Reaction kinetics – first order is a core topic for B.Pharm students studying drug stability, degradation and pharmacokinetics. First-order kinetics describe processes where the rate depends on the concentration of a single reactant and follows exponential decay, governed by the rate constant (k) and the integrated rate law ([A] = [A]0 e-kt). Key concepts include half-life (t1/2 = ln2/k), units of k (s-1 or h-1), pseudo-first order conditions, Arrhenius temperature dependence and analytical plots such as ln[A] vs t. Mastery of these ideas helps predict shelf life, drug degradation and concentration–time profiles. Now let’s test your knowledge with 30 MCQs on this topic.
Q1. What defines a first-order reaction in reaction kinetics?
- The rate is proportional to the square of the concentration of the reactant
- The rate is independent of reactant concentration
- The rate is proportional to the concentration of a single reactant
- The rate depends on the concentrations of two reactants
Correct Answer: The rate is proportional to the concentration of a single reactant
Q2. Which expression represents the integrated first-order rate law?
- [A] = [A]0 – kt
- [A] = [A]0 e-kt
- ln([A]0/[A]) = kt2
- 1/[A] = 1/[A]0 + kt
Correct Answer: [A] = [A]0 e-kt
Q3. For a first-order reaction, which plot yields a straight line?
- Plot of [A] vs t
- Plot of 1/[A] vs t
- Plot of ln[A] vs t
- Plot of [A]2 vs t
Correct Answer: Plot of ln[A] vs t
Q4. What is the slope of the ln[A] vs t plot for a first-order reaction?
- +k
- -k
- k/2
- -ln k
Correct Answer: -k
Q5. What are the SI units of the first-order rate constant k?
- mol L-1 s-1
- s-1
- mol-1 L s-1
- dimensionless
Correct Answer: s-1
Q6. Which formula gives the half-life (t1/2) for a first-order process?
- t1/2 = 1/(k[A]0)
- t1/2 = ln2 / k
- t1/2 = 2.303/k
- t1/2 = k / ln2
Correct Answer: t1/2 = ln2 / k
Q7. How does the half-life of a first-order reaction depend on initial concentration?
- It increases with increasing initial concentration
- It decreases with increasing initial concentration
- It is independent of initial concentration
- It depends on the square of initial concentration
Correct Answer: It is independent of initial concentration
Q8. If a drug follows first-order kinetics and t1/2 = 4 h, what fraction remains after 8 h?
- 50%
- 25%
- 12.5%
- 0%
Correct Answer: 25%
Q9. Which condition describes pseudo-first-order kinetics?
- The reaction is second order but both reactants are at equal low concentrations
- One reactant is in large excess so the rate depends effectively on the other reactant only
- The rate is independent of all reactant concentrations
- The reaction follows a zero-order rate law
Correct Answer: One reactant is in large excess so the rate depends effectively on the other reactant only
Q10. Which expression gives the concentration [A] at time t for a first-order reaction?
- [A] = [A]0 / (1 + kt)
- [A] = [A]0 e-kt
- [A] = [A]0 – k t
- [A] = [A]0 (1 – kt)
Correct Answer: [A] = [A]0 e-kt
Q11. For first-order degradation, the shelf-life (t90) corresponding to 10% loss is given by:
- t90 = ln(0.1)/k
- t90 = ln(0.9)/-k
- t90 = 0.1/k
- t90 = k/ln(0.9)
Correct Answer: t90 = ln(0.9)/-k
Q12. Which method is commonly used experimentally to confirm first-order kinetics?
- Plot of [A] vs 1/t
- Plot of 1/[A] vs t giving a straight line
- Plot of ln[A] vs t giving a straight line
- Plot of [A]2 vs t giving a straight line
Correct Answer: Plot of ln[A] vs t giving a straight line
Q13. If the slope of ln[A] vs t is -0.2 h-1, what is the half-life?
- 0.2 h
- 3.47 h
- ln2 × 0.2 h
- 5 h
Correct Answer: 3.47 h
Q14. A reaction showing exponential decay of concentration with time is most likely:
- Zero order
- First order
- Second order
- Mixed order
Correct Answer: First order
Q15. The initial rate of a first-order reaction is given by:
- k
- k [A]0
- [A]0/k
- k / [A]0
Correct Answer: k [A]0
Q16. If the rate constant k for a first-order process doubles, what happens to t1/2?
