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3. A certain injectable contains 2 mg of a drug per milliliter of solution.
What is the ratio strength (w/v) of the solution?
Solving by ratio and proportion:
Or, solving by dimensional analysis:
500 mL solution per gram of drug = 1 g/500 mL = 1:500 w/v
4. What is the ratio strength (w/v) of a solution made by dissolving five
tablets, each containing 2.25 g of sodium chloride, in enough water to
make 1800 mL?
Solving by ratio and proportion:
Or, solving by dimensional analysis:
160 mL solution per gram of drug = 1 g/160 mL = 1:160 w/v
In solving problems in which the calculations are based on ratio
strength, it is sometimes convenient to translate the problem into one
based on percent strength and to solve it accordingly.
5. How many grams of potassium permanganate should be used in
preparing 500 mL of a 1:2500 w/v solution?
Or,
1:2500 w/v means 1 g of potassium permanganate in 2500 mL of
solution
Solving by ratio and proportion:
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Solving by dimensional analysis:
6. How many milligrams of gentian violet should be used in preparing the
following solution?
1:10,000 means 1 g of gentian violet in 10,000 mL of solution
7. How many milligrams of hexachlorophene should be used in
compounding the following prescription?
1:400 w/w means 1 g of hexachlorophene in 400 g of ointment
Solving by ratio and proportion:
Solving by dimensional analysis:
Simple Conversions of Concentration to “mg/mL”
Occasionally, pharmacists, particularly those practicing in patient care
settings, need to rapidly convert product concentrations expressed as percent
strength, as ratio strength, or as grams per liter (as in IV infusions) to
milligrams per milliliter (mg/mL). These conversions may be made quickly
by using simple techniques. Some suggestions follow.
To convert product percent strength to mg/mL, multiply the percent
strength, expressed as a whole number by 10.
1. Convert 4% (w/v) to mg/mL
To convert product ratio strengths to mg/mL, divide the ratio strength by
1000.
2. Convert 1:10,000 (w/v) to mg/mL
To convert product strengths expressed as grams per liter (g/L) to mg/mL,
convert the numerator of milligrams and divide by the number of
milliliters in the denominator.
3. Convert a product concentration of 1 g per 250 mL to mg/mL
CALCULATIONS CAPSULE
Ratio Strength
The concentrations of dilute pharmaceutical preparations (usually weightin-volume solutions) often are expressed in terms of their ratio strengths.
Ratio strength is another way of expressing percent strength. For
example, a 1% w/v solution and a ratio strength of 1:100 w/v are
equivalent.
The preferable style of a ratio strength is to have the numeric value of
the solute as 1. This is accomplished, when calculating a ratio strength, by
setting up a proportion from the data as:
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In using a ratio strength in a calculations problem, there are two options:
(a) convert it to a percent strength and perform calculations in the usual
manner, or (b) use the ratio strength directly in a problem-solving
proportion.
a. To convert a ratio strength to a percent strength; for example,
1:10,000 w/v:
Solving for x yields percent, by definition (parts per hundred).
b. Problem-solving proportion, for example:
Parts per Million (PPM) and Parts per Billion
(PPB)
The strengths of very dilute solutions are commonly expressed in terms of
parts per million (ppm) or parts per billion (ppb), that is, the number of parts
of the agent per 1 million or 1 billion parts of the whole. For example,
fluoridated drinking water contains added fluoride at levels of between 1 to 4
parts per million (1:1,000,000 to 4:1,000,000) for the purpose of reducing
dental caries. Similar to the other expressions of concentration in this
chapter, the “parts” can be replaced by the units of grams and milliliters
depending on the mixture considered. In the example of fluoridated drinking
water above, 4 ppm (w/v) would designate 4 g of fluorine in 1,000,000 mL
of water.
