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**Dilution, Concentration and Alligation**

Dr. Osama A. A. Ahmed

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**Dilution, Concentration and Alligation**

There are occasions in which the dilution or concentration of a pharmaceutical preparation is either desirable or required. 1st quantity X 1st concentration = 2nd quantity X 2nd concentration Q1 X C1 = Q2 X C2 Example(1): if 500 ml of 15% v/v solution are diluted to 1500 ml, what will be the percentage strength (v/v) 500(ml) X 15(%) = 1500(ml) X x(%) 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)? 1 : 20 = 5% 50(ml) X 5(%) = 1000(ml) X x(%) X = 0.25% = 1: 400 Dr. Osama A. A. Ahmed

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**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: = % and : 2000 = 0.05% and 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 phenylephrine hydrochloride should be used in compounding the following prescription. R/ phenylephrine HCl % Rose water ad 30 ml Sig. For the nose 1 : = 2 % x X 2% = X % X = ml Dr. Osama A. A. Ahmed

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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. 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. 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? 1 : 1000 solution g : 500 ml 0.5 g drug in 500 ml is the same amount found in 5 ml X X = 5 g 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) X X = 0.4 g X X = ml – 300 = 700 ml Dr. Osama A. A. Ahmed

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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 make 50% v/v alcohol? Q1 X C1 = Q2 X C2 5000(ml) X 85(%) = X (ml) X 50(%) X = 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 in calculations 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? 1000 X 0.1 = 100 gm of HCl 100% in 1000 ml of 10% w/v 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: 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? Q1 X C1 = Q2 X C2 X g X 15(%) = 150g X 10(%) X = 100 g of 15% opium 150 g g = 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 2270g X 2.5(%) = X g X 20(%) X = or 284 g 2270 – 284 = 1986 g of ointment base Dr. Osama A. A. Ahmed

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**Dilution, Concentration and 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. 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 = = 400 ml 300 X X 60 = 400 X Ct Ct = 18000/400 = 45 % Dr. Osama A. A. Ahmed

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**Dilution, Concentration and 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% parts (95%) 70% 55% parts ( 55%) minus gives from Dr. Osama A. A. Ahmed

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