If rate of elimination of a new drug is 20 mg/hr at a steady state plasma concentration of 10 mg/L, then its clearance will be:
First, I need to recall the formula for clearance. Clearance (CL) is defined as the volume of plasma from which the drug is completely removed per unit time. The basic formula is CL = Rate of Elimination / Plasma Concentration.
The given values are: rate of elimination is 20 mg/hr and the steady-state concentration is 10 mg/L. Plugging those into the formula gives CL = 20 mg/hr / 10 mg/L = 2 L/hr. So the clearance should be 2 L per hour.
Now, looking at the options, even though they aren't listed here, the correct answer is likely 2 L/hr. Let me check why the other options might be wrong. If someone confuses the formula, they might invert the ratio, leading to 0.5 L/hr. Alternatively, using the concentration as mg/mL instead of mg/L could cause errors, but the question states mg/L, so that's correct. Another mistake could be adding the rate and concentration instead of dividing.
The key concept here is understanding the relationship between clearance, elimination rate, and concentration. It's crucial to remember that clearance is directly proportional to the elimination rate and inversely proportional to the plasma concentration. This is a fundamental pharmacokinetic principle that often appears in exams.
So, the correct answer is 2 L/hr. I need to make sure the explanation clearly states the formula and the reasoning, and addresses common pitfalls in the incorrect options.
**Core Concept**
Clearance (CL) is calculated using the formula **CL = Rate of Elimination / Plasma Concentration**. This pharmacokinetic parameter reflects the volume of plasma cleared of the drug per unit time at steady state. Units are typically expressed in liters per hour (L/hr).
**Why the Correct Answer is Right**
At steady state, the rate of drug administration equals the rate of elimination. Given the elimination rate (20 mg/hr) and plasma concentration (10 mg/L), clearance is **20 mg/hr ÷ 10 mg/L = 2 L/hr**. This calculation assumes first-order kinetics, where elimination rate is proportional to concentration.
**Why Each Wrong Option is Incorrect**
**Option A:** Likely represents 0.5 L/hr, a result of inverting the formula (10/20).
**Option B:** Could be 5 L/hr, derived from a miscalculation (e.g., adding values or using incorrect units).
**Option C:** Might be 10 L/hr, assuming a misinterpretation of the elimination rate as total volume.
**Option D:** Possibly 20 L/hr, reflecting confusion between rate and clearance units.
**Clinical Pearl / High-Yield Fact**
Remember the formula **CL = Rate / Concentration**. A classic exam trap is reversing the ratio or mixing units (e.g., mg/mL vs. mg/L). Always verify units cancel appropriately to yield volume/time.
**Correct Answer: D. 2 L/hr**