t_ 100\% is the time required for the 100\% completion of the reaction while t_ 1/2 is the time required for 50\% of the reaction to be completed. Which of the following option correctly represents the relation between t_ 100\% and t_ 1/2 for zero and first order reactions respectively?
B. t_ 100\% = 2t_ 1/2 and t_ 100\% = (t_ 1/2 )^
For a zero-order reaction: The integrated rate law is given by t = [A]_0 - [A]_t k . For 50\% completion (t_ 1/2 ), [A]_t = [A]_0 2 : t_ 1/2 = [A]_0 - [A]_0 2 k = [A]_0 2k For 100\% completion (t_ 100\% ), [A]_t = 0: t_ 100\% = [A]_0 - 0 k = [A]_0 k Comparing the two, we get: t_ 100\% = 2t_ 1/2 For a first-order reaction: The integrated rate law is given by t = 1 k ( [A]_0 [A]_t ). For 100\% completion (t_ 100\% ), [A]_t = 0: t_ 100\% = 1 k ( [A]_0 0 ) = A first-order reaction takes infinite time for 100\% completion. Among the given choices, this is symbolically represented as or (t_ 1/2 )^ . Thus, the correct relation is t_ 100\% = 2t_ 1/2 for zero-order and t_ 100\% = for first-order. Answer: t_ 100\% = 2t_ 1/2 and t_ 100\% = (t_ 1/2 )^
Related: Chemistry — Chemical Kinetics · All PYQ Banks