DILUTION AND CONCENTRATION OF

SOLUTIONS

By : Tewolde (B.Pharma , MSC)

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DILUTION and CONCENTRATION

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Learning objective
Upon successful completion of this lesson, the student will be able
to;

Define and know when and how to use dilution and concentration;
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-solving.

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 Introduction to Dilution and Concentration
The concentration of a solution is the amount of solute dissolved
in a specific amount of solvent.

Concentration = amount of solute

amount of solution
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 CONT’D…
Dilution is;
the process of preparing a less concentrated solution from a more
concentrated one.

the process of decreasing the concentration of a stock solution by

adding more solvent to the solution.

NB.

A stock solution is a concentrated solution that will be diluted to a

lower concentration for actual use.

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 CONT’D…
The solvent added is usually the universal solvent, known as water.
The more solvent you add, the more diluted the solution will get.

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 CONT’D…
The strength of a pharmaceutical preparation may be increased or
decreased by changing the proportion of active ingredient to the
whole.

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 CONT’D…
A preparation may be strengthened or made more concentrated by;
 the addition of active ingredient,

 admixture with a like preparation of greater strength

 through the evaporation of its vehicle, if liquid.

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 CONT’D…
The strength of a preparation may be decreased or diluted by
the addition of diluent, or

 admixture with a like preparation of lesser strength.

The diluent is selected based on its compatibility with the vehicle of

the original product; that can be, aqueous, alcoholic, hydroalcoholic,
or other.

Add Solvent

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 CONT’D…
In general,

In a dilution; In concentrated solution;

Diluent is added. preparation of greater strength

volume increases. and/or active ingredient added,

concentration decreases. vehicle evaporated, if liquid

Concentration increased.

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 Relationship between strength and total quantity

If a mixture of a given percentage or ratio strength is diluted to

twice its original quantity, its active ingredient will be contained in
twice as many parts of the whole, and its strength therefore will be
reduced by one half.

Diluent

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 CONT’D…
If, then, the amount of active ingredient remains constant, any
change in the quantity of a solution or mixture of solids is inversely
proportional to the percentage or ratio strength; that is,
the percentage or ratio strength decreases as the quantity increases,
and conversely.

This relationship is generally true for all mixtures except solutions

containing components that contract when mixed together.

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 CONT’D…
Dilution equation:

(1stquantity) x (1st concentration) = (2nd quantity) x (2nd concentration),

or Q1 x C1 = Q2 x C2

The quantity of solute in a solution refers to the total quantity of

solute in the solution.

 It is generally measured by weight (using units such as grams) or by

volume (using units such as milliliters).

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 CONT’D…

Concentration, on the other hand, refers to the amount of solute per

unit of solution.

Concentration can be expressed as a ratio; i.e.

g/ml,

ml/ml,

g/g

Concentration of solution
= amount of solute
amount of solution 14
 DILUTION AND CONCENTRATION OF LIQUIDS

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 concentration.

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?

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 CONT’D…

Given; C1 = 1: 400 = 0.25% V1 = y

C2 = 1 : 2000 = 0.05% V2 = 4 liters = 4000 mL

Soln;
V1 x C1 = V2 x C2

0.25%w/v x y mL = 4000 (mL) x 0.05% w/v

y = 800 mL Or,

1⁄400w/v x y mL = 4000 (mL) x 1⁄2000w/v,

y = 800 mL

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 CONT’D…
2, If 500 mL of a 15% v/v solution are diluted to 1500 mL, what will be the
percentage strength (v/v)?

Soln;

Given.

v1 = 500mL c1 = 15%w/v

v2 = 1,500mL c2 =y %w/v

v1 x c1 = v2 x c2
500mL x 15%w/v = 1500mL x y%w/v

y = 5%w/v
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 Dilution and concentration of solids and semisolid

The dilution of solids in pharmacy occurs when there is need to

achieve a lower concentration of an active component in a more
concentrated preparation (e.g., a powdered vegetable drug).

Reducing or enhancing the strengths of creams and ointments is a

usual part of a compounding pharmacist’s practice to meet the special
needs of patients.

