PERCENTAGE PREPARATIONS
INTRODUCTION
Many of the prescriptions received in the pharmacy have the amounts of active ingredients expressed as percentage strengths as opposed to a weight or volume which can be measured. The physician knows that each active ingredient, when given in a certain percentage strength, gives the desired therapeutic effect. Instead of the physician calculating the amount of each ingredient needed for the prescription, he will simply indicate the percentage strength desired for each ingredient and expect the pharmacy to calculate the amount of each ingredient based on its percentage strength.
There are no percentage weights for a torsion balance or percentage graduations on a graduate. The percentage values on a prescription must be changed to amounts which can be weighed (grams) or to amounts which can be measured (milliliters).
TYPES OF PERCENT
Recall that the term percent means "parts per hundred" and is expressed in the following manner:
# OF PARTS /100 PARTS
a. W/W percent or Weight/Weight percent is defined as the number of grams in 100 grams of a solid preparation.
(1) Example #1 A 5 percent (w/w) boric acid ointment would contain 5 grams of boric acid in each 100 grams of boric acid ointment.
(2) Example #2:A 3 percent (w/w) vioform powder would contain 3grams of vioform in every 100 grams of the vioform powder.
b. W/V of Weight/Volume percent is defined as the number of grams in 100 milliliters of solution.
(1) Example #1:A 10 percent (w/v) potassium chloride (KCL) elixir would contain 10 grams of potassium chloride in every 100 milliliters of KC1 elixir.
(2) Example #2:A 1/2 percent (w/v) phenobarbital elixir would contain ½ gram of phenobarbital in every 100 milliliters of phenobarbital elixir.
c. V/V percent or Volume/Volume percent is defined as the number of milliliters in every 100 ml of solution.
(1) Example #1:A 70% (v/v) alcoholic solution would contain 70 milliliters of alcohol in every 100 ml of solution.
(2) Example #2:A 0.5% (v/v) glacial acetic acid solution would contain 0.5 milliliters of glacial acetic acid in each 100 milliliters of solution.
d. When the type of percent is not stated, it is understood that dilutions of (1) dry ingredient in a dry preparation are percent W/W, (2) dry ingredients in a liquid are percent W/V, and (3) a liquid in a liquid is percent V/V.
METHODS FOR SOLVING PERCENTAGE PROBLEMS
a. Ratio and proportion:
Formula:
IF # of parts/100 = then amount of solute needed / Total volume or weight of product
b. Sample problems:
(1) Example #1:How many grams of zinc oxide are needed to make 240 grams of a 4% (w/w) zinc oxide ointment?
IF 4 g ZnO /= THEN X g ZnO/
100 g Oint 240 g Oint
NOTE: Because all the units involved in this problem are the same (grams), each unit is labeled as to what it represents. In the first ratio, the desired strength of the ointment is indicated. A four percent zinc oxide ointment contains 4 grams of zinc oxide in each 100 grams of ointment and is labeled to indicate this. Because the question asks, "how many grams of zinc oxide?," the X value must be placed opposite the grams of zinc oxide in the first ratio (see above). The 240 grams of ointment is placed opposite the grams of ointment in the first ratio.
Then: 100 X = 960
X = 9.6 g of zinc oxide
(2) Example #2: How many milliliters of a 5% (w/v) boric acid solution can be made from 20 grams of boric acid?
IF THEN
5 g / = 20 g/
100 ml X ml
5 X = 2000
X = 400
(3) Example #3: How many milliliters of paraldehyde are needed to make
120 ml of a 10% (v/v) paraldehyde solution?
_______ = ________
Answer: 12 ml of paraldehyde
NOTE: Because all of the units involved in this problem are the same (ml), they must be labeled as to what they represent. A 10% paraldehyde solution contains 10 milliliters of paraldehyde in each 100 ml of solution and the first ratio of the proportion should indicate this (see below). The question asks, "How many milliliters of paraldehyde are needed?" therefore, the X value must be placed in the proportion opposite the 10 ml of paraldehyde in the first ratio.
The 120 ml represents final solution.
IF 10 ml paraldehyde/ = THEN X ml paraldehyde/
100 ml of solution 120 ml of solution
100 X = 1200
X = 12 ml of paraldehyde
c. One percent Method: The 1 percent Method is used only to find the amount of active ingredient when the final volume or weight of the preparation is known. This method cannot be used to calculate the amount of preparation that can be made when the percentage strength and the amount of active ingredient is known. 1 percent Method:
Formula:
(1 percent of the total amount of preparation) X (number of percent) = The amount of active ingredient)
NOTE: 1 percent of the total amount of preparation can be found by moving the decimal point on the total amount of preparation two places to the left.
Sample Problems:
(1) Example #1: How many grams of ephedrine sulfate are needed to make
120 ml of a 2% (w/v) ephedrine sulfate solution?
(a) Find the total amount of preparation:
The total amount is 120 ml
(b) Find 1 percent of the total amount:
1 percent of 120 = 1.2
(c) One percent of volume times the number of percent = Amount of
active ingredient.
1.2 X 2 = 2.4 grams of ephedrine sulfate needed.
NOTE: When calculating percentage problems in the metric system, the unit designation is dependent upon whether the active ingredient is a solid or a liquid.
Because ephedrine sulfate is a solid, the unit designation is grams.
(2) Example #2: How many grams of boric acid are needed to make 240 ml
of a 5% (w/v) boric acid solution?
(a) The total amount of preparation is 240 ml.
(b) 1 percent of 240 = 2.4
(c) 2.4 X 5 = 12 grams of boric acid required.
(3) Example #3: How many grams of zinc oxide are needed to make 120 grams of 20% zinc oxide paste?
(a) The total amount of the preparation is __________ grams.
(b) 1 percent of the total amount is ____________.
(c) ______X______ = ________ grams of zinc oxide needed.
Solution:
(a) The total amount of the preparation is 120 grams.
(b) 1 percent of the total amount is 1.2.
(c) 1.2 X 20 = 24 grams of zinc oxide required.