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Файл:Ординатура / Хирургия / Библиотека им академика М.И. Перельмана / Книга_5334_Библиотеки_им_академика_М_И_Перельмана
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2. In preparing 250 mL of a certain lotion, a pharmacist used 4 mL of
liquefied phenol. What was the percent (v/v) of liquefied phenol in the
lotion?
Note: The amount of liquefied phenol in milliliters can be divided by
the volume of solution in milliliters and simply multiplied by 100 to
convert to percent strength.
3. A solution is prepared by diluting 800 g of a liquid with a specific gravity
of 0.8 in enough water to make 4000 mL. What is the percent strength
v/v of this solution?
4. If a veterinary liniment contains 30% v/v of dimethyl sulfoxide (DMSO),
how many milliliters of the liniment can be prepared from 1 lb of
dimethyl sulfoxide (sp gr 1.10)?
Or, solving by dimensional analysis:
Percent Weight-in-Weight
Percent weight-in-weight indicates the number of parts by weight of active
ingredient contained in the total weight of the preparation. As with
calculations in the previous section, all weights should be converted to
grams, and quantities should be labeled with the ingredient or preparation to
minimize the risk of errors. Furthermore, particular attention should be paid
to determining the final weight of the preparation, because the ingredients
may have to be added to calculate the total weight of some formulations
before calculating the percent strength of an ingredient in the formula.
Examples of weight-in-weight calculations
1. A hydrocortisone cream contains 1% w/w hydrocortisone. Calculate the
grams of hydrocortisone used to prepare each 15-g tube of product.
Solving by ratio and proportion:
Or, solving by dimensional analysis:
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2. FINACEA gel contains 15% w/w azelaic acid in 50-g tubes. How much
azelaic acid is in each tube of product? How much gel base would be
contained in each tube?
3. ANDROGEL 1.62% is a testosterone gel for topical use. Calculate the
grams of gel required to provide a 40.5-mg dose of testosterone.
Or, solving by dimensional analysis:
Proof:
4. How many grams of a drug substance are required to make 120 mL of a
20% (w/w) solution having a specific gravity of 1.15?
Or, solving by dimensional analysis:
Sometimes in a weight-in-weight calculation, the weight of one
component is known but not the total weight of the intended
preparation. This type of calculation is performed as demonstrated by
the following example.
5. How many grams of a drug substance should be added to 240 mL of
water to make a 4% (w/w) solution?
100% – 4% = 96% (by weight) of water
240 mL of water weigh 240 g
It is usually impossible to prepare a specified volume of a solution or
liquid preparation of given weight-in-weight percent strength because
the volume displaced by the active ingredient cannot be known in
advance. If an excess is acceptable, we may make a volume somewhat
more than that specified by taking the given volume to refer to the
solvent or vehicle and from this quantity calculating the weight of the
solvent or vehicle (the specific gravity of the solvent or vehicle must be
known). Using this weight, we may follow the method just described to
calculate the corresponding weight of the active ingredient needed.
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6. How should you prepare 100 mL of a 2% (w/w) solution of a drug
substance in a solvent having a specific gravity of 1.25?
Therefore, dissolving 2.55 g of drug substance in 125 g (or 100 mL) of
solvent will produce the desired 2% w/w concentration, but the final
volume will be >100 mL depending on the volume displacement of the
drug.
7. If 1500 g of a solution contains 75 g of a drug substance, what is the
percent strength (w/w) of the solution?
Or, solving by dimensional analysis:
8. If 5 g of boric acid are added to 100 mL of water, what is the percent
strength (w/w) of the solution?
9. If 1000 mL of syrup with a specific gravity of 1.313 contain 850 g of
sucrose, what is its percent strength (w/w)?
10. A 60-g tube of DESONATE gel contains 0.05% w/w desonide. Calculate
the concentration of desonide on a mg/g basis.
11. DIPROLENE lotion contains 0.05% w/w betamethasone dipropionate.
If the specific gravity of the lotion is 0.96, how many milligrams of
betamethasone dipropionate would be present in a 60-mL container of
the lotion?
12. What weight of a 5% (w/w) solution can be prepared from 2 g of active
ingredient?
Or, solving by dimensional analysis:
13. How many milligrams of hydrocortisone (HC) should be used in
compounding the following prescription?
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14. How many grams of benzocaine should be used in compounding the
following prescription?
2 g × 24 = 48 g, total weight of mixture
48 g × 0.02 = 0.96 g benzocaine
Or, solving by dimensional analysis:
CALCULATIONS CAPSULE
Percent Concentration
The amounts of therapeutically active and/or inactive ingredients in certain
types of pharmaceutical preparations are expressed in terms of their
percent concentrations.
