Dilution Conc and Alligation 15

7/28/2019 Dilution Conc and Alligation 15

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Dilution, Concentration and Alligation

Dr. Osama A. A. Ahmed


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Dr. Osama A. A. Ahmed 3

Dilution, Concentration and Alligation 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. 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(%) X = 800 ml

Example(2): How many milliliters of a 1:50 stock solution of phenylephrinehydrochloride should be used in compounding the following prescription.

R/ phenylephrine HCl 0.25%

Rose water ad 30 ml

Sig. For the nose

1 : 50 = 2 %

x X 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 itmust be determined.

e.g. when the pharmacist need to prepare and dispense a concentrated solution anddirect the patient to use small volume (5 ml, teaspoonful) and dilute it in a specifiedvolume of water.

Example(1): How much drug should be used in preparing 50 ml of a solution such that5 ml diluted to 500 ml will yield a 1:1000 solution?

1 : 1000 solution 0.5 g : 500 ml

0.5 g drug in 500 ml is the same amount found in 5 ml

0.5 5

X 50 X = 5 g

Example(2): How many milliliters of water should be added to 300 ml of a 1:750 w/vsolution of benzalkonium chloride to make a 1:2500 w/v solution? (Page 242)

1 750

X 300 X = 0.4 g

1 2500

0.4 X X = 1000 ml 1000300 = 700 ml


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Dilution, Concentration and Alligation Dilution of alcohol: when water and alcohol are mixed there is a physical contraction

in the resultant volume.

Example: How much water should be mixed with 5000 ml 85% v/v alcohol to make50% v/v alcohol?

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.

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 incalculations

Example: How many mls of 37% w/w HCl having a specific gravity of 1.20 arerequired to make 1000 ml of dil HCl 10% w/v?

1000 X 0.1 = 100 gm of HCl 100% in 1000 ml of 10% w/v

Q1 X C1 = Q2 X C2

100g X 100(%) = X (ml) X 37(%) X = 270 g of 37% acid

270/1.2 = 225 ml


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Dilution, Concentration and Alligation Dilution and concentration of solids and semisolids:

Example: How many grams of opium containing 15 w/w of morphine and how manygrams of lactose should be used to prepare 150 g of opium containing 10% w/w of

morphine?

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

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?

5 lb = 454 g X 5 = 2270 g

Q1 X C1 = Q2 X C2

2270g X 2.5(%) = X g X 20(%) X = 283.75 or 284 g

2270284 = 1986 g of ointment base


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Dilution, Concentration and Alligation

Alligation

Arithmatical method of solving problems that involves the mixing ofsolutions 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.

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 %


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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.

Example: in what proportion should alcohol 95% and 55% strengths be mixed to make

70% alcohol?

Available strength desired strength number of parts

95% 15 parts (95%)

70%

55% 25 parts ( 55%)

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Dilution Conc and Alligation 15