Alligation Danielle DelVillano PharmD Objectives Perform calculations for altering product strength by dilution concentration or fortification Perform calculations for the preparation and use of stock solutions ID: 612438
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Slide1
Pharmaceutical Calculations: Altering Product Strength, Use of Stock Solutions, and Alligation
Danielle DelVillano, Pharm.D.Slide2
Objectives
Perform calculations for altering product strength by dilution, concentration, or fortification
Perform calculations for the preparation and use of stock solutions
Apply
alligation
medial and
alligation
alternate in problem solvingSlide3
Keep in mind
Solution = solute + solvent
If
w/v
– solute in
g
/
solution
in
mL
If
v/v
– solute in
mL
/
solute+solvent
in
mL
If
w/w
– solute in
g
/
solute+solvent
in
g
Changing
x
% to fraction
X
g
/ 100
mL
Changing 1:x ratio strength to fraction
1
g
/
x
mLSlide4
Altering Product Strength
Concentrated
Addition of active ingredient
Diluted
Addition of
diluent
Fortification
Addition of a calculated quantity of additional therapeutic agent Slide5
Relationship between Strength and Total Quantity
If mixture is diluted to twice its original quantity, then strength will be reduced by one half
Start with 100
mL
of 5% solution (5
g
drug)
Add 100
mL
, now 200
mL
of 2.5% solution (5
g
drug)
If a mixture is concentrated by evaporation to one half its original quantity, the strength will be doubled
Start with 100
mL
of 5% solution (5
g
drug)
Evaporate, now 50
mL
of 10% solution (5
g
drug)Slide6
Several Methods for Solving
Inverse proportions
Q1C1 = Q2C2
Determine the quantity of active solute needed and then calculate the quantity of available solution to provide needed amount
“Box method”Slide7
Box method
Always keep it the same
When setting it up
Fill in everything from the problem
Circle what you are trying to solve for
Keep your units
Total
amount of solution
Strength
(% or ratio)
Amount of soluteSlide8
Problem 1
If 500
mL
of a 15%
v/v
solution are diluted to 1500
mL
, what will be the percentage strength (
v/v
)?
500
mL
solution
15%
75
g
drug
1500
mL solution5%75 g drug
Dilute with 1000 mL water
15 g = x g 100 mL 500 mL x = 75 g drug
This stays the same
x
g
=
75
g
100
mL
1500
mL
x
=
5 %Slide9
Problem 2
If a syrup containing 65%
w/v
of sucrose is evaporated to 85% of its volume, what percentage (
w/v
) of sucrose will it contain?
(No volume given,
chose your own) 100
mL
65%
65
g
drug
(0.85 * 100
mL
=) 85
mL
76.5%
65 g drug
Evaporate to 0.85 orioinal vol
This stays the same 65 g = x g 100 mL 100 mL x =
65 g drug
x
g
=
65
g
100
mL
85
mL
x
=
76.5% Slide10
Problem 3
How many milliliters of a 1:5000
w/v
solution of the preservative
laurakonium
chloride can be made from 125
mL
of a 0.2% solution?
125
mL
0.2%
0.25
g
drug
1250
mL
1:5000
0.25
g drug
This stays the same
0.2 g = x g 100 mL 125 mL x = 0.25 g drug
1 g = 0.25 g
5000
mL
x
mL
x
=
1250
mLSlide11
Problem 4
If a cough syrup contains in each teaspoonful, 1 mg of
chlorpheniramine
maleate
and if a pharmacist desired to double the strength, how many milligrams of that ingredient would be needed to be added to a 60
mL
container of the syrup? Assume no increase in volume.
60
mL
1 mg / 5
mL
60
mL
Want to double this
amnt
= +
x
mgSlide12
Problem 5
How many milliliters of a 1:400
w/v
stock solution should be used in preparing 1 gallon of a 1:2000
w/v
solution?
1:400
(1
gallon) 3785
mL
1:2000
This stays the same
Add
x
amount of
diluent
Slide13
Problem 6
How many milliliters of a 1:16 solution of sodium hypochlorite should be used in preparing 5000
mL
of a 0.5% solution of sodium hypochlorite for irrigation?Slide14
Problem 7
How much drug should be used in preparing 50
mL
of a solution such that 5
mL
diluted to 500
mL
will yield a 1:1000 solution?Slide15
Problem 8
How many milliliters of a 17% concentrate of
benzalkonium
chloride should be used in preparing 300
mL
of a stock solution such that 15
mL
diluted to 1 liter will yield a 1:5000 solution?Slide16
Problem 9
How many milliliters of water should be added to a pint of 5%
w/v
solution to make a 2%
w/v
solution?Slide17
Problem 10
How many milliliters of 85%
w/w
phosphoric acid having a specific gravity of 1.71 should be used in preparing 1 gallon of ¼%
w/v
phosphoric acid solution to be used for bladder irrigation?Slide18
Problem 11
How many grams of 20%
benzocaine
ointment and how many grams of ointment base (
diluent
) should be used in preparing 5 lbs of 2.5%
benzocaine
ointment
?Slide19
Problem 12
How many grams of coal tar should be added to 3200
g
of 5% coal tar ointment to prepare an ointment containing 20% coal tar?Slide20
Alligation Medial
“Weighted average” percentage strength of a mixture of two or more substances can be calculated
Percentage strength of compound is multiplied by its corresponding quantity
Sum is divided by total quantity of the mixture to give percentage strength of the mixtureSlide21
Problem 13
What is the percentage of zinc oxide in an ointment prepared by mixing 200
g
of 10% ointment, 50
g
of 20% ointment, and 100
g
of 5% ointment?
0.10
g
* 200
g
= 20
g
x
g = 35 g 0.20 * 50 g = 10 g 100 g
350 g 0.05 * 100 g = 5 g x = 10%TOTALS 350 g 35 gSlide22
Problem 14
What is the percentage strength of alcohol in a mixture of 500
mL
of a solution containing 40%
v/v
alcohol, 400
mL
of a second solution containing 21%
v/v
alcohol, and a sufficient quantity of a nonalcoholic third solution to make a total of 1000
mL
?Slide23
Alligation AlternateSlide24
Problem 15
In what proportion should 20%
benzocaine
ointment be mixed with an ointment base to produce a 2.5%
benzocaine
ointment?
20%
0%
2.5%
2.5 parts
17.5 parts
20 total parts
The 20%
benzocaine
and ointment base
shoule
be mixed at a 2.5:17.5 ratio, or 1:7.Slide25
Problem 16
A hospital pharmacist wants to use three lots of zinc oxide containing, respectively, 50%, 20% and 5% zinc oxide. In what proportion should they be mixed to prepare a 10% zinc oxide ointment?
50%
20%
5%
10%
5 parts
5 parts
10 parts + 40 parts = 50 parts
60 parts total ointment
The 50%, 20% and 5% lots should be mixed in a 5:5:50 proportion (or 1:1:10)Slide26
Problem 17
How many milliliters of 50%
w/v
dextrose solution and how many milliliters of 5%
w/v
dextrose solution are required to prepare 4500
mL
of a 10%
w/v
solution?Slide27
Problem 18
In what proportion must glycerin with a specific gravity of 1.25 and water be mixed to prepare a liquid having a specific gravity of 1.10?Slide28
QuestionsSlide29
Reference
Ansel
, H. C. (2009)
Phamaceutical
Calculations
(13th Ed.).
Philadelphia:Lippincott
Williams & Wilkins, and
Wolters
Kluwer
Publishers