Dilution and Concentration

There are instances in pharmacy practice when a medication needs to be diluted or concentrated. For example, a prescriber may require a concentrated solution or a concentrated syock solution to be diluted for use in a patient. Dilution is achieved by addition of a diluent to the medication. When diluting a medication, the amount of drug doesn’t change but the concentration changes.

The simplest way to solve these problems is by using the equation:

$$ V^o \times C^o = V^n \times C^n $$


Solved Problem: How many milliliters of 50% (w/v) dextrose would be needed to make 1000 ml of 35 % (w/v) dextrose?

Approach: Use the equation stated above (inverse proportion calculation):

$$ 50 \times x = { 35 \times 1000, \ x} = \ 700 \ ml$$

Answer: 700 ml of 50 % dextrose would be mixed with 300 ml of sterile water of injection to make a 1000 ml of 35 % dextrose solution.

Solved Problem: If an injection containing a medication, 50 mg/10 ml is diluted to 1 L, calculate the percent strength of resulting solution.

Approach: Solve by traditional calculation

$$ 50 \ mg = { 0.05 \ g } $$

$$ { 0.05 \ g \over 1000 \ ml } \times 100 ={ 0.005 \% } $$

Answer: 0.005 % w/v

Solved Problem: Calculate the ratio strength after a 500 ml solution of ratio strength 1:600 is diluted to 2L.

Approach: Express the ratio strength as a fraction and use an inverse proportion calculation.

$${ 500 \ ml \times {1 \over 600}} = { 2000 \ ml \times x }; x \ = \ 0.00041667 \ = \ 1:2400$$

Answer: 1:2400