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 CONT’D…
E.g. If 30 g of a 1% hydrocortisone ointment were diluted with 12g
of Vaseline, what would be the concentration of hydrocortisone in the
mixture?

Soln:

Given;

Hydrocortisone total weight = 30 g x 1%w/w = 0.3 g

Total weight of mixture = 30 g + 12 g = 42 g,

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 CONT’D…
Concentration of hydrocortisone in preparation

= amount of solute / total amount of preparation

= 0.3 g/42 g x 100%

= 0.71%w/w, Or

= 30 x 1%w/w = 42 x y

y = 0.71%w/w

Q1 x C1 = Q2 x C2

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 CONT’D…

2. 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?
Soln;
Q1 x C1 = Q2 x C2

x g X 15%w/v = 150g X 10%w/v

x = 100 g of opium containing 15%morphine

150 g - 100g = 50 g of lactose

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 Triturations

Trituration is a dilution of a potent drug powder with an inert

diluent powder, usually lactose, in a definite proportion by weight.

prepared by diluting one part by weight of the drug with nine parts
of finely powdered lactose.

They are, therefore,10% or1:10 w/w mixtures

We can then remove a weighable portion (aliquot) of the mixture

containing the desired quantity of substance to maintain an
acceptable range of accuracy.

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 CONT’D…
The trituration is done by dissolving in
sterile water

sodium chloride for injection, or

finely powdered lactose prior to administration.

Lactose is the most commonly used diluent in solid dosage form

pharmaceuticals such as powders, tablets and capsules; b/c of its
extremely low incidence of side effects, ready availability, and low
cost.

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 CONT’D…
Ratio and proportion can be used to determine the weight of drug
and lactose required to make the trituration as well as the weight of
the aliquot to be used to fill the prescription.

Wt of drug in trituration = W t of drug in aliquot

Wt of trituration Wt of aliquot

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 CONT’D…
E.g. How many grams of a 1:10 trituration are required to obtain 25
mg of drug?

Sol/n;
1:10 trituration means, 10 g of trituration contain 1 g of drug

25 mg = 0.025 g

Wt of drug in trituration = W t of drug in aliquot

Wt of trituration Wt of aliquot
1(g) = 0.025 (g)
10 (g) x (g) x = 0.25 g

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 CONT’D…

2. How many milliliters of an injection prepared by dissolving 100

mg of a 1:10 trituration of mechlorethamine hydrochloride in
sufficient water for injection to prepare 10 mL of injection, is
required to obtain 5 mg of drug?

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 CONT’D…
Soln;

NB.
 1:10 trituration = 1mg of drug in 10ml of solution for injection

100 mg of trituration = 10 mg of drug

10 mg of drug in 10 mL of injection

10 (mg)/5 (mg) = 10 (mL)/x (mL)

x = 5 mL, answer.

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QUESTION

How many milligrams of a 110 dilution of colchicine

should be used by a manufacturing pharmacist in
preparing 100 capsules for a clinical drug study if each
capsule is to contain 0.5 mg of colchicine?

Answer =500 mg

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 Alligation

Alligation is an arithmetical method of solving problems that

involves the mixing of solutions or mixtures of solids possessing
different percentage strengths.( tying together)

There are two types of alligation methods.

A, Alligation Medial.

B, Alligation alternate

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 CONT’D…

A, Alligation medial

Is 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. By this method, the percentage
strength of each component, expressed as a decimal fraction, is
multiplied by its corresponding quantity; then the sum of the products
is divided by the total quantity of the mixture; and the resultant
decimal fraction is multiplied by 100 to give the percentage strength of
the mixture.
Of course, the quantities must be expressed in a common 30
denomination, whether of weight or volume.
E.g.

1) What is the percentage strength (v/v) of alcohol in a mixture of

3000 mL of 40% v/v alcohol, 1000mL of 60% v/v alcohol, and
1000 mL of 70% v/v alcohol?

Assume no contraction of volume after mixing.

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 CONT’D…
Soln; Total quantity of alcohol
0.40 x 3000 mL = 1200 mL
0.60 x 1000 mL = 600 mL
0.70 x 1000 mL = 700 mL

Total 5000 mL = 2500 mL

Total volume of solution total volume of alcohol

Alcohol strength = 2500mL x 100%

5000 mL

= 50%v/v
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 CONT’D…
B, Alligation alternate
It is a method by which we may calculate the number of parts of
two or more components of a given strength when they are to be
mixed to prepare a mixture of desired strength.

