Rate of elimination of a new drug is 20 mg/hr at a steady state plasma concentration of 10 mg/L, then its renal clearance will be:
First, I remember that clearance (CL) is calculated by the formula CL = Rate of elimination / Plasma concentration. The rate of elimination here is given as 20 mg per hour, and the plasma concentration is 10 mg per liter. So plugging in the numbers: CL = 20 mg/hr / 10 mg/L = 2 L/hr. That seems straightforward.
Wait, but the question specifically asks for renal clearance. Is there a difference between total clearance and renal clearance? Oh right, renal clearance is a component of total clearance if the drug is excreted by the kidneys. However, in this case, since the question mentions "rate of elimination" without specifying other routes, I think they're referring to total clearance. Unless there's more to it, maybe the rate of elimination given is specifically renal. Hmm. The question is a bit ambiguous, but typically, if the rate of elimination is given without other info, it's assumed to be total. But since the answer is 2 L/hr, that would be the total clearance. But the question says "renal clearance," so maybe they are considering that the elimination is entirely renal. So the calculation remains the same.
Let me double-check the formula. Clearance is indeed rate of elimination divided by plasma concentration. So 20 divided by 10 is 2. The units would be liters per hour because mg/hr divided by mg/L gives L/hr.
Now, looking at the options, which are not provided here. But the correct answer is 2 L/hr. The user's correct answer is missing the options, but the answer they provided is the calculation.
For the explanation, the core concept is the clearance formula. The correct answer is right because applying the formula. The wrong options might be other values, like 0.5, 5, 10, maybe due to miscalculations. For example, if someone confused mg/L with mg/hr or did division in the wrong order.
Clinical pearl: Remember that clearance is rate divided by concentration. This is a fundamental pharmacokinetic principle. Students often mix up the formula, so emphasizing that rate (mg/hr) divided by concentration (mg/L) gives L/hr is key.
**Core Concept** Clearance (CL) is calculated using the formula **CL = Rate of elimination / Plasma concentration**. This principle applies to all elimination pathways, including renal clearance, where the drug is removed via the kidneys. Units must be carefully analyzed to ensure dimensional consistency.
**Why the Correct Answer is Right**
Given: Rate of elimination = 20 mg/hr, Plasma concentration = 10 mg/L.
Renal clearance (CL) = **Rate of elimination / Plasma concentration** = 20 mg/hr ÷ 10 mg/L = **2 L/hr**.
This calculation assumes steady-state conditions, where the rate of elimination equals the rate of administration. The units confirm validity: (mg/hr) ÷ (mg/L) = L/hr.
**Why Each Wrong Option is Incorrect**
**Option A:** Incorrect if it assumes CL = concentration × rate (e