Half Life of Reactions - UNSOLVED PRACTICE SET
Chapter: Chemical Kinetics | Topic: Half Life of Reactions
HALF LIFE OF REACTIONS - UNSOLVED PRACTICE SET
Topic: Half Life of Reactions
Multiple Choice Questions
Q1. The half-life of a reaction is defined as:
- The time required for the reaction to complete 50%
- The time required for the concentration of reactant to reduce to half its initial value
- The time required for the rate to become half
- The time required for the product concentration to double
Q2. For a first-order reaction, if t₁/₂ = 30 minutes, the time required for 75% completion is:
- 45 minutes
- 60 minutes
- 90 minutes
- 120 minutes
Q3. The half-life of a zero-order reaction depends on:
- Only the rate constant
- Initial concentration and rate constant
- Only the initial concentration
- Temperature only
Q4. For a first-order reaction, after two half-lives, the fraction of reactant remaining is:
- 1/2
- 1/4
- 1/8
- 1/16
Q5. If the half-life of a first-order reaction is 20 minutes, the rate constant is approximately:
- 0.035 min⁻¹
- 0.693 min⁻¹
- 1.386 min⁻¹
- 20 min⁻¹
Q6. For a second-order reaction, the half-life is:
- Independent of initial concentration
- Directly proportional to initial concentration
- Inversely proportional to initial concentration
- Directly proportional to the rate constant
Short Answer Questions
Q7. Derive the expression for half-life of a first-order reaction in terms of the rate constant.
Q8. A first-order reaction has a half-life of 10 minutes. What fraction of the reactant will remain after 30 minutes?
Q9. Compare the half-life of zero-order and first-order reactions. How does each depend on initial concentration?
Q10. The half-life of a radioactive isotope is 5730 years. What does this tell you about its rate constant? Calculate the approximate value.
Q11. For a first-order reaction, show that the time required for the concentration to drop from [A]₀ to [A]₀/8 is equal to 3t₁/₂.
Q12. A medicine has a half-life of 4 hours in the human body. If a patient takes 200 mg of the medicine, how much remains after 12 hours? (Assume first-order elimination kinetics.)
Long Answer Questions
Q13. Explain the concept of half-life for different orders of reactions. Derive expressions for t₁/₂ for zero-order, first-order, and second-order reactions and discuss how t₁/₂ depends on initial concentration in each case.
Q14. (a) The half-life of a first-order reaction is 100 s. Calculate:
(i) The rate constant
(ii) The time required for 90% completion
(iii) The time required for 99% completion
(b) Why is the concept of half-life particularly useful for first-order reactions?
Q15. (a) Define the half-life period of a reaction.
(b) For a zero-order reaction, the concentration drops from 1.0 M to 0.5 M in 20 minutes. Calculate:
(i) The rate constant
(ii) The time required for the concentration to drop from 0.5 M to 0.25 M
(iii) Explain why this time is different from the first half-life
Numerical / Application-Based Problems
Q16. A first-order reaction has a rate constant of 2.0 × 10⁻³ s⁻¹.
(a) Calculate the half-life of the reaction.
(b) Calculate the time required for the reactant concentration to drop to:
(i) 1/4 of initial
(ii) 1/8 of initial
(iii) 1/16 of initial
(c) What pattern do you observe? Generalize your finding.
Q17. The following data is for the decomposition of a reactant A:
| Order | t₁/₂ (min) when [A]₀ = 0.20 M | t₁/₂ (min) when [A]₀ = 0.40 M |
|---|---|---|
| 0 | 10 | 20 |
| 1 | 15 | 15 |
| 2 | 20 | 10 |
(a) Verify the relationship between t₁/₂ and [A]₀ for each order using the given data.
(b) For a first-order reaction with t₁/₂ = 15 min, calculate the rate constant.
(c) For a zero-order reaction with t₁/₂ = 10 min at [A]₀ = 0.20 M, calculate the rate constant.
Q18. In a hospital, a doctor administers a drug to a patient. The drug follows first-order elimination kinetics with a half-life of 6 hours.
(a) If the initial dose is 500 mg, calculate the amount remaining after 24 hours.
(b) The doctor wants to maintain a minimum effective concentration of 62.5 mg. After how many hours should the next dose be given?
(c) Why is understanding half-life important in medical dosing?