The reaction A`rarr` X is a first order reaction which takes place in a vessel with initial concentration of A as 10 M. The rate constant for this reaction is 4.16`h^(-1)` . In the presence of a catalyst, the reaction A`rarr`Y follows second-order kinetics and the rate constant is 0.2 `min^(-1) M^(-1)` . What should be the initial concentration of A in the presence of catalyst so that the value of `t_(1//2)` for both the reactions is the same?

Options

A. 30.0 M
B. 0.5 M
C. 5.0 M
D. 10.0 M

Answer

B

Explanation

From Arrhenius equation `k=Ae^(-E_(a)//RT)`
Let the rate in the absence of catalyst be `k_(1)=Ae^(-24//RT)` and the presence of catalyst is `k_(2)=Ae^(24/4RT)`
Therefore `(K_(2))/(K_(1))=e rarrIn (k_(2))/(k_(1))=(18xx1000)/(2xx300)=30`
`log(k_(2))/(k_(1))=(30)/(2.3030)=13 (k_(2))/(k_(1))=1xx10^(13)`
Since rate `prop` rate constant so `(r_(2))/(r_(1))=(k_(2))/(k_(1))=1.0 xx10^(13)`