Dilution, Concentration and Alligation
Dr. Osama A. A. Ahmed
Dilution, Concentration and Alligation
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There are occasions in which the dilution or concentration of a pharmaceutical
preparation is either desirable or required.
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1st quantity X 1st concentration = 2nd quantity X 2nd concentration
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Q1 X C1 = Q2 X C2
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Example(1): if 500 ml of 15% v/v solution are diluted to 1500 ml, what will be the
percentage strength (v/v)
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Q1 X C1 = Q2 X C2
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500(ml) X 15(%) = 1500(ml) X x(%)
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X = 5%
Example(2): if 50 ml of 1: 20 w/v solution are diluted to 1000 ml, what is the ratio
strength (w/v)?
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•
•
Dr. Osama A. A. Ahmed
1 : 20 = 5%
Q1 X C1 = Q2 X C2
50(ml) X 5(%) = 1000(ml) X x(%)
X = 0.25% = 1: 400
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Dilution, Concentration and Alligation
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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 concentrations.
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Example(1): How many milliliters of a 1:400 w/v stock solution should be used to
make 4 liters of a 1 : 2000 w/v solution?
•
1:400 = 0.25%
and
•
1: 2000 = 0.05%
and
4 liters = 4000 ml
Q1 X C1 = Q2 X C2
•
4000(ml) X 0.05(%) = X (ml) X 0.25(%)
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Example(2): How many milliliters of a 1:50 stock solution of phenylephrine
hydrochloride should be used in compounding the following prescription.
•
R/ phenylephrine HCl
•
Rose water
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Sig. For the nose
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1 : 50
•
x X 2%
Dr. Osama A. A. Ahmed
X = 800 ml
0.25%
ad 30 ml
=2%
=
30
X 0.25%
X = 3.75 ml
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Dilution, Concentration and Alligation
•
Some calculations used in pharmacy 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.
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e.g. when the pharmacist need to prepare and dispense a concentrated solution and
direct the patient to use small volume (5 ml, teaspoonful) and dilute it in a specified
volume of water.
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Example(1): 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?
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1 : 1000 solution 0.5 g : 500 ml
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0.5 g drug in 500 ml is the same amount found in 5 ml
•
0.5
•
X
5
50
X=5g
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Example(2): How many milliliters of water should be added to 300 ml of a 1:750 w/v
solution of benzalkonium chloride to make a 1:2500 w/v solution? (Page 242)
•
1
750
•
X
300
•
1
2500
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0.4
X
Dr. Osama A. A. Ahmed
X = 0.4 g
X = 1000 ml
1000 – 300 = 700 ml
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Dilution, Concentration and Alligation
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Dilution of alcohol: when water and alcohol are mixed there is a physical contraction
in the resultant volume.
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Example: How much water should be mixed with 5000 ml 85% v/v alcohol to make
50% v/v alcohol?
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Q1 X C1 = Q2 X C2
5000(ml) X 85(%) = X (ml) X 50(%)
X = 8500 ml
so enough water is added to make 8500 ml.
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Dilution of acids: the strength of concentrated acids (official) are expressed as % w/w,
while diluted acids are expressed as w/v. Consider the specific gravity of conc. Acids in
calculations
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Example: How many mls of 37% w/w HCl having a specific gravity of 1.20 are
required to make 1000 ml of dil HCl 10% w/v?
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1000 X 0.1 = 100 gm of HCl 100% in 1000 ml of 10% w/v
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Q1 X C1 = Q2 X C2
100g X 100(%) = X (ml) X 37(%)
X = 270 g of 37% acid
270/1.2 = 225 ml
Dr. Osama A. A. Ahmed
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Dilution, Concentration and Alligation
• Dilution and concentration of solids and semisolids:
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Example: How many grams of opium containing 15 w/w of morphine and how many
grams of lactose should be used to prepare 150 g of opium containing 10% w/w of
morphine?
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Q1 X C1 = Q2 X C2
X g X 15(%) = 150g X 10(%)
X = 100 g of 15% opium
150 g - 100g = 50 g of lactose
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Example: How many grams of 20% benzocaine ointment and how many grams of
ointment base (diluent) should be used in preparing 5 lb. of 2.5 % benzocaine
ointment?
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5 lb = 454 g X 5 = 2270 g
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Q1 X C1 = Q2 X C2
2270g X 2.5(%) = X g X 20(%)
X = 283.75 or 284 g
2270 – 284 = 1986 g of ointment base
Dr. Osama A. A. Ahmed
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Dilution, Concentration and Alligation
• Alligation
• Arithmatical method of solving problems that involves the mixing of
solutions or mixtures of solids possessing different percentage strengths.
•
•
Alligation medial
A method by which the weighted average percentage strength of a mixture of two
or more substances of known quantity and concentration may be easily calculated.
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Example: what is the percentage (v/v) of alcohol in a mixture of 300 ml 40% (v/v)
alcohol and 100 ml 60% (v/v) alcohol ?
Q1C1 + Q2C2 + Q3C3 +…….. = QtCt
Qt = 300+100 = 400 ml
300 X 40 + 100 X 60 = 400 X Ct
Ct = 18000/400 = 45 %
Dr. Osama A. A. Ahmed
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Dilution, Concentration and Alligation
• Alligation
•
•
Alligation alternate
A method by which we may calculate the number of parts of two or more components
of a given strength when they are mixed to prepare a mixture of desired strength. A
final proportion permits us to translate relative parts to any specific denomination.
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Example: in what proportion should alcohol 95% and 55% strengths be mixed to make
70% alcohol?
• Available strength
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95%
•
•
desired strength
number of parts
15 parts (95%)
70%
55%
Dr. Osama A. A. Ahmed
25 parts ( 55%)
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