Numerical problems on kinetics MCQs With Answer are essential for B.Pharm students to master reaction rates, rate constants, reaction order, half-life, integrated rate laws, and Arrhenius behavior in pharmaceutical contexts. These practice questions focus on drug degradation kinetics, zero/first/second-order reactions, pseudo-first-order approximations, units of k, and simple numerical calculations used in stability testing and formulation science. Working through calculation-based MCQs builds skills in interpreting kinetic plots (ln[A] vs t, 1/[A] vs t), determining activation energy, and applying kinetic models to predict shelf-life and dosing. Clear stepwise numerical practice strengthens competency for exams and lab analysis. Now let’s test your knowledge with 30 MCQs on this topic.
Q1. For a reaction with rate proportional to [A]^2, what is the order of the reaction?
- Zero order
- First order
- Second order
- Third order
Correct Answer: Second order
Q2. Which statement correctly describes the half-life of a first-order reaction?
- Half-life decreases as initial concentration increases
- Half-life increases as initial concentration increases
- Half-life is independent of initial concentration
- Half-life depends only on activation energy
Correct Answer: Half-life is independent of initial concentration
Q3. Which integrated rate law corresponds to a second-order reaction with a single reactant A?
- [A] = [A]0 – kt
- ln[A] = ln[A]0 – kt
- 1/[A] = kt + 1/[A]0
- [A] = [A]0 e^{-kt}
Correct Answer: 1/[A] = kt + 1/[A]0
Q4. What are the units of the rate constant k for a second-order reaction in concentration units of mol L^-1 and time in seconds?
- s^-1
- M s^-1
- M^-1 s^-1
- mol L^-1 s^-1
Correct Answer: M^-1 s^-1
Q5. For a first-order reaction with k = 0.693 h^-1, what is the half-life?
- 0.5 h
- 1 h
- 2 h
- 10 h
Correct Answer: 1 h
Q6. A second-order reaction has k = 1 M^-1 s^-1. If [A]0 = 0.10 M, how long will it take for [A] to reach 0.050 M?
- 5 s
- 10 s
- 20 s
- 100 s
Correct Answer: 10 s
Q7. In a pseudo-first-order reaction where B is in large excess, the observed first-order rate constant k_obs equals:
- The true k divided by [B]
- The true k independent of [B]
- The true k multiplied by [B]
- The true k squared
Correct Answer: The true k multiplied by [B]
Q8. According to the Arrhenius equation, what happens to the rate constant k when the activation energy Ea increases (at constant temperature)?
- k increases
- k decreases
- k remains unchanged
- k becomes zero
Correct Answer: k decreases
Q9. A first-order reaction has k = 0.023 min^-1. What fraction of reactant remains after 60 minutes?
- ~5.0%
- ~12.5%
- ~25.2%
- ~50.0%
Correct Answer: ~25.2%
Q10. What are the units of the rate constant k for a zero-order reaction with concentration in mol L^-1 and time in seconds?
- M s^-1
- M^-1 s^-1
- s^-1
- mol^-1 L s
Correct Answer: M s^-1
Q11. For a second-order reaction, how does the half-life depend on initial concentration [A]0?
- t1/2 is independent of [A]0
- t1/2 ∝ [A]0
- t1/2 ∝ 1/[A]0
- t1/2 ∝ [A]0^2
Correct Answer: t1/2 ∝ 1/[A]0
Q12. For the reaction A + B → products, experiments show rate doubles when [A] doubles (with [B] constant) and doubles when [B] doubles (with [A] constant). What is the rate law order?
- Zero order overall
- First order overall
- Second order overall
- Third order overall
Correct Answer: Second order overall
Q13. If rate = k[A]^2 and measured rate = 0.02 M s^-1 when [A] = 0.10 M, what is k?
- 0.2 M^-1 s^-1
- 2 M^-1 s^-1
- 20 M^-1 s^-1
- 0.02 M^-1 s^-1
Correct Answer: 2 M^-1 s^-1
Q14. A drug shows first-order degradation with a half-life of 8 days. What is the rate constant k (day^-1)?
