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Файл:Ординатура / Хирургия / Библиотека им академика М.И. Перельмана / Книга_5576_Библиотеки_им_академика_М_И_Перельмана
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To double the strength, 12 mg of additional chlorpheniramine maleate would
be required.
In products containing a volatile liquid, evaporation may cause an
increase in concentration of the active ingredient. The volume of the
preparation decreases while the amount of drug remains the same, thus
resulting in a higher concentration of the drug.
Flexible Collodion USP contains 2% w/w camphor and has a specific
gravity of 0.78. The cap is broken on a one-pint bottle and most of the ether
evaporates, leaving a volume of 135 mL. What is the concentration of
camphor in the evaporated solution expressed as % w/v?
CASE IN POINT 15.1
A pharmacist received a prescription for 100 mL of a cefuroxime axetil
suspension to contain 300 mg of drug in each 5 mL. The pharmacist has
100 mL of a suspension containing 250 mg/5 mL and also has 250-mg
scored tablets of the drug. How many tablets should be pulverized and
added to the suspension to achieve the desired strength? Assume no
increase in the volume of the suspension.
A SECOND LOOK
The pharmacist observed that after adding the pulverized tablets, the
suspension measured 102 mL in volume. Calculations revealed that rather
than the prescribed drug strength of 300 mg/5 mL, there were 294.12
mg/5 mL. What could the pharmacist do to bring the suspension to the
desired strength?
Stock Solutions
Stock solutions are concentrated solutions of active (e.g., drug) or inactive
(e.g., colorant) substances and are used by pharmacists as a convenience to
prepare solutions of lesser concentration. In solving these problems, the
equation presented in the previous section can be used, or the amount of
drug needed to prepare a formulation can be determined, then the amount of
stock solution to supply the necessary amount of drug can be calculated.
Example calculations of stock solutions
1. How many milliliters of a 10% w/v stock solution should be used in
preparing 1 gallon of a 0.05% w/v solution?
Or by solving by equation:
2. How many milliliters of a 1% w/v stock solution of a certified red dye
should be used in preparing 4000 mL of a mouthwash that is to contain
1:20,000 w/v of the certified red dye as a coloring agent?
Some interesting calculations are used in pharmacy practice in which
the strength of a diluted portion of a solution is defined, but the strength
of the concentrated stock solution used to prepare it must be
determined. This may be further explained by the need of a pharmacist
to prepare and dispense a concentrated solution of a drug and direct the
patient to use a specific household measure of a solution (e.g., 1
teaspoonful) in a specified volume of water (e.g., a pint) to make the
solution of the desired concentration (e.g., for irrigation or soaking).
This permits the dispensing of a relatively small volume of liquid,
enabling a patient to prepare relatively large volumes as needed, rather
than carrying home large volumes of a diluted solution from a
pharmacy.
3. How much drug should be used in preparing 50 mL of a stock solution
such that 5 mL diluted to 500 mL will yield a 1:1000 w/v solution?
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Thus, 0.5 g of drug would be in the 500 mL of the 1:1000 w/v diluted
solution, and importantly, the source of that 0.5 g of drug is the 5 mL of
the stock solution. If 0.5 g of drug is in each 5 mL of the stock solution,
calculate the grams of drug needed to prepare the 50 mL of stock
solution:
The accompanying diagram demonstrates the problem.
4. How many grams of sodium chloride should be used in preparing 500
mL of a stock solution such that 50 mL diluted to 1000 mL will yield a
0.3% w/v solution for irrigation?
which is also the amount in 50 mL of the stock solution.
Thus, the amount of sodium chloride in 500 mL of the stock solution is:
5. How many milliliters of a 17% w/v concentrate of benzalkonium chloride
should be used in preparing 100 mL of a stock solution such that 5 mL
diluted to 60 mL will yield a 0.13% w/v solution of benzalkonium
chloride?
which is also the amount in 5 mL of the stock solution.
Thus, the amount of benzalkonium chloride in 100 mL of the stock
solution is:
and the amount of the 17% w/v concentrate to use is:
Concentrated acids are a special type of stock solutions utilized in preparing
diluted acids. These acid dilutions can cause some confusion because the
strength of a concentrated acid is most commonly expressed as percent
weight-in-weight, unlike most liquid solutions that are expressed as a
weight-in-volume strength. For example, concentrated lactic acid, used in
some topical formulations, has a strength of 90% w/w lactic acid. A
significant error in measurement of the amount of acid to be used in a
compounded solution would occur if the strength of the acid is mistakenly
read as 90% w/v. Because concentrated acids are liquids and measured by
volume, the specific gravity must be employed to convert the weight of the
concentrated acid to the corresponding volume, as shown in the following
problem.
How many milliliters of 70% w/w concentrated glycolic acid (sp.gr. =
1.27) would be needed to prepare 2 fl.oz. of a 7.25% w/v solution?
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Dilution and Fortification of Solids and Semisolids
1. If 30 g of a 1% w/w hydrocortisone ointment are mixed with 12 g of a
nonmedicated ointment base, what would be the resulting concentration
of hydrocortisone in the mixture?
