and Bioreactors
Derive: Theta
\( \frac{dM}{dt} = -k_P [M] \sum R_j = -k_P M R_{10} = -k_P M_o \)
Note: Here Mo = M¥ – Io where M¥ is the initial concentration of monomer before the initiator was added. Mo is the concentration of monomer the instant after the initiator has been added and completely consumed to form R1 at time t = 0+
\( M = M_o e^{-I_o k_P t} \)
\( \theta = \int_{0}^{t} k_P M dt = M_o k_P \int_{0}^{t} e^{-I_o k_P t} dt \)
\( \theta = \frac{M_o}{I_o} \left( 1 - e^{-I_o k_P t} \right) \)