Chapter 9: Reaction Mechanisms, Pathways, Bioreactions and Bioreactors

Derive: Monomer Concentration as A Function of Time

\( -\frac{dM}{dt} = k_p M \sum R_j = k_p M R^* = k_p M \sqrt{\frac{2 k_o (I_2) f}{k_t}} \)

\( -\frac{dI_2}{dt} = k_o I_2 \)

\( T = 0, \quad I_2 = I_0 \)

\( I_2 = I_{20} e^{-k_o t} \)

\( -\frac{dM}{dt} = k_p \sqrt{\frac{2 k_o I_{20} f}{k_t}} e^{-k_o t/2} M \)

\( \ln \frac{M}{M_o} = \left( \frac{8 f k_p^2 I_{20}}{k_o k_t} \right)^{1/2} \left[ \exp \left( \frac{-k_o t}{2} \right) - 1 \right] \)

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