Rate of elimination of a new drug is 20mg/hr it is steady state plasma concentration of 10mg/L, then it’s renal clearance will be
Hmm, first, I need to recall the formula for renal clearance. I remember that clearance (CL) is calculated by dividing the elimination rate (ER) by the plasma concentration (Cp). So, CL = ER / Cp. Let me check the units. The elimination rate is in mg per hour, and plasma concentration is in mg per liter. So, mg/hr divided by mg/L would give L/hr, which makes sense for clearance units.
So plugging in the numbers: 20 mg/hr divided by 10 mg/L equals 2 L/hr. Therefore, the renal clearance should be 2 L/hr.
Now, the options aren't given, but the correct answer is 2 L/hr. The user probably expects me to explain why this is the case. Let me make sure there's no confusion with other formulas. Sometimes, people mix up elimination rate with clearance. But the formula is straightforward here. Also, it's important to note that this is renal clearance, assuming the elimination rate is solely due to the kidneys. If there were other elimination routes, the calculation might differ, but the question doesn't mention that.
For the incorrect options, common mistakes might include using the wrong formula, like multiplying instead of dividing, or confusing mg/L with other units. For example, someone might mistakenly calculate 20/10 as 2 mg/L instead of L/hr. Also, converting units incorrectly could lead to errors, like hours to minutes or liters to milliliters.
The clinical pearl here is remembering that clearance equals elimination rate divided by plasma concentration. That's a key formula for pharmacokinetics. Students should also be cautious about units, as they can easily lead to errors if not handled properly.
Putting it all together, the correct answer is 2 L/hr. The explanation should cover the formula, the calculation, and why other options are wrong, along with a high-yield fact about units and the formula.
**Core Concept**
Renal clearance is calculated using the formula: **Clearance (CL) = Elimination Rate (ER) / Plasma Concentration (Cp)**. This quantifies the volume of plasma from which a drug is completely removed per unit time.
**Why the Correct Answer is Right**
Given: Elimination rate (ER) = 20 mg/hr, Steady-state plasma concentration (Cp) = 10 mg/L.
Renal clearance (CL) = ER / Cp = 20 mg/hr ÷ 10 mg/L = **2 L/hr**.
This calculation assumes all drug elimination occurs via the kidneys and that the drug concentration in renal venous blood equals plasma concentration (valid for most drugs).
**Why Each Wrong Option is Incorrect**
**Option A:** Incorrect if it suggests 2 mg/hr (unit mismatch; clearance is in L/hr).
**Option B:** Incorrect if it uses Cp × ER instead of ER ÷ Cp, leading to 200 mg²/L·hr.
**Option C:** Incorrect if it ignores unit conversion (e.g., 2000 mL/hr instead of 2 L/hr).