Answer :
For a first order reaction, the time required for completion of 99.9% of the reaction is approximately 10 times the half-life of the reaction, which is answer choice A, 10t.Therefore the correct option is A.
In a first order reaction, the time taken for the completion of 50 percent of the reaction, known as the half-life (t), is a constant. Since the reaction's half-life remains constant regardless of concentration, we can calculate the time required to reach any given percent completion using the half-life. After one half-life, the concentration is reduced to 50%. After two half-lives, it's reduced to 25% (half of 50%), and so on. By this pattern, we know that 99.9% completion correlates to the concentration being reduced to 0.1% of its initial value. This would take:
- 1 half-life to reach 50%
- 2 half-lives to reach 25%
- 3 half-lives to reach 12.5%
- 4 half-lives to reach 6.25%
- 5 half-lives to reach 3.125%
- 6 half-lives to reach 1.5625%
- 7 half-lives to reach ~0.781%
- 8 half-lives to reach ~0.39%
- 9 half-lives to reach ~0.195%
- 10 half-lives to reach ~0.0975%
Considering that after 10 half-lives we reach just below 0.1% (which is close to 99.9% completion), the correct answer is that the time required for the completion of 99.9 percent of the reaction is approximately 10 times the half-life (10t), or answer choice A.