2. As a part of a clinical study, a pharmacist is asked to prepare
modifications of standard 22 g 2% w/w mupirocin ointments by adding
the needed quantities of either mupirocin powder or a nonmedicated
ointment base. Required for the study are a 1.75% w/w mupirocin
ointment and a 2.25% w/w mupirocin ointment. For each modified
ointment, calculate the quantity of component to add to a standard
ointment.
For the 1.75% w/w ointment:
Consider the following:
Dilution with the nonmedicated ointment base is required.
The quantity of mupirocin in the standard ointment is 0.44 g (22 g × 2%
w/w).
From 0.44 g of mupirocin, 25.14 g of a 1.75% w/w mupirocin ointment
may be prepared (0.44 g X 100 g / 1.75 g = 25.14 g.
Because the standard ointment weighs 22 g, the addition of 3.14 g of
nonmedicated ointment base is required (25.14 g − 22 g = 3.14 g).
Proof: 0.44 g (mupirocin) in 25.14 g (diluted ointment) = 1.75% w/w
For the 2.25% w/w ointment:
Consider the following:
Fortification with mupirocin powder is required.
22 g of the 2% w/w mupirocin ointment contains 0.44 g of mupirocin
(22 g × 2% w/w).
The remainder, 21.56 g (22 g − 0.44 g), is the nonmedicated portion
(ointment base) of the standard ointment.
If the fortified ointment is to contain 2.25% w/w mupirocin, the
nonmedicated portion, or 21.56 g, would then represent 97.75% of the
whole.
If 21.56 g is equal to 97.75% of the whole, 100% would be equal to
22.056 g (21.56 g × 100%/97.75%), and the difference, 0.496 g (22.056
g − 21.56 g), is the total required mupirocin in the final product.
Because the original ointment contains 0.44 g of mupirocin, the
addition of 0.056 g of mupirocin is required.
Proof: 0.496 g (mupirocin) in 22.056 g (fortified ointment) = 2.249% ≈
2.25% w/w
NOTE: This problem should be reworked later in the chapter using the
alligation alternate method.
Alligation
Alligation is an arithmetical method of solving problems that involve the
mixing of solutions or mixtures of solids of different percentage strengths.
When utilizing alligation in solving mixtures of liquids, the volumes must be
additive, such as in mixing aqueous solutions, or the final volume of the
mixture must be known.
Alligation medial
This is a method by which the “weighted average” strength of a mixture of
two or more substances of known quantity and concentration may be
calculated.
Example Calculations Using Alligation Medial
1. What is the percentage of zinc oxide (ZnO) in an ointment prepared by
mixing 200 g of 10% ointment, 50 g of 20% ointment, and 100 g of 5%
ointment?
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In some problems, the addition of a diluent or vehicle must be
considered and treated as zero percent strength, as in the following
example.
2. What is the percentage strength of sucrose in a mixture of 500 mL of an
aqueous solution containing 40% w/v sucrose, 400 mL of a second
aqueous solution containing 21% w/v sucrose, and 100 mL of purified
water to make a total of 1000 mL?
3. A pharmacist–herbalist wishes to consolidate the following assayed
batches of Gingko biloba leaves: 200 g containing 22% w/w glycosides,
150 g containing 26% w/w glycosides, and 80 g containing 27% w/w
glycosides. Calculate the percent of glycosides in the combined
mixture.
Alligation alternate
This is a method used to determine the quantities of ingredients of differing
strengths needed to make a mixture of a desired strength. It involves
matching pairs of ingredients, one higher in strength and one lower in
strength than the desired strength, which lies somewhere in between. As
shown in the following example, the desired strength is placed in the center
of the working diagram.
Example Calculations Using Alligation Alternate
1. In what proportion should 8% w/w and 2.5% w/w calamine ointments be
mixed to make 5% w/w calamine?
Note that the difference between the strength of the stronger component
(8%) and the desired strength (5%) indicates the number of parts of the
weaker to be used (3 parts), and the difference between the desired
strength (5%) and the strength of the weaker component (2.5%)
indicates the number of parts of the stronger to be used (2.5 parts).
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The mathematical validity of this relationship can be demonstrated.
Given these data, the ratio of x to y may be derived algebraically as
follows:
Given a = 8%, b = 2.5%, and c = 5%, we may therefore solve the
problems as follows:
The result can be shown to be correct by alligation medial:
The customary layout of alligation alternate, used in the subsequent
examples, is a convenient simplification of the preceding diagram.
2. In what proportion should 20% benzocaine ointment be mixed with an
ointment base to produce a 2.5% benzocaine ointment?
Note that an “ointment base” has no drug content and thus is
represented by a zero in the scheme.
3. A hospital pharmacist wants to use three lots of zinc oxide ointment
containing, respectively, 50%, 20%, and 5% of zinc oxide. In what
proportion should they be mixed to prepare a 10% zinc oxide ointment?
Note that pairs must be used in each determination, one lower and one
greater in strength than the desired strength.
Other answers are possible, of course, by using alternate pairings.
4. In what proportions may a manufacturing pharmacist mix 20%, 15%,
5%, and 3% zinc oxide ointments to produce a 10% ointment?
Each of the weaker lots is paired with one of the stronger to give the
desired strength, and because we may pair them in two ways, we may
get two sets of correct answers.
5. How many milliliters each of a 50% w/v dextrose solution and a 5% w/v
dextrose solution is required to prepare 4500 mL of a 10% w/v
solution?
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