The shelf-life for a new product known as “Hyperclear” is reported by the manufacturer to be 28 days. Since the active pharmaceutical ingredient (API) within “Hyperclear” undergoes photochemical degradation, it is stored in light-protective bottles. The API concentration in the “Hyperclear” formulation is 0.092 mol/L.An attentive and concerned pharmacist notices that the expiration date printed on the bottles currently in storage was exactly 4 week(s) ago. The pharmacist needs to dispose of the medication, but they are curious to know how much of the API is still present within the formulation. Whilst the exact value for the rate constant of the API degradation is not available, it is typically reported in the units of M s-1.Determine the remaining concentration of the API at the time of the pharmacist’s discovery. Report your answer in mol/L to 3 decimal places.

Question

BlackTom AI · Accepted Answer

Zero-order kinetics apply because the rate constant is stated in units of M s^-1 (concentration change per time). For zero-order degradation the concentration falls linearly: [A] = [A]0 − k t. In pharmaceutical practice “shelf-life” normally means t90, the time to lose 10% of the initial API (i.e., 90% remaining).

1) Determine the fraction remaining at the time of discovery:
- Shelf-life t90 = 28 days. The expiration date was printed 4 weeks (28 days) ago, so the product has existed for 28 days (to reach expiration) + 28 days (since expiration) = 56 days total.
- For zero-order kinetics the loss after time t is proportional to t/t90: a loss of 10% occurs in 28 days, so in 56 days the loss is 2 × 10% = 20%.

2) Numerical calculation with the given initial concentration:
- Initial concentration [A]0 = 0.092 mol/L.
- Remaining fraction = 1 − 0.20 = 0.80.
- Remaining concentration = 0.092 mol/L × 0.80 = 0.0736 mol/L.

3) Rounding to three decimal places:
- 0.0736 → 0.074 mol/L.

Why this approach is correct:
- The key indicator of zero-order kinetics is the unit M s−1 for k; that makes the linear-decrease formula appropriate, and t90 corresponds to a 10% absolute loss for zero-order. Using these facts gives the simple proportional scaling of loss with time (20% loss in 56 days).

Why other kinetics would be incorrect:
- First-order kinetics (k in s−1) would lead to exponential decay and a different remaining concentration; the problem’s specified units rule that out. Second-order kinetics likewise have different units and decay behavior and are not consistent with the given information.

Conclusion: The remaining API concentration at discovery is 0.074 mol/L, which matches the provided answer.

类似问题

Question textFor a first-order reaction, it was found that the initial reactant concentration of 0.66 M reduced to 0.22 M after 3.0 minutes. The rate constant of this reaction is Answer 1 Question 3[input] s-1.

The half-life / shelf-life does not depend on the initial concentration of the reactant. This statement is TRUE for

Question textFor a first-order reaction, it was found that the initial reactant concentration of 0.66 M reduced to 0.22 M after 3.0 minutes. The rate constant of this reaction is Answer 1 Question 3[input] s-1.Check Question 3

A drug (0.045 M solution) undergoes hydrolysis with a rate constant of 2.0 × 10–2 min–1. The concentration of this drug after 1 hour is

Question at position 28 The decomposition of hydrogen peroxide is a first-order process with a rate constant of 1.06 × 10 ̶ 3 min ̶ 1. How long will it take for the concentration of hydrogen peroxide to drop from 0.0200 M to 0.0120 M? 4550 min 482 min < 1 min 221 min 7.55 min

The first-order reaction, SO2Cl2→ SO2 + Cl2, has a rate constant equal to 2.20 × 10-5 s-1 at 593 K. What percentage of the initial amount of SO2Cl2 will remain after 3.00 hours?

For a first-order reaction, which expression describes the relationship between the rate constant, k, and the half-life, t1/2?

更多留学生实用工具

智能学习助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单