During the decomposition of a gas on the surface of a solid catalyst, the pressure of the gas at different times was observed to be as follows : {:(t//s,,,""0,,,""100,,,""200,,,""300),(p//Pa,,,5*00xx10^(3),,,4*20xx10^(3),,,3*40xx10^(3),,,2*60xx10^(3)):} Calculate order, rate constant and half-life period of this reaction.

During the decomposition of a gas on the surface of a solid catalyst,

1.	During the decomposition of a gas on the surface of a solid catalyst, the pressure of the gas at different times was observed to be as follows : {:(t//s,,,""0,,,""100,,,""200,,,""300),(p//Pa,,,500xx10^(3),,,420xx10^(3),,,340xx10^(3),,,260xx10^(3)):} Calculate order, rate constant and half-life period of this reaction.
Answer» Solution :Let us FIRST calculate rates of reaction during different intervals of time `{:("Interval",,,,"Rate of reaction"),(0-100" s",,,,-((4.20-500)xx10^(3)PA)/(100s)=8Pa" s"^(-1)),(100-200" s",,,,-((340-420)xx10^(3)Pa)/(100s)=8Pa" s"^(-1)),(200-300" s",,,,-((260-340)xx10^(3)Pa)/(100s)=8Pa" s"^(-1)):}` As the rate of reaction constant THROUGHOUT, therefore, the reaction is of zero order. Alternatively, let us test it by integrated rate equation `{:(t(sec),,,,k=(1)/(t)[P_(0)-P]),(100,,,,k=(1)/(100s)(500-420)xx10^(3)Pa=8" Pa "s^(-1)),(200,,,,k=(1)/(200s)(500-340)xx10^(3)Pa=8" Pa "s^(-1)),(300,,,,k=(1)/(300s)(500-260)xx10^(3)Pa=8" Pa "s^(-1)):}` As k cmes out to be constant, the reaction is of zero order. Rate constant, `k=8" Pa "s^(-1)` Half-life period, `t_(1//2)=([P_(0)])/(2k)=(500xx10^(3)Pa)/(2xx8Pa" s"^(-1))=312*5` s.