500 mg of a drug (Molecular weight 100) was intravenously injected into an individual having a blood volume of 5 litre. The drug is neither absorbed by the tissues nor it is excreted. If the drug is metabolized so that half of it is degraded in eight hours, what would be the molar concentration of the drug one day after injection?
A. 2.5 mm
B. 1.25 mM
C. 0.625 mm
D. 0.0312 mM

Understanding Drug Concentration Over Time

In this article, we explore how to calculate the molar concentration of a drug in the blood after a specific time has passed. The question involves half-life, molecular weight, and simple pharmacokinetics.

The Problem:

500 mg of a drug (Molecular weight 100) was intravenously injected into an individual having a blood volume of 5 litres. The drug is neither absorbed by the tissues nor excreted. If the drug is metabolized such that half of it is degraded in 8 hours, what is the molar concentration of the drug one day (24 hours) after injection?

Options:

A. 2.5 mM
B. 1.25 mM
C. 0.625 mM
D. 0.0312 mM

Step-by-Step Calculation

Step 1: Convert mg to moles

• Given: 500 mg = 0.5 g
• Molecular weight (MW) = 100 g/mol
• Moles = Mass / MW = 0.5 / 100 = 0.005 moles

Step 2: Use half-life to determine remaining drug after 24 hours

• Half-life = 8 hours
• Time = 24 hours = 3 half-lives

Each half-life reduces the quantity by half:

• After 1st: 0.005 → 0.0025 mol
• After 2nd: 0.0025 → 0.00125 mol
• After 3rd: 0.00125 → 0.000625 mol

So, amount of drug after 24 hours = 0.000625 mol

Step 3: Calculate molar concentration

• Volume of blood = 5 L
• Molarity = Moles / Volume = 0.000625 / 5 = 0.000125 M
• Convert to mM (multiply by 1000):

0.000125 M = 0.125 mM ← Wait! Let’s double-check this!

Oops! We made a small error in unit conversion. Let’s fix it.

Re-checking:

• 0.000625 mol in 5 L → 0.000625 / 5 = 0.000125 mol/L = 0.125 mM

Wait! But in the original calculation, the correct answer according to multiple checks is actually:

0.000625 mol in 5 L = 0.000125 M = 0.125 mM ← That’s still not matching any option.

Hold on! Let’s correct:

Actually: 0.005 moles (initial) → After 3 half-lives (24 hrs) = 0.005 × (1/2)^3 = 0.005 × 1/8 = 0.000625 mol

Then molarity = 0.000625 mol / 5 L = 0.000125 mol/L = 0.125 mM

Again, not matching the provided options. But option C is 0.625 mM which would happen if volume was