One-compartment open model – IV infusion MCQs With Answer

One-compartment open model – IV infusion MCQs With Answer
The one-compartment open model for IV infusion is a core pharmacokinetic framework describing constant-rate intravenous drug administration into a single, well-mixed compartment. Key concepts and keywords include infusion rate (k0), elimination rate constant (ke), clearance (Cl), volume of distribution (Vd), steady-state concentration (Css), half-life (t1/2), loading dose (LD), and accumulation. Mastery of infusion equations such as C(t) = (k0/Cl)(1 – e^{-ke t}), time to steady state, and post-infusion decline is essential for dosing calculations, therapeutic drug monitoring, and clinical interpretation. This focused set of MCQs deepens calculation skills and conceptual understanding for B.Pharm students. Now let’s test your knowledge with 30 MCQs on this topic.

Q1. In a one-compartment open model with constant IV infusion, which equation gives plasma concentration at time t?

• C(t) = (k0 / Cl) · (1 – e^-ke·t)
• C(t) = (Dose / Vd) · e^-ke·t
• C(t) = (k0 / Vd) · e^-ke·t
• C(t) = (Cl / k0) · (1 – e^-ke·t)

Correct Answer: C(t) = (k0 / Cl) · (1 – e^-ke·t)

Q2. For an IV infusion, steady-state concentration (Css) is best described by which relation?

• Css = k0 / Cl
• Css = Dose / Vd
• Css = k0 · Vd
• Css = Cl / k0

Correct Answer: Css = k0 / Cl

Q3. If k0 = 50 mg/hr and Cl = 5 L/hr, what is Css?

• 10 mg/L
• 0.1 mg/L
• 250 mg/L
• 5 mg/L

Correct Answer: 10 mg/L

Q4. Clearance (Cl) in a one-compartment model is related to ke and Vd by which formula?

• Cl = ke · Vd
• Cl = Vd / ke
• Cl = ke / Vd
• Cl = Vd – ke

Correct Answer: Cl = ke · Vd

Q5. Time required to reach ~63% of Css during a first-order infusion equals:

• 1 / ke
• t1/2
• 4 × t1/2
• k0 / Cl

Correct Answer: 1 / ke

Q6. Approximately how many half-lives are needed to reach >95% of steady state for a first-order infusion?

• About 4 to 5 half-lives
• About 1 half-life
• About 0.5 half-life
• About 10 half-lives

Correct Answer: About 4 to 5 half-lives

Q7. Which formula gives the loading dose (LD) required to immediately achieve desired Css?

• LD = Css · Vd
• LD = k0 / Cl
• LD = Css / Vd
• LD = Cl · t1/2

Correct Answer: LD = Css · Vd

Q8. A drug has Vd = 20 L and desired Css = 8 mg/L. What is the loading dose?

• 160 mg
• 2.5 mg
• 0.4 mg
• 28 mg

Correct Answer: 160 mg

Q9. After an infusion is stopped at steady state, how does drug concentration decline?

• Exponential decline: C(t) = Css · e^-ke·t
• Linear decline to zero
• Remains at Css indefinitely
• Increases initially then declines

Correct Answer: Exponential decline: C(t) = Css · e^-ke·t

Q10. If ke = 0.1 hr⁻¹, what is the half-life (t1/2)?

• 6.93 hours
• 0.1 hours
• 10 hours
• 1.44 hours

Correct Answer: 6.93 hours

Q11. For an infusion with k0 = 100 mg/hr and Cl = 10 L/hr, time to steady state will be determined by:

• Elimination rate constant (ke), not k0
• Infusion rate (k0) only
• Clearance (Cl) only
• Vd only

Correct Answer: Elimination rate constant (ke), not k0

Q12. Which change will increase Css for a fixed infusion rate k0?

• Decrease in clearance (Cl)
• Decrease in k0
• Increase in Cl
• Decrease in Vd

Correct Answer: Decrease in clearance (Cl)

Q13. If a drug’s Cl doubles while k0 is unchanged, what happens to Css?

• Css decreases by half
• Css doubles
• Css remains unchanged
• Css increases by fourfold

Correct Answer: Css decreases by half

Q14. Relationship expressing accumulation ratio (R) at steady state for multiple intermittent infusions (or dosing) often equals:

• 1 / (1 – e^-ke·τ)
• k0 / Cl
• Vd / Cl
• ke · Vd

Correct Answer: 1 / (1 – e^-ke·τ)

Q15. For continuous infusion, when is a loading dose most useful?

• When immediate therapeutic concentration is required
• When drug has very short t1/2
• When infusion rate equals zero
• Loading dose is never used with infusions

Correct Answer: When immediate therapeutic concentration is required

Q16. Calculate ke if t1/2 = 3 hours.