A final proportion permits us to translate relative parts to any

specific denomination.

The strength of a mixture must lie somewhere between the strengths

of its components; that is, the mixture must be somewhat stronger
than its weakest component and somewhat weaker than its strongest.
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EXAMPLES;

1. In what proportion should alcohols of 95% and 50% strengths be

mixed to make 70% alcohol?

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 CONT’D…
NB.

The difference between the strength of the stronger component

(95%) and the desired strength (70%) indicates the number of parts of
the weaker to be used (25 parts), and

The difference between the desired strength (70%) and the strength
of the weaker component (50%) indicates the number of parts of the
stronger to be used (20 parts).

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this ‘‘weighted’’ average can be found by means of
an extremely simple scheme, as illustrated in the
subsequent diagram.

95% 20
Minus
PARTS OF 95 % ALCOHOL

Gives

RELATIVE AMOUNT 20 : 25
70%

From Gives 25

50% PARTS OF 50% ALCOHOL

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The mathematical validity of this relationship can be
demonstrated

Proportional
Percent given Percent parts required
desired

a X
c
b Y

Given these data, the ratio of x to y may be derived algebraically as

follows:
ax + by = c(x + y)
ax + by = cx + cy
ax - cx = cy - by
x(a - c) = y(c - b) 37
 𝑋 𝑐 −𝑏
=
𝑌 𝑎 −𝑐

Soln;
= 95 * x + 50 * y = 70(x + y) or

= 0.95 * x + 0.5 * y = 0.7(x + y)

= 0.95x + 0.5y = 0.7x + 0.7y

= 0.95x – 0.7x = 0.7y – 0.5y

= 0.25x = 0.2y

= x/y = 0.2/0.25

= 4parts/5parts = 4 : 5, answer

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 CONT’D…

The result can be shown to be correct by alligation medial:

95 x 4 = 380

50 x 5 = 250

Totals: 9 = 630

630/9 = 70%

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 CONT’D…
2. In what proportion should 20% benzocaine ointment be mixed
with an ointment base to produce a 2.5% benzocaine ointment?

Soln; 20% 2 .5% 2.5 parts of 20% ointment

0% 17.5 parts of ointment base

Relative amounts: 2.5 : 17.5, or 1 : 7, answer

Prove: 20 x 1 = 20

0x 7 = 0

Totals: 8 = 20 20 / 8 = 2.5%
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 Specific gravity of mixtures

The methods of alligation medial and alligation alternate may be

used in solving problems involving the specific gravities of different
quantities of liquids of known specific gravities
provided no change in volume occurs when the liquids are mixed
and that they are measured in a common denomination of volume.

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 CONT’D…

Examples;

1. What is the specific gravity of a mixture of 1000 mL of syrup with

a specific gravity of 1.300, 400 mL of glycerin with a specific gravity
of 1.250, and 1000 mL of an elixir with a specific gravity of 0.950?

Soln;
1.300 x 1000 = 1300
1.250 x 400 = 500
0.950 x 1000 = 950
Totals: 2400 = 2750
2750/2400 = 1.146
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 CONT’D…
2. 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?

Soln;

1.25 1.10 0.10 parts of glycerin

1.00 0.15 parts of water

Relative amounts: 0.10 : 0.15, or 2 : 3, answer.

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 QUIZ

1. In what proportion should a preparation of 50% and

20% strengths be mixed to make 10% strength of the
preparation?

2. What is the percentage strength (v/v) of alcohol in a

mixture of 3000 mL of 30% v/v alcohol, 1000mL of
50% v/v alcohol, and 1000 mL of 40% v/v alcohol?

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3. How many milliliters of a 1 :5000 w/v solution of the
preservative lauralkonium chloride can be made from 125
mL of a 0.2% solution?

4. How many milliliters of a 1% stock solution of a

certified red dye should be used in preparing 4000 mL of
a mouthwash that is to contain 1 :20,000 w/v of the
certified red dye as a coloring agent

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Thank you !!

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