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 750 000 units. What volume V do you draw up? Round to one decimal place.
Practice exercise (made-up values, not clinical guidance). You must prepare 600 mL of 5% sodium chloride by mixing 23% and 3% sodium chloride. How many mL V of the 23% solution do you need? Round to the nearest whole mL.
How many milligrams of drug m are in 50 mL of a 5% (w/v) solution?
The prescription is 260 units of a drug that comes as 1000 units/mL. Draw up the dose in the 1 mL syringe: what volume V do you give?
Practice exercise (made-up values, not clinical guidance). An 85 kg patient receives a theophylline infusion. The clearance is 0.04 L/kg/h. What infusion rate R in mg/h gives a steady-state level of 12 mg/L?
Practice exercise (made-up values, not clinical guidance). A 57 kg patient on regular tobramycin doses is at steady state. The target is a peak of 7 mg/L and a trough of 1 mg/L, and the volume of distribution is 0.25 L/kg. Assuming rapid IV doses, what dose D raises the level from the trough to the peak?
Answer: V = 1.5 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 = 60 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: 60 mL of 23% + 540 mL of 3% = 600 mL.
Answer: m = 2500 mg
Solution strengths: a percentage strength is grams per 100 mL, so 1% = 1 g/100 mL = 10 mg/mL. A ratio strength 1:1000 means 1 g in 1000 mL = 1 mg/mL; 1:10 000 is 0.1 mg/mL. For a dilution the amount of drug stays the same: C₁·V₁ = C₂·V₂.
Answer: V = 0.26 mL
Drawing up a dose: volume = (prescribed dose/stock strength) × stock volume. Convert to the same units first, then check that the volume fits the syringe and lands on one of its graduations.
On this 1 mL syringe every small line is 0.01 mL.
Answer: R = 40.8 mg/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: D = 85.5 mg
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.
In practice the dose is rounded to a convenient amount.
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