Formula sheets, the key method steps for every topic and 6 practice problems, with full solutions at the back.
Practice exercise (made-up values, not clinical guidance). A vial of penicillin G contains 5 000 000 units. Its practice label gives three strengths (see the table). You add 8.2 mL of diluent. The prescribed dose is 600 000 units. What volume V do you draw up? Round to one decimal place.
A vial holds 2000 mg of powder. You add 9.2 mL of diluent, and the powder adds 0.8 mL of volume. The prescription is 920 mg. Draw up the dose: what volume V do you give?
A patient weighs 18 kg. The prescribed dose is 10 mg/kg per day, given in 3 equal doses. How many milligrams D are given per dose?
A patient weighs 143 lb. The prescription is 1 mg/kg as a single dose, and the stock contains 125 mg in 5 mL. Using 1 kg = 2.2 lb, what volume V do you give?
Practice exercise (made-up values, not clinical guidance). A patient receives an IV bolus of 210 mg of tobramycin. The level back-extrapolated to time zero is 10 mg/L and the half-life is 2 h. Find the clearance CL in L/h.
Practice exercise (made-up values, not clinical guidance). A vancomycin infusion runs at 60 mg/h with no loading dose. The patient's clearance is 3 L/h and the half-life is 6 h. What is the level C after 14 h?
Answer: V = 1.2 mL
Reconstitution: the powder takes up space, so the final volume is the diluent plus the powder volume. Concentration = drug in the vial/final volume, and the volume to give = dose/concentration. On a multi-strength label, use the concentration that belongs to the amount of diluent you actually added. The numbers are for practice only; at the bedside always follow local protocols and have high-risk doses double-checked.
Answer: V = 4.6 mL
Strength to volume: turn the strength into mg per mL first. A w/v percentage is grams per 100 mL, so x% = 10x mg/mL. A ratio strength 1:n is 1 g in n mL. After reconstitution the concentration is the powder's dose over the final volume (diluent + powder volume). Then volume = dose/concentration.
Answer: D = 60 mg
Dose calculation: the amount to give equals what is prescribed divided by what you have, times the quantity it comes in: amount = (desired dose/stock strength) × stock volume. Always keep the units the same (convert g to mg, mg to mcg first) and check that the answer is sensible.
Answer: V = 2.6 mL
Dose calculation: the amount to give equals what is prescribed divided by what you have, times the quantity it comes in: amount = (desired dose/stock strength) × stock volume. Always keep the units the same (convert g to mg, mg to mcg first) and check that the answer is sensible.
Answer: CL = 7.278 L/h
Clearance and volume: at steady state the dosing rate equals the elimination rate, so the maintenance rate = CL × Css. A loading dose is LD = Vd × C/(S × F), with S the salt factor (fraction of active drug in the salt) and F the bioavailability (1 for IV). From two levels, k = ln(C₁/C₂)/Δt; for an IV bolus Vd = dose/C₀ and CL = k × Vd. The numbers are for practice only; at the bedside always follow local protocols and have high-risk doses double-checked.
Answer: C = 16.03 mg/L
Designing a regimen: with rapid IV doses the level falls from peak to trough during the interval, so τ = ln(Cpeak/Ctrough)/k and the dose that restores the peak is Vd × (Cpeak − Ctrough). The average steady-state level is Css,avg = S·F·dose/(CL·τ). An infusion rises as C = (R/CL)(1 − e−kt). For a drug cleared by the kidneys, the dose is scaled with the creatinine clearance. The numbers are for practice only; at the bedside always follow local protocols and have high-risk doses double-checked.
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