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?

Step-by-step solution

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.