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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