First Order Reactions - UNSOLVED PRACTICE SET
Chapter: Chemical Kinetics | Topic: First Order Reactions
FIRST ORDER REACTIONS - UNSOLVED PRACTICE SET
Topic: First Order Reactions
Multiple Choice Questions
Q1. For a first-order reaction, the rate of reaction is:
- Independent of concentration
- Directly proportional to the concentration of reactant
- Proportional to the square of concentration
- Inversely proportional to concentration
Q2. The integrated rate equation for a first-order reaction is:
- [A] = [A]₀ – kt
- k = (2.303/t) log([A]₀/[A])
- 1/[A] = 1/[A]₀ + kt
- [A] = [A]₀e^(kt)
Q3. The unit of rate constant for a first-order reaction is:
- mol L⁻¹ s⁻¹
- L mol⁻¹ s⁻¹
- s⁻¹
- mol² L⁻² s⁻¹
Q4. For a first-order reaction, a plot of log[A] vs. time gives:
- A straight line with a positive slope
- A straight line with a negative slope
- A curve
- A horizontal line
Q5. The half-life of a first-order reaction is:
- Directly proportional to initial concentration
- Inversely proportional to initial concentration
- Independent of initial concentration
- Proportional to the rate constant
Q6. If the initial concentration of a reactant in a first-order reaction is 0.10 M and after 20 minutes it becomes 0.05 M, the half-life is:
- 10 minutes
- 20 minutes
- 40 minutes
- Cannot be determined
Short Answer Questions
Q7. Derive the relationship between half-life (t₁/₂) and rate constant (k) for a first-order reaction.
Q8. For a first-order reaction, show that the time required for 99.9% completion is approximately 10 times the half-life.
Q9. The rate constant for a first-order reaction is 5.0 × 10⁻⁴ s⁻¹. Calculate the time required for the concentration to drop to 25% of its initial value.
Q10. Why is radioactive decay considered a first-order reaction? Explain with the example of carbon-14 dating.
Q11. Draw a rough sketch showing how log[A] varies with time for a first-order reaction. How can you determine the rate constant from this graph?
Q12. A first-order reaction is 20% complete in 10 minutes. Calculate the time required for 80% completion.
Long Answer Questions
Q13. Derive the integrated rate equation for a first-order reaction: A → Products. Show that a plot of log[A] vs. time is a straight line and explain how k and t₁/₂ can be determined.
Q14. (a) List four characteristics of a first-order reaction.
(b) The decomposition of N₂O₅ is a first-order reaction: 2N₂O₅ → 4NO₂ + O₂. Explain why it follows first-order kinetics even though the stoichiometric coefficient of N₂O₅ is 2.
Q15. (a) Show that for a first-order reaction, the time taken for any fraction of completion is independent of the initial concentration.
(b) A first-order reaction has a rate constant of 1.15 × 10⁻³ s⁻¹. Calculate:
(i) The half-life
(ii) The time for 90% completion
(iii) The time for 99% completion
Numerical / Application-Based Problems
Q16. The decomposition of azomethane (CH₃N₂CH₃) follows first-order kinetics:
CH₃N₂CH₃(g) → C₂H₆(g) + N₂(g)
At 600 K, the rate constant is 2.0 × 10⁻³ s⁻¹.
(a) Calculate the half-life of the reaction.
(b) Calculate the time required for the pressure of azomethane to drop to 25% of its initial value.
(c) If the initial pressure is 100 mmHg, what will be the total pressure after one half-life?
Q17. For a first-order reaction, the following data was obtained:
| Time (min) | [A] (mol L⁻¹) |
|---|---|
| 0 | 0.80 |
| 10 | 0.64 |
| 20 | 0.512 |
| 30 | 0.410 |
(a) Show that this reaction is first order by calculating k at different intervals.
(b) Determine the average value of k.
(c) Calculate the time required for [A] to become 0.20 M.
(d) Calculate the time required for 75% completion of the reaction.
Q18. In a school science fair, a student sets up an experiment to study the decomposition of hydrogen peroxide catalyzed by iodide ions:
2H₂O₂ → 2H₂O + O₂
The reaction follows first-order kinetics with respect to H₂O₂. The student measures the volume of O₂ evolved at different times.
(a) How can the student determine the rate constant from the volume-time data?
(b) If 50 mL of O₂ is collected at infinite time and 30 mL is collected at time t, how is the concentration of H₂O₂ at time t related to these volumes?
(c) If the rate constant is 6.0 × 10⁻² min⁻¹, calculate the time required to collect 40 mL of O₂.