measured, giving

either Eq$.($i$)$ or Eq$.($ii$)$ then eliminates $C_{As}$ which cannot

$r_{A1}^{\text{'}\text{'}}=r_{A2}^{\text{'}\text{'}}=r_A^{\text{'}\text{'}}=-\frac{1}{\frac{1}{k_l}+\frac{1}{k^{\text{'}\text{'}}}}{C}_{Al}=-k_{\text{o}\text{v}\text{e}\text{r}\text{a}\text{l}\text{l}}{C}_{Al},[\frac{\text{m}\text{o}\text{l}}{m^2*s}]$

Comment This result shows that $\frac{1}{k_l}$ and $\frac{1}{k^{\text{'}\text{'}}}$ are additive resistances. It so happens that the addition of resistances to obtain on overall resistance is permissible only when the rate is a linear function of the driving force and when the processes occur in series.

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

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