Dilution of liquid preparations (calculations)

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The dilution of a liquid dosage form, as a solution or suspension, may be desired to provide a product strength more suitable for use by a particular patient (e.g., pediatric, elderly, those in disease states).The diluent is selected based on its compatibility with the vehicle of the original product; that is, aqueous, alcoholic, hydroalcoholic, or other. The dilution of a solid dosage form (as a powder or the contents of a capsule) or a semisolid dosage form (as an ointment or cream) also may be performed to alter the dose or strength of a product. Again, the diluent is selected based on its compatibility with the original formulation.

Dilution of liquid oral preparation

For many liquid oral preparations (e.g. mixture, elixir, linctuses) Bp and PCx state that when a dose ordered or prescribed is less than or not a multiple of 5ml preparation should be diluted with the vehicle used in the preparation or with diluent specified in the individual monograph so that the dose to be measured by the patient is 5ml spoonful (usually taken as a tea spoonful) or multiple thereof

Formula 1 (using factor as in reducing)

Example 1

Codeine phosphate syrup PCx

Codeine phosphate                 5g

Purified water, freshly boiled and cooled      15ml

Chloroform spirit                    25ml

Syrup               to 1000ml

Sig: 2.5 ml q.i.d 4/7


This prescribed amount is 2.5ml * 4 * 4 = 40ml (desired)

Factor is 0.04

As 2.5 ml is less than 5 ml each single dose should be diluted with 2.5 ml of diluent in this case syrup (adding 2.5 ml of syrup in each 2.5 ml single dose to make it 5 ml) so that the patient can measure the dose in terms of teaspoonfuls

Amount of diluent: 2.5 ml * 4 * 4 = 40 ml

As volume of the undiluted preparation is 40 ml and the same amount of diluent is added, the volume of the dispensed medicine will be 80 ml

Dilution of stock solution

Stock solutions are solutions of known concentration that are frequently prepared for convenience in dispensing. They are usually strong solutions from which weaker ones may be made conveniently. When correctly prepared, these solutions enable the pharmaceutical staff to obtain small quantities of medicinal substances that are to be dispensed in solution

Stock solutions are invariably prepared on a weight in volume (w/v) basis and their concentration is expressed as ratio strength or less frequently, as percentage strength.


Dilution of alcohol

When water and alcohol are mixed, there is a physical contraction such that the resultant volume is less than the total of the individual volumes of the two liquids. Thus, to prepare a volume-in-volume strength of an alcohol dilution, the alcohol ‘‘solute’’ may be determined and water used to ‘‘q.s.’’ to the appropriate volume. Because the contraction of the liquids does not affect the weights of the components, the weight of water (and from this, the volume) needed to dilute alcohol to a desired weight-in-weight strength may be calculated.

Dilution of acid

The strength of an official undiluted (concentrated) acid is expressed as percentage weight-in-weight. For example, Hydrochloric Acid, NF, contains not less than 36.5% and not more than 38.0%, by weight, of HCl. However, the strength of an official diluted acid is expressed as percentage weight-in-volume. For example, Diluted Hydrochloric Acid, NF, contains, in each 100 mL, not less than 9.5 g and not more than 10.5 g of HCl.

It is necessary, therefore, to consider the specific gravity of concentrated acids in calculating the volume to be used in preparing a desired quantity of a diluted acid.

Formula 2:  Inverse proportion

(1st quantity) * (1st concentration) = (2nd quantity) * (2nd concentration), or Q1 * C1 = Q2 * C2.

Example 1 (stock solution)

How many milliliters of 1:400 (w/v) of stock solution should be used to make 4 liters of a 1: 2000 (w/v) solution?


Example 2 (alcohol)

How much water should be mixed with 5000 mL of 85% v/v alcohol to make 50% v/v alcohol?


Q1 = 5000 ml, C1 = 85%, Q2 = 50%, Q 2 =?

Q1*C1 = Q2*C2

5000 * 85% = Q2 * 50%

Q2 = 8500 ml

Example 3 (acid)

How many milliliters of 37% w/w hydrochloric acid having a specific gravity of 1.20 are required to make 1000 mL of diluted hydrochloric acid 10% w/v?



How many milliliters of 85% w/w phosphoric acid having a specific gravity of 1.71 should be used in preparing 1 gallon of 1⁄4% w/v phosphoric acid solution to be used for bladder irrigation?



Pharmaceutical Calculations;13th Edition: Howard C. Ansel, PhD Professor and Dean Emeritus College of Pharmacy University of Georgia Athens, Georgia

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