The presence of trace amounts of contaminants in drinking water, food,
and pharmaceutical ingredients can pose a risk to health and safety. Many
pharmacists serve on community committees and boards that address
environmental issues, and their backgrounds and interest in public health
make them invaluable members of such bodies. Pharmacists have a special
leadership role in providing guidance in the safe disposal of unused and/or
expired medications.4,5 Federal regulations and guidelines have been
established to address this issue.6,
7
Example calculations of parts per million and parts
per billion
1. Express 5 ppm (w/v) of iron in water in percent strength and ratio
strength.
5 ppm = 5 g iron in 1,000,000 mL water
2. The concentration of a drug additive in an animal feed is 12.5 ppm. How
many milligrams of the drug should be used in preparing 5.2 kg of feed?
12.5 ppm = 12.5 g drug in 1,000,000 g feed
Or, solving by dimensional analysis:
3. Arnica Tincture is prepared by dissolving 6 g of arnica in enough solvent
to produce a final volume of 30 mL. However, the arnica in the tincture
is found to contain 550 ppb w/w helenalin which is a toxin found in
arnica. How much helenalin would be contained in 30 mL of the
tincture?
550 ppb w/w = 550 g helenalin in 1,000,000,000 g arnica
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1.
4.
5.
6.
7.
Or, solving by dimensional analysis:
PRACTICE PROBLEMS
Weight-in-Volume Calculations
CLOBEX lotion contains 0.05% w/v clobetasol propionate in 118-mL
containers. Calculate the content of drug, in milligrams.
How many milligrams of ofloxacin are contained in each milliliter of
the dispensed prescription?
Calculate the percent strength of dexamethasone sodium phosphate in
the prescription.
a. How many grams of benzalkonium chloride would be contained in
20 μL of a 50% w/v solution?
b. If the volume in (a) is diluted to 100 mL, what is the percent
strength of benzalkonium chloride in the solution?
A tissue plasminogen activator (TPA) ophthalmic solution is prepared
to contain 25 μg/100 μL.
a. Calculate the percent concentration of TPA in the solution.
b. What volume of a solution containing TPA, 50 mg/50 mL, should
be used to prepare each 100 μL of the ophthalmic solution?
How many milligrams of methylparaben are needed to prepare 8
fluidounces of a solution containing 0.12% w/v of methylparaben?
A pharmacist emptied the contents of eight capsules, each containing
300 mg of clindamycin phosphate, into a liquid vehicle to prepare 60
9.
10.
11.
12.
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14.
mL of a suspension. Calculate the percent strength of clindamycin
phosphate in the preparation.
How many milligrams of the active constituent would be present in
each drop of the ophthalmic solution if the dropper service delivers 20
drops per milliliter?
a. 0.25 mg
b. 25 mg
c. 0.025 mg
d. 1.25 mg
A formula for an antifungal shampoo contains 2% w/v ketoconazole.
How many grams of ketoconazole would be needed to prepare 240 mL
of the shampoo?
The biotechnology drug interferon gamma-1b (ACTIMMUNE)
contains 100 mcg/0.5 mL. Calculate the percent strength of the
solution.
Filgrastim (NEUPOGEN) prefilled syringes contain 480 mcg of active
constituent in each 0.8 mL. The equivalent concentration is:
a. 0.6%
b. 0.384 mg/mL
c. 0.06%
d. 0.6 g/mL
Levofloxacin infusion solution contains 5 mg/mL of levofloxacin and
5% of dextrose. How much of each would be delivered to a patient
upon the administration of a 100-mL injection?
a. 5 g levofloxacin and 5 g dextrose
b. 50 mg levofloxacin and 5 g dextrose
c. 500 mg levofloxacin and 500 mg dextrose
d. 0.5 g levofloxacin and 5 g dextrose
An injection contains, in each milliliter, 60 μg of darbepoetin alfa
(ARANESP), 0.05 mg of polysorbate 80, and 8.18 mg of sodium
chloride. Calculate the percent of each in the injection.
