**Question:** A 70 kg man was given a drug in a dose of 100 mg/kg body weight. Its t1/2, is 10 hours, initial plasma concentration is 1.9 mg/ml. True statement is: a) CL is 0.02 litre/hr, b) CL is 20 litre/hr, c) k is 0.0693, d) k is 6.93, e) CL is 0.2 litre/hr

**Core Concept:** Drug pharmacokinetics and elimination rate constants

**Why the Correct Answer is Right:**

The given information includes the initial plasma concentration (1.9 mg/ml), body weight (70 kg), dose (100 mg/kg), and half-life (t1/2, 10 hours). To calculate the clearance (CL), we can use the following equations:

1. CL = (2*dose) / t1/2
2. k = ln(2) / t1/2

**Why Each Wrong Option is Incorrect:**

a) CL calculation: CL = (2*100) / 10 = 20 liters/hr -> This is incorrect because we need the inverse of t1/2 (0.0693) to calculate CL.

b) CL calculation: CL = (2*100) / 10 = 20 liters/hr -> Similar to option A, this is incorrect as it uses the wrong formula.

c) k value: k = ln(2) / 10 = 0.0693 -> This is the correct value of the elimination rate constant (k).

d) k value: k = ln(2) / 10 = 0.0693 -> This is the correct value of the elimination rate constant (k).

e) CL calculation: CL = (2*100) / 10 = 20 liters/hr -> Similar to options A and B, this is incorrect as it uses the wrong formula.

**Why the Correct Answer is Right:**

The correct answer is option D (k = ln(2) / 10 = 0.0693) and option D (k = ln(2) / 10 = 0.0693). This is because we can calculate the elimination rate constant (k) using the formula:

k = ln(2) / t1/2

**Clinical Pearls:**

1. The elimination rate constant (k) is a measure of the rate at which a drug is cleared from the body. A smaller k indicates faster clearance and vice versa.
2. The half-life (t1/2) is the time it takes for a drug's concentration to decrease to half of its initial value.
3. The elimination rate constant and half-life are inversely related: as k increases, t1/2 decreases, and vice versa.

**Explanation of Wrong Options:**

A and E are