They’re giving a lot of confusing extra information here, maybe to trip us up. They just want volume of distribution, simple as that.

Vd = [drug administered] ÷ [plasma drug concentration]

First convert it all to g/L because this is how the answer will be:

administered: 80 mg = 0.08 g plasma concentration: 4 ug/ml = 0.004 g/L

Thus,

Vd = 0.08 grams ÷ 0.004 g/L = 20 L

Clearance of drug is not a huge factor because the half life is so long that the drug is distributing before significant clearance occurs.

Vd = amount of drug in body / plasma drug concentration.

Amount of drug in body = 80mg

Plasma drug concentration = 4 micrograms/mL = 4mg/L

Vd = 80mg/(4mg/L) = 20L

Distribution half-life is 3 minutes so after 30 min we can assume the drug is maximally distributed. Elimination half-life is 24 hours so we can assume a neglible amount of drug lost

you could also have used the loading dose equation (because they gave you loading dose and told you it was IV) LD= (Vd x Cp)/ F if you freak out at converting units like I do

no need for any conversion to g/l.

as long as you can cross out the weight.

to be faster, make both to mg.

vd= dosage/conc. aka i call it vd= do/co

4microgram/ml = 4 miligram/litre

v.d= 80/4= 20

tip. in calculation questions. jump to the final line to know what theyre asking , making a mental note of the formula if you can remember and solve.

becuase instinctively our brain feels obligated to use all the values, and they use that to our disadvantage !