Chapter 9: Reaction Mechanisms, Pathways, Bioreactions and Bioreactors

Given that for reaction (3): \( \frac{r_{NO_2}}{2} = r_{3NO_3^*} = - k_3 C_{NO_3} \cdot C_{NO} = k_3 [NO_3^*][NO] \)

All specific reaction rates are defined with respect to \( NO_3^* \)

Assume that all reactions are elementary reactions, such that:

\( r_{1 NO_3^\bullet} = k_1 [NO][O_2] \)

\( r_{2 NO_3^\bullet} = -k_2 [NO_3^*] \)

\( r_{3 NO_3^\bullet} = - k_3 [NO_3^*][NO] \)

The net reaction rate for \( NO_3^* \) is the sum of the individual reaction rates for \( NO_3^* \):

\( r_{NO_3^\bullet} = r_{1 NO_3^\bullet} + r_{2 NO_3^\bullet} + r_{3 NO_3^\bullet} \)

\( r_{NO_3^\bullet} = k_1 [NO][O_2] - k_2 [NO_3^*] - \frac{1}{2} k_3 [NO_3^*][NO] \)

The PSSH assumes that the net rate of \( NO_3^* \) is zero:

\( r_{NO_3^*} \approx 0 = k_1 (NO)(O_2) - k_2 (NO_3^*) - k_3 (NO_3^*)(NO) \)

\( 0 = k_1 [NO][O_2] - k_2 [NO_3^*] - \frac{1}{2} k_3 [NO_3^*][NO] \)

\( 0 = k_1 [NO][O_2] - [NO_3^*] \left( k_2 + k_3 [NO] \right) \)

\( [NO_3^*] = \frac{k_1 [NO][O_2]}{k_2 + k_3 [NO]} \)