Final answer:
To find the time required for the reactant concentration to decrease from 0.085 M to 0.021 M in a first-order reaction with a 13-minute half-life, we observe that after two half-lives, the concentration is approximately 0.021 M, indicating that the time needed is just under 26 minutes.
Step-by-step explanation:
The question is about calculating the time it will take for the concentration of a reactant to decrease from 0.085 M to 0.021 M in a first-order reaction with a half-life of 13 minutes. By using the concept of half-lives, we can determine that each half-life cuts the reactant concentration in half. To go from 0.085 M to 0.021 M, we need to determine how many half-lives have passed:
- After one half-life (13 min), the concentration goes from 0.085 M to 0.0425 M.
- After another half-life (total of 26 min), it would go from 0.0425 M to 0.02125 M.
Since the desired concentration is 0.021 M, which is slightly less than the concentration after two half-lives (0.02125 M), the total time required will be slightly less than 26 minutes. Thus, the correct answer is (d) 26 minutes, recognizing the closest approximation provided.