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 contains ampicillin 1000 mg as a powder. The practice label says to add 3.5 mL of sterile water; the powder adds 0.5 mL to the volume. What is the concentration C in mg/mL after reconstitution?
Practice exercise (made-up values, not clinical guidance). You must prepare 750 mL of 5% sodium chloride by mixing 23% and 3% sodium chloride. How many mL V of the 3% solution do you need? Round to the nearest whole mL.
A patient weighs 12 kg. The prescribed dose is 5 mg/kg per day, given in 2 equal doses. How many milligrams D are given per dose?
A patient weighs 55 lb. The prescription is 1 mg/kg as a single dose, and the stock contains 200 mg in 5 mL. Using 1 kg = 2.2 lb, what volume V do you give? Round to two decimal places.
Practice exercise (made-up values, not clinical guidance). After an IV dose of vancomycin, the level is 25 mg/L at 1 h and 9.9 mg/L at 9 h. Assume first-order elimination. Find the half-life t½.
Practice exercise (made-up values, not clinical guidance). A 68 kg patient takes oral theophylline (F = 1) every 8 h. The clearance is 0.035 L/kg/h. Each dose is 500 mg of theophylline. Find the average steady-state level Css,avg.
Answer: C = 250 mg/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 = 675 mL
Alligation: to mix a higher strength H and a lower strength L into a target strength T, take (T − L) parts of H and (H − T) parts of L. The parts are crossed: each stock gets the distance from the target to the other stock. Water or a plain base counts as 0%. The numbers are for practice only; at the bedside always follow local protocols and have high-risk doses double-checked.
Check: 75 mL of 23% + 675 mL of 3% = 750 mL.
Answer: D = 30 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 = 0.63 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: t½ = 5.986 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: Css,avg = 26.26 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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