The time required for 90 % completion of a certain first order reaction is 1 hour. Calculate the time required for 99.9 % completion of the same reaction.

Step-by-step solution

For a first order reaction, the rate constant k is given by k = 2.303 t ( a a-x ) For 90 % completion, t_ 90 % = 1 hour. k = 2.303 1 ( 100 100-90 ) = 2.303 10 = 2.303 hour ⁻¹ For 99.9 % completion, the time required is: t_ 99.9 % = 2.303 k ( 100 100-99.9 ) t_ 99.9 % = 2.303 2.303 ( 100 0.1 ) t_ 99.9 % = 1000 = 3 hours. Answer: 3 hours.