Chapter 9: Reaction Mechanisms, Pathways, Bioreactions and Bioreactors

Derive: Case 1 Rate Law

\(- \frac{dM}{dt} = kM^3 \), \( M \) is the concentration of functional groups of either hydroxyl or carboxyl groups

\( 2kt = \frac{1}{M^2} - \frac{1}{M_o^2} \)

\( p \) = fraction of carboxyl groups reacted

\( M = M_o = pM_o = M_o(1 - p) \)

\( 2kt = \frac{1}{M_o^2 (1 - p)^2} - \frac{1}{M_o^2} \)

Multiplying by \( M_o \) and rearranging

\(\frac{1}{(1 - p)^2} = 2kM_o^2 t + 1 \)

Back to Chapter 9