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25.
27.
28.
29.
If 50 glycerin suppositories are made from the following formula,
how many milliliters of glycerin, having a specific gravity of 1.25,
would be used in the preparation of 96 suppositories?
26.
The specific gravity of light mineral oil is 0.85 and that of
polysorbate 80 is 1.08. Calculate the milliliters of each needed to
fill the prescription.
A formula for an anesthetic ointment is:
Polyethylene glycol 400 is a liquid, sp gr 1.13; benzocaine and
polyethylene glycol 3350 are powders. How many milliliters of
polyethylene glycol 400 would be used in the formula?
Prior to a computerized tomographic scan (CT scan) of the
abdomen, a patient is instructed to drink 450 mL of a barium
suspension. If the suspension has a specific gravity of 1.05,
calculate the weight of the suspension.
Using Specific Gravity to Determine Weight/Volume Costs
An international supplier sells castor oil at $1200 a metric ton
(1000 kg). Using the information in Table 5.1 and the previously
30.
1.
2.
3.
4.
learned conversion factors, calculate the corresponding price of a
pint of the oil.
The formula for 1000 g of polyethylene glycol ointment calls for
600 g polyethylene glycol 400. At $19.15 per pint, what is the cost
of the polyethylene glycol 400, specific gravity 1.140, needed to
prepare 4000 g of the ointment?
CALCQUIZ
5.A.Syrup NF is prepared by dissolving 850 g of sucrose in sufficient
purified water to make 1000 mL of syrup. Syrup has a specific gravity
of 1.31. How many milliliters of water are used to prepare a liter of
syrup?
5.B.A saturated solution of potassium iodide contains, in each 100
mL, 100 g of potassium iodide. The solubility of potassium iodide is 1
g in 0.7 mL of water. Calculate the specific gravity of the saturated
solution.
5.C.Cocoa butter (theobroma oil) is used as a suppository base. It
is a solid at room temperature, melts at 34°C, and has a specific
gravity of 0.86. If a formula for medicated suppositories calls for 48
mL of theobroma oil, how many grams are equivalent?
ANSWERS TO “CASE IN POINT” AND
PRACTICE PROBLEMS
Case in Point 5.1
Quantity of lactic acid needed to fill prescription : 1.5 g
Practice Problems
0.812 g/mL
8.933 g/mL
1.133
1.285
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1.30
1.25
0.97
0.86
1.05
0.950
1.007
0.959
82.2 g solution
28.11 mL fish oil
6.81 mL methyl salicylate
a. 79 g acetone
b. 87 g liquid petrolatum
c. 131 g syrup
d. 159 g nitroglycerin
e. 1360 g mercury
9.2 kg
4.86 kg sorbitol solution
1646.48 g mineral oil
a. 108.7 mL peanut oil
b. 104.17 mL castor oil
c. 92.59 mL polysorbate 80
d. 58.82 mL phosphoric acid
e. 7.35 mL mercury
405.36 mL benzyl benzoate
1.54 g liquefied phenol
63.04 g propylene glycol
258.75 g
44.44 mL polysorbate 80
139.78 mL glycerin
11.76 mL light mineral oil
0.93 mL polysorbate 80
530.97 mL polyethylene glycol 400
472.5 g barium suspension
$0.54
30.
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2.
3.
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5.
$85.23
References
US Pharmacopeial Convention, Inc. General Notices and Requirements. 8.240 Weights
and Measures. United States Pharmacopeia 42 National Formulary 37 [book online].
Rockville, MD: US Pharmacopeial Convention, Inc.; 2019.
American Society of Health-System Pharmacists. ASHP guidelines on the safe use of
automated compounding devices for the preparation of parenteral nutrition admixtures.
American Journal of Health-System Pharmacy 2000;57:1343–1348.
MedlinePlus. Urine specific gravity. Available at:
http://www.nlm.nih.gov/medlineplus/ency/article/003587.htm. Accessed March 7, 2020.
The Internet Pathology Laboratory for Medical Education. Urinalysis tutorial. Available at:
http://library.med.utah.edu/WebPath/TUTORIAL/URINE/URINE.html. Accessed March
7, 2020.
Allen LV Jr, ed. Compounding ophthalmic preparations. International Journal of
Pharmaceutical Compounding 1998;2:58.
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6
Percent Strength, Ratio Strength,
and Other Expressions of
Concentration
OBJECTIVES
Upon successful completion of this chapter, the student will be able to:
Perform calculations based on percent weight in volume, percent
volume in volume, and percent weight in weight.
Perform calculations based on ratio strength.
Convert percent strength to ratio strength and ratio strength to percent
strength.
Utilize other expressions of concentration in calculations, such as parts
per million and mg/mL.
Percent
The term percent and the corresponding “%” sign indicate the number of
parts in a hundred. The quantity also may be expressed as a common or
decimal fraction. Thus, 50%, 50/100, and 0.5 are equivalent.
For the purposes of computation, percents are usually changed to
equivalent decimal fractions. This change is made by dropping the percent
sign (%) and dividing the expressed numerator by 100. Thus, 12.5% =
12.5/100, or 0.125, and 0.05% = 0.05/100, or 0.0005. We must not forget that
in the reverse process (changing a decimal to a percent), the decimal is
multiplied by 100 and the percent sign (%) is affixed.
Percent is an essential component of pharmaceutical calculations. It is
used to (a) express the strength of a component in a pharmaceutical
preparation as well as to (b) determine the quantity of a component to use
when a certain percent strength is desired.
