Calculating the percentage or ratio strength of a solution made by diluting or concentrating a solution is daily tasks for a dispensing or compounding pharmacist.
Drug Concentration Calculations
Drug concentrations, when put as percentages (%) either mean:
- weight/weight (w/w)%
- weight/volume (w/v)%
- volume/volume (v/v)%
X% (w/v) of a drug denotes X grams of the drug (solute) in 100 ml solution (solvent). For example, 2% Lidocaine solution contains 2g of lidocaine in 100 ml solution.
Drug Dilution Calculations
Anything represented in X:Y means X g of drug is divided by Y ml of solution. For example, 1:100 of an epinephrine solution contains 1 g epinephrine in 100 ml solution.
- 1:1 solution means 100 g solute in 100 ml solvent (100% solution)
- 1:10 solution means 10 g solute in 100 ml solvent (10% solution)
- 1:100 solution means 1 g solute in 100 ml solvent (1% solution)
Pharmacy Dilution and Concentration Calculation Example
1. How many milligrams of epinephrine are present in 10 ml of a 1:1000 preparation?
- 1000 ml solution contains 1 g epinephrine (1000 mg epinephrine)
- So, 10 ml contains 10 mg epinephrine
2. Express 0.5% (w/v) in mg/ml.
-0.5 g/100 ml
-500 mg/100 ml
-5 mg/5 ml
3. Hydrocortisone is available in a vial of 100 mg in 2 ml. You are to prepare 24 ml of 5 mg/ml hydrocortisone dilution using the available stock vials. How much hydrocortisone and diluent (in milliliters) you will need?
Here,
- 5 mg/ml = 0.5% solution
- 100 mg/2 ml = 0.1 g/2 ml = 5% solution
Now apply following equation,
V1×C1 = V2×C2
V1×5 = 24×0.5
V1 = 2.4 ml
So, Hydrocortisone is required = 2.4 ml
And, Diluent is required = (24-2.4) ml = 21.6 ml
4. How much (in milliliters) of a 1:400 w/v stock solution should be used to make 5 L of a 1:2000 w/v solution?
5 L = 5000 mL
1:400 = 0.25% & 1:2000 = 0.05%
Apply,
V1xC1 = V2xC2
X (mL) × 0.25% = 5000 mL × 0.05(%)
X = 100 mL
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