Question

For a first-order reaction, the ratio of time for 99.9% of the reaction to complete and half of the reaction to complete is

(a) 1
(b) 2
(c) 4
(d) 10

Answer 1

The ratio of time for a first-order reaction to complete 99.9% to the time it takes to complete 50% is 10, because a first-order reaction's half-life is constant, and it takes 10 half-lives to reach 99.9% completion. The correct answer is option: (d) 10

Step-by-step explanation:

To determine the ratio of the time it takes for a first-order reaction to reach 99.9% completion to the time it takes to reach 50% (half-life), we need to consider the properties of first-order reactions.

A first-order reaction has a constant half-life, regardless of the concentration of the reactants. This is because the time it takes for the concentration of a reactant to decrease by half is independent of the starting concentration.

For a first-order reaction:

• The time it takes to go from 100% to 50% (1 half-life) is t1/2.
• The time it takes to go from 50% to 25% (2 half-lives) is 2 x t1/2.
• The time it takes to reach 99.9% completion is 10 half-lives, based on the equation: (1/2)^10 = 0.1% remaining.

Therefore, the ratio of the time to reach 99.9% completion to the time of one half-life is:

Time for 99.9% completion / Time for 50% completion = 10 x t1/2 / t1/2 = 10

The answer is (d) 10.