- It doubles
- It halves
- It remains unchanged
- It becomes zero
Correct Answer: It halves
Q17. Radioactive decay follows which kinetic order?
- Zero order
- First order
- Second order
- Third order
Correct Answer: First order
Q18. Which statement about pseudo-first-order reactions is true?
- The observed rate constant equals the true k only when concentrations are equal
- The observed rate constant is independent of excess reagent concentration
- The observed rate constant equals k multiplied by the constant concentration of the excess reagent
- Pseudo-first-order conditions only occur in gas-phase reactions
Correct Answer: The observed rate constant equals k multiplied by the constant concentration of the excess reagent
Q19. For a first-order reaction with k = 0.693 day-1, what is t1/2?
- 0.693 day
- 1 day
- 2 days
- ln(2) days
Correct Answer: 1 day
Q20. Calculate k (in h-1) if t1/2 = 10 h.
- 0.0693 h-1
- 0.693 h-1
- 10 h-1
- 1.0 h-1
Correct Answer: 0.0693 h-1
Q21. A drug concentration decreases from 100 µg/mL to 50 µg/mL in 6 hours. Assuming first-order kinetics, what is k (h-1)?
- 0.1155 h-1
- 0.693 h-1
- 6 h-1
- 0.5 h-1
Correct Answer: 0.1155 h-1
Q22. For first-order kinetics, how long will it take to reduce the concentration to 10% of initial if k = 0.23 h-1?
- ln(0.1)/-0.23 ≈ 10 h
- ln(0.9)/-0.23 ≈ 0.46 h
- ln(10)/0.23 ≈ 10 h
- ln(0.1)/0.23 ≈ -10 h
Correct Answer: ln(0.1)/-0.23 ≈ 10 h
Q23. Which kinetic parameter often used in stability studies is independent of initial concentration for first-order decay?
- Initial rate
- Half-life
- Initial concentration
- Activation energy
Correct Answer: Half-life
Q24. The Arrhenius equation relates the rate constant k to:
- Pressure only
- Temperature and activation energy
- Concentration and volume
- Catalyst concentration only
Correct Answer: Temperature and activation energy
Q25. In a first-order irreversible consecutive reaction A → B → C, the formation rate of B initially is approximately:
- k2[B]
- k1[A]
- k1[B]
- k2[A]
Correct Answer: k1[A]
Q26. Which experimental observation would suggest first-order kinetics for drug degradation?
- Plot of [drug] vs time is linear
- Plot of 1/[drug] vs time is linear
- Plot of ln[drug] vs time is linear
- Rate of degradation is constant over time
Correct Answer: Plot of ln[drug] vs time is linear
Q27. If a first-order reaction has k = 0.3465 h-1, what is the time to reduce concentration to 25%?
- ln(0.25)/-0.3465 ≈ 4 h
- ln(0.75)/-0.3465 ≈ 0.8 h
- ln(4)/0.3465 ≈ 4 h
- ln(0.25)/0.3465 ≈ -4 h
Correct Answer: ln(0.25)/-0.3465 ≈ 4 h
Q28. Which of the following best describes the concentration–time profile for a first-order elimination process in pharmacokinetics?
- Linear decline with time
- Exponential decline with time
- Parabolic decline with time
- Instantaneous drop to zero
Correct Answer: Exponential decline with time
Q29. To determine k from experimental data you should:
- Fit [A] vs t to a straight line
- Fit ln[A] vs t to a straight line and take negative slope
- Fit 1/[A] vs t to a straight line and take intercept
- Measure pH changes over time
Correct Answer: Fit ln[A] vs t to a straight line and take negative slope
Q30. Which factor does NOT directly affect the first-order rate constant k for a given reaction?
- Temperature
- Presence of catalyst
- Initial concentration of reactant
- Activation energy
Correct Answer: Initial concentration of reactant
I am a Registered Pharmacist under the Pharmacy Act, 1948, and the founder of PharmacyFreak.com. I hold a Bachelor of Pharmacy degree from Rungta College of Pharmaceutical Science and Research. With a strong academic foundation and practical knowledge, I am committed to providing accurate, easy-to-understand content to support pharmacy students and professionals. My aim is to make complex pharmaceutical concepts accessible and useful for real-world application.
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