Dilution, Concentration and Alligation

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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)
• Q1 X C1
  Q2 X C2
• 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
• 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

• 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 1400 w/v
  stock solution should be used to make 4 liters of
  a 1 2000 w/v solution?
• 1400 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 150 stock
  solution of phenylephrine hydrochloride 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 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 11000 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 1750 w/v solution of
  benzalkonium chloride to make a 12500 w/v
  solution? (Page 242)
• 1 750
• X 300 X 0.4 g
• 1 2500
• 0.4 X X
  1000 ml 1000 300 700 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 make 50 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 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
• 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 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 - 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
• 2270 284 1986 g
  of ointment base

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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.
• 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 300100 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)