Unless otherwise indicated:
a. Solid components in liquid preparations have weight-in-volume
relationships with the percent strength indicated as follows:
This expression can then be used to determine the amount of
component in a given volume of preparation, or the volume of
preparation needed to provide a given amount of component.
b. Liquid components in liquid preparations have volume-in-volume
relationships with the percent strength indicated as follows:
c. Solid or semisolid components in solid or semisolid preparations
have weight-in-weight relationships with the percent strength
indicated as follows:
Use of Percent in Compendial Standards
Percent is used in the United States Pharmacopeia to express the degree of
tolerance permitted in the purity of single-chemical entities and in the labeled
quantities of ingredients in dosage forms. For instance, according to the
United States Pharmacopeia,2 “Aspirin contains not less than 99.5% and not
more than 100.5% of C9H8O4 (pure chemical aspirin) calculated on the dried
basis.” Further, “Aspirin Tablets contain not less than 90.0% and not more
than 110.0% of the labeled amount of C9H8O4.” Although dosage forms are
formulated with the intent to provide 100% of the quantity of each ingredient
declared on the label, some tolerance is permitted to allow for analytic error,
unavoidable variations in manufacturing and compounding, and for
deterioration to an extent considered insignificant under practical conditions.
The following problem demonstrates calculations involving percent in
compendial standards.
If ibuprofen tablets are permitted to contain not less than 90% and not
more than 110% of the labeled amount of ibuprofen, what would be the
permissible range in content of the drug, expressed in milligrams, for
ibuprofen tablets labeled 200 mg each?
CASE IN POINT 6.1
3
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A patient with myasthenia gravis has undergone treatment to separate and
remove certain abnormal antibodies and other unwanted elements from
the blood (plasmapheresis). The desired red blood cell component is then
returned back to the blood, but the patient has lost protein and blood
volume.
The patient’s physician orders 2000 mL of a 5% w/v solution of
albumin in 0.9% w/v sodium chloride injection to replace lost protein and
fluid.
In filling the order, the pharmacist decides to use a piece of automated
equipment to compound the mixture. The equipment must be programmed
with the specific gravities of the solutions being mixed. The pharmacist
selects to use a 25% w/v albumin solution as the source of the albumin
plus a 0.9% w/v sodium chloride injection.
From the literature, the pharmacist finds that 0.9% w/v sodium
chloride has a specific gravity of 1.05. Using a precise 25-mL pycnometer
with a tare weight of 28 g, the pharmacist fills it with the 25% w/v
albumin solution and determines the weight of the flask and its content to
be 58 g.
a. What is the specific gravity of the albumin solution?
b. How many milliliters of the 25% w/v albumin solution are needed
to make 2000 mL containing 5% w/v albumin?
c. What is the weight of the 25% w/v albumin solution needed to fill
the order?
d. If the pharmacist mixed the required number of milliliters of the
25% w/v albumin solution with a sufficient 0.9% w/v sodium
chloride injection to make the required 2000-mL mixture, what
would be the specific gravity of the resultant solution? (Assume
volumes are additive.)
CASE IN POINT 6.2
3
A pharmacist receives the following prescription but does not have
hydrocortisone powder on hand. However, the pharmacist does have an
injection containing 100 mg of hydrocortisone per milliliter of injection. A
search of the literature indicates that the injection has a specific gravity of
1.5.
a. How many milligrams of hydrocortisone are needed to fill the
prescription?
b. How many milliliters of the hydrocortisone injection would provide
the correct amount of hydrocortisone?
c. How many grams of cold cream are required?
Ratio Strength
Percent strength itself indicates a ratio; that is, a solution which is 5% in
strength represents the ratio of 5 parts in 100 parts, or the ratio 5:100. In
expressing ratio strength, it is customary to have the first figure a 1; thus,
5:100 would be reduced to 1:20.
When a ratio strength, for example, 1:1000, is used to designate a
concentration, it is to be interpreted as follows:
For solids in liquids = 1 g of solute or constituent in 1000 mL of
solution or liquid preparation.
For liquids in liquids = 1 mL of constituent in 1000 mL of solution or
liquid preparation.
For solids in solids = 1 g of constituent in 1000 g of mixture.
The ratio and percent strengths of any solution or mixture of solids are
proportional, and either is easily converted to the other by the use of
proportion or dimensional analysis.
Example calculations using ratio strength
1. Express 0.02% as a ratio strength.
2. Express 1:4000 as a percent strength.
NOTE: To change ratio strength to percent strength, it is sometimes
convenient to “convert” the last two zeros in a ratio strength to a percent
sign (%) and change the remaining ratio first to a common fraction and
then to a decimal fraction in expressing percent:
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