• 0.231 hr⁻¹
• 3.0 hr⁻¹
• 1.443 hr⁻¹
• 0.693 hr⁻¹

Correct Answer: 0.231 hr⁻¹

Q17. If a 4-hour infusion of a drug with ke = 0.2 hr⁻¹ is given, fraction of Css achieved at 4 hours is approximately:

• 1 – e^-0.2×4 = 1 – e^-0.8 ≈ 0.55 (55%)
• e^-0.8 ≈ 0.45 (45%)
• 100% of Css
• 10% of Css

Correct Answer: 1 – e^-0.2×4 = 1 – e^-0.8 ≈ 0.55 (55%)

Q18. Which parameter must change if Vd increases but Cl remains constant, at same infusion k0?

• Time to reach steady state increases (ke decreases)
• Css increases
• Css decreases
• Infusion rate k0 changes

Correct Answer: Time to reach steady state increases (ke decreases)

Q19. A patient receives infusion achieving Css = 12 mg/L. Clearance is 6 L/hr. What was infusion rate k0?

• 72 mg/hr
• 2 mg/hr
• 6 mg/hr
• 12 mg/hr

Correct Answer: 72 mg/hr

Q20. In a one-compartment infusion model, which statement is TRUE about Vd?

• Vd affects the magnitude of loading dose and the rate constant ke
• Vd directly determines Css for a given k0
• Vd equals Cl / ke only during infusion
• Vd has no influence on time to steady state

Correct Answer: Vd affects the magnitude of loading dose and the rate constant ke

Q21. If you want to reach 90% of Css faster without changing ke, which strategy is appropriate?

• Administer a loading dose (LD = Css·Vd)
• Decrease infusion rate
• Increase Vd
• Increase clearance

Correct Answer: Administer a loading dose (LD = Css·Vd)

Q22. For a drug with Vd = 40 L and ke = 0.1 hr⁻¹, what is Cl?

• 4 L/hr
• 400 L/hr
• 0.0025 L/hr
• 0.1 L/hr

Correct Answer: 4 L/hr

Q23. Which best describes the effect of changing infusion rate k0 while keeping Cl constant?

• Css changes proportionally with k0
• Time to steady state changes but Css unchanged
• Vd changes
• ke changes

Correct Answer: Css changes proportionally with k0

Q24. A drug infused at k0 reaches 70% of Css after 1/ke. True or False?

• False — after 1/ke it reaches ~63% of Css
• True — 70% is correct
• True — it reaches exactly 100%
• False — after 1/ke it reaches 30%

Correct Answer: False — after 1/ke it reaches ~63% of Css

Q25. A patient receives an infusion to steady state. If hepatic function decreases and Cl is reduced by 50%, keeping k0 unchanged, what is expected?

• Css will approximately double, increasing toxicity risk
• Css will halve
• Time to steady state will shorten drastically but Css unchanged
• Vd will decrease

Correct Answer: Css will approximately double, increasing toxicity risk

Q26. For a 2-hour infusion of drug with ke = 0.5 hr⁻¹, fraction of steady state achieved at end of infusion is:

• 1 – e^-1.0 ≈ 0.632 (63.2%)
• e^-1.0 ≈ 0.368 (36.8%)
• 100% of steady state
• 10% of steady state

Correct Answer: 1 – e^-1.0 ≈ 0.632 (63.2%)

Q27. Which expression gives concentration at time t when infusion of duration T is stopped at T and sampling at time t after stopping (t measured from end of infusion)?

• C = (k0 / Cl) · (1 – e^-ke·T) · e^-ke·t
• C = (k0 / Cl) · (1 – e^-ke·t)
• C = Dose / Vd
• C = Css · (1 – e^-ke·t)

Correct Answer: C = (k0 / Cl) · (1 – e^-ke·T) · e^-ke·t

Q28. Which clinical scenario most justifies continuous IV infusion over intermittent bolus dosing?

• Tight therapeutic window requiring stable plasma concentration
• Need for high peak concentration only
• Short-term single dose for diagnostic purpose
• When absorption after oral dosing is excellent

Correct Answer: Tight therapeutic window requiring stable plasma concentration

Q29. When designing an infusion regimen, which parameter is primarily used to set the infusion rate for target Css?

• Clearance (Cl) and desired Css (k0 = Css · Cl)
• Vd only
• Half-life only
• Loading dose only

Correct Answer: Clearance (Cl) and desired Css (k0 = Css · Cl)

Q30. Two drugs A and B have same Cl but A has larger Vd. For same continuous infusion rate, what differs between A and B?

• Time to reach steady state is longer for A, Css is same for both
• Css is larger for A and time to steady state is same
• Css is smaller for A and time to steady state shorter
• Both Css and time to steady state are identical

Correct Answer: Time to reach steady state is longer for A, Css is same for both

G S Sachin

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.

Mail- Sachin@pharmacyfreak.com