- 0.0087 day^-1
- 0.0866 day^-1
- 0.693 day^-1
- 8 day^-1
Correct Answer: 0.0866 day^-1
Q15. For a zero-order reaction with k = 0.01 M min^-1 and initial concentration 0.20 M, how long until the reactant is fully consumed?
- 2 min
- 10 min
- 20 min
- 200 min
Correct Answer: 20 min
Q16. A drug follows first-order kinetics with k = 0.1 h^-1. How long to decrease to 10% of initial concentration?
- 2.3 h
- 6.9 h
- 23.0 h
- 100 h
Correct Answer: 23.0 h
Q17. If experimental rate is unchanged when [A] changes, the reaction is:
- First order in A
- Second order in A
- Zero order in A
- Pseudo-first order in A
Correct Answer: Zero order in A
Q18. Which expression gives the half-life for a first-order reaction?
- t1/2 = 1/(k[A]0)
- t1/2 = ln2 / k
- t1/2 = [A]0 / k
- t1/2 = 2.303 / k
Correct Answer: t1/2 = ln2 / k
Q19. If the rate law is rate = k[A]^1[B]^0, what is the overall order?
- Zero order overall
- First order overall
- Second order overall
- Mixed order overall
Correct Answer: First order overall
Q20. A plot of ln[A] versus time is a straight line with slope = -0.02 s^-1. What is the rate constant k?
- 0.02 s^-1
- -0.02 s^-1
- 2.0 s^-1
- 0.0002 s^-1
Correct Answer: 0.02 s^-1
Q21. For a second-order reaction, a plot of 1/[A] vs time gives a slope of 0.5 M^-1 s^-1. What is k?
- 0.25 M^-1 s^-1
- 0.5 M^-1 s^-1
- 1.0 M^-1 s^-1
- 2.0 M^-1 s^-1
Correct Answer: 0.5 M^-1 s^-1
Q22. The observed rate constant for a first-order decomposition at 25°C is 2 × 10^-3 s^-1. What are the units of k?
- M s^-1
- s^-1
- M^-1 s^-1
- Pa s^-1
Correct Answer: s^-1
Q23. If the half-life of a first-order reaction is 1 hour, what fraction remains after 3 hours?
- 50%
- 25%
- 12.5%
- 6.25%
Correct Answer: 12.5%
Q24. For rate = k[A]^2 with k = 0.5 M^-1 s^-1 and [A] = 0.02 M, what is the initial rate?
- 2.0 × 10^-3 M s^-1
- 2.0 × 10^-4 M s^-1
- 5.0 × 10^-4 M s^-1
- 1.0 × 10^-5 M s^-1
Correct Answer: 2.0 × 10^-4 M s^-1
Q25. If doubling the concentration of a reactant doubles the rate, the reaction is:
- Zero order in that reactant
- First order in that reactant
- Second order in that reactant
- Fractional order in that reactant
Correct Answer: First order in that reactant
Q26. Given k1 = 1.0 × 10^-4 s^-1 at 300 K and activation energy Ea = 40 kJ mol^-1, approximate k2 at 310 K (use R = 8.314 J mol^-1 K^-1).)
- ~1.0 × 10^-4 s^-1
- ~1.7 × 10^-4 s^-1
- ~4.0 × 10^-4 s^-1
- ~1.0 × 10^-3 s^-1
Correct Answer: ~1.7 × 10^-4 s^-1
Q27. For a rate law rate = k[A]^1[B]^2, if [A] is doubled and [B] is halved, the rate changes by what factor?
- ×4 increase
- ×2 increase
- ×0.5 (half)
- ×0.25 (quarter)
Correct Answer: ×0.5 (half)
Q28. For a second-order reaction with k = 0.1 L mol^-1 s^-1 and [A]0 = 0.20 M, what is the half-life?
- 5 s
- 25 s
- 50 s
- 100 s
Correct Answer: 50 s
Q29. For a first-order reaction with [A]0 = 0.50 M and [A] = 0.125 M, and k = 0.03 s^-1, how much time has elapsed?
- 11.6 s
- 23.1 s
- 46.2 s
- 92.4 s
Correct Answer: 46.2 s
Q30. In pharmaceutical kinetics, activation energy Ea is commonly expressed in which units?
- J
- J mol^-1
- kJ mol^-1
- mol kJ^-1
Correct Answer: kJ mol^-1
