A drug suspension is prepared with concentration of 0.03 M. It hydrolyses at 25°C with a rate constant of 0.023 M/h. What is the half-life of this suspension? Report your answer in hours to 2 decimal places.

Question

BlackTom AI · Accepted Answer

Zero-order kinetics apply because the given rate constant has units of concentration per time (M/h), indicating the reaction rate is independent of concentration.

1) Relevant knowledge points and concepts
- Reaction order is determined from the units of the rate constant: for zero-order k has units M·time^-1, for first-order k has units time^-1, and for second-order k has units M^-1·time^-1.
- For a zero-order reaction the half-life is t1/2 = [A]0 / (2k).
- For a first-order reaction the half-life would be t1/2 = ln(2) / k, but this applies only when k has units of time^-1.

2) Complete reasoning process step by step
- Identify order: k = 0.023 M/h → units M·h^-1 → zero-order kinetics.
- Use zero-order half-life formula: t1/2 = [A]0 / (2k).
- Substitute the known values: initial concentration [A]0 = 0.03 M, k = 0.023 M/h.

3) Calculations with intermediate steps
- Compute denominator: 2k = 2 × 0.023 M/h = 0.046 M/h.
- Divide: t1/2 = 0.03 M ÷ 0.046 M/h = 0.652173913... h.
- Round to two decimal places: t1/2 ≈ 0.65 h.

4) Why the correct answer is correct
- Because the rate constant’s units identify the reaction as zero-order, the correct half-life expression is [A]0/(2k). Applying that expression with the given numbers yields 0.652... hours, which rounded to two decimals is 0.65 h.

5) Why other formulas or interpretations are incorrect
- Using the first-order formula t1/2 = ln(2)/k would be inappropriate here because that formula requires k in h^-1. If incorrectly applied, ln(2)/0.023 ≈ 30.13 h, which is inconsistent with the units and the kinetics described.

6) Conclusion and confirmation
- Therefore the half-life of the suspension is 0.65 hours, which matches the provided answer 0.65.

A drug suspension is prepared with concentration of 0.03 M. It hydrolyses at 25°C with a rate constant of 0.023 M/h. What is the half-life of this suspension? Report your answer in hours to 2 decimal places.数值题

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