Chemical Kinetics

To determine the time required for 99.9% completion of a first-order reaction with a half-life of 1 second, we can demonstrate that this time is 10 times the reaction's half-life ( ).When a reaction is 99.9% complete, the remaining concentration is only 0.1% of the initial concentration. This can be expressed as .Using the first-order kinetics equation: To find the time at which the reaction is 99.9% complete: Thus: For the half-life of a first-order reaction: Comparing the times: Therefore, the time required for 99.9% completion is approximately 10 times the half-life, or 10 seconds. This coincides with option C, 10 seconds.

On the basis of the unit of the reaction we can see that the reaction is a zero order reaction.$ \mathrm{L}^{-1} k $Reactienorderthits of rete conatantZero order reaction0molL−1s×1(molL−1)6=molL−1s−1molL−1s×1molL−16=molL−1s−1(molL^(-1))/((s))xx(1)/(((mol)L^(-1))^(6))=molL^(-1)s^(-1)First order reaction1molL−1s×1(molL−1)1=s−1molL−1s×1molL−11=s−1(molL^(-1))/((s))xx(1)/(((mol)L^(-1))^(1))=s^(-1)Second order reaction2molL−1×1s×mol−1Ls−1molL−1×1s×mol−1Ls−1(molL)/()^(-1)xx(1)/(s)xxmol^(-1)Ls^(-1)Fig. 3.3: Variation in the concentration vs time plot for a zero order reaction