Sequential Kinetics

I was solving some problems on chemical kinetics, then I was just struck at some ques of sequential reaction kinetics. 


Given reactions $$\ce{O\_3 + Cl \rightarrow O\_2 + ClO ~~~ k\_1=5.2 \times 10^9~Lmol^{-1}s^{-1}}$$


and $$\ce{ClO + O \rightarrow O\_2 + Cl ~~~ ~~~ k\_2=2.6 \times 10^{10} ~Lmol^{-1}s^{-1}}$$


So, which value is closest to rate const of overall net reaction? $$\ce{O\_3 + O \rightarrow 2O\_2}$$


and the answer given was $=5.2 \times 10^9 ~\mathrm{Lmol^{-1}s^{-1}}$


Therefore I am confused, how did they find the rate const of the net reaction?




The rate constant of the overall reaction is determined by the rate constant of the RDS, Rate Determining Step.


The RDS is the one with the lowest rate constant. Hence in this case the overall rate of the reaction is $5.2 \times 10^9 Lmol^{-1}s^{-1}$


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