Integrated Rate Equations - UNSOLVED PRACTICE SET
Chapter: Chemical Kinetics | Topic: Integrated Rate Equations
INTEGRATED RATE EQUATIONS - UNSOLVED PRACTICE SET
Topic: Integrated Rate Equations
Multiple Choice Questions
Q1. The integrated rate equation for a zero-order reaction is:
- ln[A] = ln[A]₀ – kt
- [A] = [A]₀ – kt
- 1/[A] = 1/[A]₀ + kt
- [A] = [A]₀e^(-kt)
Q2. For a first-order reaction, the slope of the plot of ln[A] vs. time is:
- K
- –k
- 2.303k
- –2.303k
Q3. The integrated rate equation helps us to:
- Determine the mechanism of the reaction
- Calculate the concentration at any given time
- Find the activation energy
- Determine the molecularity
Q4. For a second-order reaction, the correct integrated rate equation is:
- 1/[A] = 1/[A]₀ + kt
- [A] = [A]₀ – kt
- ln[A] = ln[A]₀ – kt
- [A]² = [A]₀² – kt
Q5. The half-life of a first-order reaction can be obtained from the integrated rate equation as:
- t₁/₂ = [A]₀/2k
- t₁/₂ = 0.693/k
- t₁/₂ = 1/k[A]₀
- t₁/₂ = 2.303/k
Q6. The time required for a first-order reaction to reach 50% completion is:
- Equal to 2/k
- Equal to 0.693/k
- Equal to [A]₀/2k
- Infinite
Short Answer Questions
Q7. Write the integrated rate equations for zero-order and first-order reactions. How can you distinguish between them graphically?
Q8. For a first-order reaction, derive the expression for the time required for the concentration to drop to one-fourth of its initial value.
Q9. The following data were obtained for a reaction:
| Time (min) | [A] (M) |
|---|---|
| 0 | 1.00 |
| 10 | 0.80 |
| 20 | 0.60 |
| 30 | 0.40 |
Determine the order of the reaction using the integrated rate equation method.
Q10. Show that for a first-order reaction, the time required for any given fraction of completion is independent of the initial concentration.
Q11. Write the integrated rate equation for a first-order reaction in terms of partial pressures, for a gaseous reaction where one mole of gas decomposes.
Q12. For a zero-order reaction with k = 2.0 × 10⁻² M min⁻¹ and [A]₀ = 0.50 M, calculate the time required for the concentration to become zero. What is the significance of this time?
Long Answer Questions
Q13. Derive the integrated rate equation for a first-order reaction starting from the differential rate equation. Show all steps clearly and explain the significance of each term.
Q14. (a) Explain how integrated rate equations can be used to determine the order of a reaction experimentally.
(b) For the reaction A → Products, the following data were obtained:
| Time (min) | [A] (mol L⁻¹) |
|---|---|
| 0 | 1.00 |
| 50 | 0.90 |
| 100 | 0.81 |
| 150 | 0.73 |
Using the trial method with integrated rate equations, determine the order of the reaction and calculate the rate constant.
Q15. (a) What are integrated rate equations? Why are they important?
(b) For a first-order gas phase reaction: A(g) → B(g) + C(g), the total pressure at time t = 0 is P₀ and at time t is Pₜ. Derive the integrated rate equation in terms of P₀ and Pₜ.
Numerical / Application-Based Problems
Q16. The decomposition of a reactant A follows first-order kinetics. The initial concentration is 0.50 M.
(a) Write the integrated rate equation.
(b) If after 30 minutes the concentration is 0.25 M, calculate the rate constant.
(c) Calculate the concentration after 60 minutes.
(d) Calculate the time required for 90% completion.
Q17. For a reaction A → Products, the following concentration-time data were collected:
| Time (min) | [A] (mol L⁻¹) |
|---|---|
| 0 | 2.00 |
| 10 | 1.60 |
| 20 | 1.20 |
| 30 | 0.80 |
(a) Test whether this is a zero-order reaction by checking if [A] vs. t is linear.
(b) Test whether this is a first-order reaction by checking if ln[A] vs. t is linear.
(c) Determine the correct order and calculate the rate constant.
(d) Predict [A] at t = 50 min.
Q18. In a school experiment, students study the hydrolysis of sucrose using a polarimeter. The reaction is first order. The observed rotation changes from +24° at t = 0 to +12° at t = 20 minutes, and to +6° at t = 40 minutes.
(a) Explain why optical rotation can be used to monitor this reaction.
(b) Using the integrated rate equation, verify that the reaction is first order.
(c) Calculate the rate constant.
(d) Predict the time when the rotation will become +3°.