A first-order reaction takes 30 minutes for 50 % completion. The time required for 93.75 % completion of the same reaction will be :

Step-by-step solution

The time required for 50 % completion is the half-life ( t_ 1/2 ) of the reaction. Therefore, t_ 1/2 = 30 minutes . For 93.75 % completion, the percentage of reactant remaining is: 100 % - 93.75 % = 6.25 % Convert the remaining percentage to a fraction: 6.25 100 = 1 16 Express the fraction in terms of powers of 1/2 : 1 16 = ( 1 2 )^4 This means 4 half-lives are required for the reaction to be 93.75 % complete. Total time = n t_ 1/2 = 4 30 minutes = 120 minutes . Answer: 120 minutes