An injection of adalimumab (HUMIRA) contains 40 mg/0.8 mL.
Calculate the percent concentration of the injection.
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16.
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21.
22.
a. What is the percent strength of erythromycin lactobionate in the
prescription?
b. If glycerin has a specific gravity of 1.25, what is its percent
concentration in the prescription?
CIPRODEX, an otic suspension, contains 0.3% w/v ciprofloxacin and
0.1% w/v dexamethasone in 7.5-mL drop containers. Calculate the
quantities of each agent based on mg/mL.
A 180-mL bottle of an oral solution contains sodium oxybate, 0.5
g/mL. Calculate (a) the quantity of sodium oxybate, in grams, in the
bottle and (b) the percent strength of sodium oxybate in the solution.
In the preparation of an intravenous infusion, a vial containing 115 mg
of drug is diluted to 5 mL with sodium chloride for injection. Then, the
contents of the vial are added to 110 mL of an infusion solution.
Calculate the drug strength of the final infusion in (a) mg/mL, (b)
percent strength, and (c) ratio strength.
An ophthalmic solution contains tafluprost, 0.0015% w/v, available in
0.3-mL containers for single use. Calculate (a) the quantity of
tafluprost, in micrograms, in each container and (b) the number of
single-use containers that the manufacturer may prepare from each 1 g
of drug.
How much of a 70% w/v sorbitol syrup can be prepared from 2 oz. of
sorbitol powder?
Calculate the percentage strength of an injection that contains 2 mg of
hydromorphone hydrochloride in each milliliter of injection.
VIRAMUNE oral suspension contains 1% w/v of nevirapine.
Calculate the milligrams of nevirapine present in a 240-mL bottle of
the suspension.
Calculate the strength of misoprostol in the prescription.
a. 2.4% w/v misoprostol
b. 0.0002% w/v misoprostol
c. 0.024 mg/mL misoprostol
25.
26.
27.
28.
29.
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d. 2.4 mcg/mL misoprostol
Calculate the percentage concentration of fentanyl citrate in the
prescription.
Bepotastine besilate (BEPREVE) ophthalmic solution contains 1.5%
w/v of the therapeutic agent. Express this concentration in mg/mL.
If 100 mL of a solution for patient-controlled anesthesia contains 200
mg of morphine sulfate and 8 mg of droperidol, calculate the
percentage strength of each of these ingredients in the solution.
Oxycodone hydrochloride oral concentrate solution contains 20
mg/mL. If a dose of 0.75 mL is added to 30 mL of juice prior to
administration, calculate (a) the milligrams of oxycodone
hydrochloride administered and (b) the percent concentration of
oxycodone hydrochloride in the drink, assuming that volumes are
additive.
Calculate the percent strength of morphine sulfate in an injectable
solution with a concentration of 10 mg/mL.
A topical solution contains 3% w/v hydroquinone. How many liters of
the solution can be prepared from 30 g of hydroquinone?
Volume-in-Volume Calculations
What is the percent strength (v/v) if 225 g of a liquid having a specific
gravity of 0.8 are added to enough water to make 1.5 L of the solution?
Cyclosporine (NEORAL) capsules contain a dispersion of 25 mg of
cyclosporine in a hydroalcoholic vehicle. The labeled content of
absolute alcohol content is “11.9% v/v equivalent to 9.5% w/v.” From
these data, calculate the specific gravity of absolute alcohol.
A lotion vehicle contains 15% v/v of glycerin (sp gr 1.25). How much
glycerin should be used in preparing 5 gallons of the lotion?
a. 2271 g glycerin
b. 3339.7 mL glycerin
c. 2671.8 g glycerin
d. 3548.4 g glycerin
The formula for 1 L of an elixir contains 0.25 mL of a flavoring oil.
What is the percent strength of the flavoring oil in the elixir?
How much 95% v/v ethanol solution can be prepared from one pint of
pure ethanol?
Weight-in-Weight Calculations
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