Concept of zero order and first order

Question

!! A -> !! Products [:Zero order]

!!B -> !! Products [:First order]

For what initial concentration of !!A!! are the half lives of two reactions equal? [Both have same rate of reaction]

a) !!(log_e 4)!!M

b) !!2!! M

c) !!2 log2!! M

d) !!ln2!! M

Solution

For zero order reaction,

!!x=kt!!

Therefore, !!a/2 = kxxt_(1//2)!!

!!=> t_(1//2)= a/(2k)....(1)!!

For first order reaction,

!!t_(1//2)= (log_e 2)/k.......(2)!!

From equation !!(1)!! and !!(2)!!, we get

!! a/(2k)= (log_e 2)/k!! [given that]

!!=> a = 2log_e 2= log_e 4!!

Therefore, option (A)is correct.