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Dilution
&
Concentration

Dilution and concentration of solutions
• After dilution or concentration of a solution, the change in the
volume or the quantity is inversely proportional to the ratio or
percentage strength.
Concentration X Volume = Concentration X Volume
(before dilution)
(after dilution)

C1V1 = C2V2

• C= Concentration (% strength) , V= Volume

C1Q1 = C2Q2

• C= Concentration (% strength), Q= Quantity

Dilution and concentration of solutions
• Ex: If 500 mL of a 15% v/v solution of methyl salicylate in
alcohol is diluted to 1500 mL, what is the percentage
strength v/v?

Solution
C1V1 = C2V2
15 (%) X 500 (ml) = C2 X 1500 (ml)
C2= (15*500)/1500 = 5%

Dilution and concentration of solutions
• Ex: If 50 mL of a 1:20 w/v solution of aluminum acetate is
diluted to 1000 mL, what is the ratio strength w/v?

Solution
1:20= 5%
C1V1 = C2V2
5 (%) X 50 (ml) = C2 X 1000 (ml)
C2= (5*50)/1000 = 0.25% = 1:400

Alligation
• Alligation
is
a
practical
method
of
solving arithmetic problems related to mixtures
of ingredients.
a) Alligation medial: is used to determine the average
percent strength of a mixture of two or more
ingredients of known quantities and concentration.
b) Alligation alternate: is used to determine the
number of parts of two or more components of a
given strength, required to give a mixture of the
desired strength.

Alligation medial
(1) Find the percent strength of ethyl alcohol in a mixture
obtained by mixing 300 ml of 40% , 100 ml of 60% and
100 ml of 70% solutions of ethyl alcohol.

% strength
40
60
70

Volume
Alcohol 1
X
300
= 12,000
Alcohol 2
X
100
= 6,000
Alcohol 3
X
100
= 7,000
500
25,000
% strength of mixture= 25,000/500= 50%

Alligation medial
(2) Find the concentration of NaOH when 2000 ml of 20%,
4000 ml of 10% solutions and 4000 ml water are mixed
together.

% strength
20
10
0

Volume
20% NaOH
X
2000
= 40,000
10% NaOH
X
4000
= 40,000
Water
X
4000
=0
10,000
80,000
Concn of NaOH= 80,000/10,000= 8%

Alligation medial
(3) Find the concentration of Zinc oxide ointment prepared
by mixing 500 g of 50% , 300 g of 40% zinc oxide
ointments and 200 g of Vaseline.

% strength
50
40
0

Amount
50% oint.
X
500
= 25,000
40% oint.
X
300
= 12,000
Vaseline
X
200
=0
1000
37,000
Concn of ZnO oint.= 37,000/1000= 37%

Alligation alternate
(1) In what proportion should 15% boric acid be mixed
with Vaseline to produce 2% boric acid ointment?
% given
Boric acid

Desired concn

15%

Proportional parts required

2

2 parts of boric acid

13

13 parts of Vaseline

2%
Vaseline

0%

15 parts
Boric acid : Vaseline= 2:13


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