Numerical problems on kinetics MCQs With Answer

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