Percent Preparations
The percent concentrations of active and inactive constituents in various
types of pharmaceutical preparations are defined as follows by the United
States Pharmacopeia1:
Percent weight in volume (w/v) expresses the number of grams of a
constituent in 100 mL of solution or liquid preparation and is used
regardless of whether water or another liquid is the solvent or vehicle.
Expressed as: ________ % w/v.
Percent volume in volume (v/v) expresses the number of milliliters of a
constituent in 100 mL of solution or liquid preparation. Expressed as:
_________ % v/v.
Percent weight in weight (w/w) expresses the number of grams of a
constituent in 100 g of solution or preparation. Expressed as:
__________ % w/w.
The term percent, or the symbol %, when used without qualification means:
For solutions or suspensions of solids in liquids, percent weight in
volume
For solutions of liquids in liquids, percent volume in volume
For mixtures of solids or semisolids, percent weight in weight
For solutions of gases in liquids, percent weight in volume
Figures 6.1 and 6.2 show product labels for different forms of clindamycin
phosphate (CLEOCIN T), both 1% in strength. Figure 6.1 is the label of a
topical solution containing active ingredient, 10 mg/mL (1% w/v), whereas
Figure 6.2 is the label of a topical gel containing active ingredient, 10 mg/g
(1% w/w).
FIGURE 6.1 A product label depicting the strength of the active
ingredient on a w/v basis, 1% or 10 mg/mL. (Source:
https://dailymed.nlm.nih.gov/dailymed/drugInfo.cfm?
setid=4a3901a4-194f-4a15-9c85-3d0982afcf31. Courtesy of Pfizer,
Inc.)
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FIGURE 6.2 A product label depicting the strength of the active
ingredient on a w/w basis, 1% or 10 mg/g. (Source:
https://dailymed.nlm.nih.gov/dailymed/drugInfo.cfm?
setid=4a3901a4-194f-4a15-9c85-3d0982afcf31. Courtesy of Pfizer,
Inc.)
Special Considerations in Percent Calculations
In general, the physical nature of the ingredients in a pharmaceutical
preparation determines the basis of the calculation. That is, a powdered
substance dissolved or suspended in a liquid vehicle would generally be
calculated on a weight-in-volume basis; a powdered substance mixed with a
solid or semisolid, such as an ointment base, would generally be calculated
on a weight-in-weight basis; and a liquid component in a liquid preparation
would be calculated on a volume-in-volume basis. If the designation of the
term of a calculation (e.g., w/v, w/w, or v/v) is not included in a problem, the
appropriate assumption must be made.
The use of percent to indicate the strength of a product generally is
limited nowadays to certain topical products, such as ointments, creams, and
eyedrops. However, there are some notable exceptions, such as 5% dextrose
injection, used in intravenous infusions. In most other instances, product
strengths are expressed in specific quantitative terms, such as 10-mg tablets
and 2-mg/mL injections. [The problems in this chapter take certain liberties
from this standard practice in order to afford a broad experience in the
calculations process.]
Percent Weight-in-Volume
In calculating percent weight-in-volume (w/v) problems, the percent strength
of the preparation can be used to determine the amount of active ingredient
in a certain volume of the liquid formulation, or to calculate the volume of
liquid formulation to deliver a certain amount of an ingredient. Likewise, the
amount of the active ingredient in grams and the volume of the mixture in
milliliters can be used to determine the percent strength of the preparation.
The units of grams and milliliters must be indicated appropriately as shown
in the following example problems.
Examples of weight-in-volume calculations
1. How many grams of dextrose are required to prepare 4000 mL of a 5%
w/v solution?
5% w/v = 5 g of dextrose in 100 mL of solution
Solving by ratio and proportion:
Or, solving by dimensional analysis:
2. How many grams of potassium permanganate should be used in
compounding the following prescription?
Solving by ratio and proportion:
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Or, solving by dimensional analysis:
3. A cyclosporine ophthalmic emulsion (RESTASIS) contains 0.05% w/v
cyclosporine in 0.4-mL vials. Calculate the content of cyclosporine, in
micrograms, per vial.
4. The topical antibacterial solution HIBICLENS contains 4% w/v
chlorhexidine gluconate in 4-fluidounce containers. Calculate the
content of chlorhexidine gluconate, in grams.
5. Bimatoprost ophthalmic solution (LUMIGAN) is available in 2.5-mL
containers and contains 0.03% w/v bimatoprost. How much solution
can be prepared from 150 mg of bimatoprost, and how many 2.5-mL
containers can be filled?
6. An ophthalmic solution contains 0.1 mg of travoprost (TRAVATAN Z) in
2.5-mL containers. Calculate the percent strength of travoprost in the
solution.
Note: The amount of drug in grams can be divided by the volume of solution
in milliliters and simply multiplied by 100 to convert to percent strength.
Percent Volume-in-Volume
Liquids are usually measured by volume, and the percent strength indicates
the number of parts by volume of an ingredient contained in the total volume
of the liquid preparation. To minimize the risk of errors, all volumes should
be converted to milliliters, and quantities should be labeled with the
ingredient or preparation as shown in the example problems that follow.
Examples of volume-in-volume calculations
1. How many milliliters of liquefied phenol should be used in compounding
the following prescription?
2.5% v/v = 2.5 mL of liquefied phenol in 100 mL of solution
Solving by ratio and proportion:
Or, solving by dimensional analysis:
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