OVERALL RATE FOR A NONLINEAR PROCESS

Repeat Example $17\mathrm{.}3$ with just one change: let the reaction step be second order with respect to A$,$ or

$r_{A2}^{\text{'}\text{'}}=-k^{\text{'}\text{'}}{C}_A^2$

SOLUTION

Combining the reaction steps to eliminate $C_{As},$ as was done in Example $17\mathrm{.}3,$ is now not so simple, and gives

$-r_A^{\text{'}\text{'}}=-r_{A1}^{\text{'}\text{'}}=-r_{A2}^{\text{'}\text{'}}=\frac{k_l}{2k^{\text{'}\text{'}}}(2k^{\text{'}\text{'}}{C}_{Al}+k_1-\sqrt[\phantom{2}]{k_l^2+4k^{\text{'}\text{'}}{k}_l{C}_{A1}}),[\frac{\text{m}\text{o}\text{l}}{m^2*s}]$