For a first-order reaction, what is the ratio of the time required for 99 % completion to the time required for 90 % completion?

Step-by-step solution

For a first-order reaction, the time required is given by the integrated rate equation: t = 2.303 k ( [A]₀ [A]_t ) For 99 % completion, the amount remaining is [A]_t = 100 - 99 = 1 % of [A]₀ . t_ 99 % = 2.303 k ( 100 1 ) = 2.303 k 2 For 90 % completion, the amount remaining is [A]_t = 100 - 90 = 10 % of [A]₀ . t_ 90 % = 2.303 k ( 100 10 ) = 2.303 k (10) = 2.303 k 1 Taking the ratio of the two times: Ratio = t_ 99 % t_ 90 % = 2 1 = 2 . Answer: 2