ALLIGATION
LAB 11
ALLIGATION
 alligation is an arithmetical method of solving problems that
involves the mixing of solutions or mixtures of solids possessing
different percentage strength.
TYPES OF ALLIGATION
1. Alligation medial.
2. Alligation alternate.
ALLIGATION MEDIAL
 Is a method to calculate the ‘ weighted average’ percentage
strength of a mixture of two or more substances of known
quantity and concetration.
 Example:
what is the percentage strength (v/v) of alcohol in a mixture of
300o mL of 40% v/v alcohol, 1000 mL of 60% v/v alcohol, and
1000 mL of 70% v/v alcohol?
0.4 X 3000 mL = 1200 mL
0.6 X 1000 mL = 600 mL
0.7 X 1000 mL = 700 mL
total:
5000 mL
2500 mL
2500 mL / 5000 mL = 0.5 X 100 = 50%
ALLIGATION ALTERNATE
 It ’s a method to calculate the number of parts of two or more
components of a given strength when they mixed to prepare a
mixture of desired strength.
 The strength of the mixture must lie between the strengths of its
components.
ALLIGATION ALTERNATE
 Example:
In what proportion should alcohols of 95% and 50% strengths be
mixed to make 70% alcohol ?
95 X 4 = 380
50 X 5 = 250
total:
9 630
630/9= 70%
ALLIGATION ALTERNATE
 Example:
A hospital pharmacist wants to use three lots of zinc oxide ointment
containing, respectively 50%, 20% and 5% of zinc oxide. In what
proportion should they be mixed to prepare a 10% zinc oxide
ointment?
The two lots containing more than the desired percentage (50% and
20%) may be separately linked to the lot containing less(5%) than
the desired percentage.
50%
5 parts of 50%
20%
5 parts of 20%
10%
5%
10+ 40 = 50 parts of 5 %
Relative amount 5:5:50 or 1:1:10
PRACTICE PROBLEMS
1. In what proportion should 20% benzocaine ointment be mixed
with an ointment base to produce a 2.5% benzocaine
ointment?
2. What is the percentage strength of alcohol in a mixture of 500
mL of solution containing 40% v/v alcohol, 400 mL of second
solution containing 21% v/v alcohol, and sufficient quantity of
non alcoholic third solution to make a total of 1000 mL?
3. In what proportion may manufacturing pharmacist mix 20%,
15%, 5% and 3% zinc oxide ointments to make a 10% ointment?
4. How many grams of 2.5% hydrocortisone cream should be
mixed with 360 g of 0.25% cream to make a 1% hydrocortisone
cream?
PRACTICE PROBLEMS
5. A solution of benzalkonium chloride is available in
concentration of 1:750 w/v. how many mililiters of purified
water should be added to 30 mL of the solution to prepare
1:5000 benzalkonium chloride solution?
6. How many grams of zinc oxide should be added to 3200 g of 5%
zinc oxide ointment to prepare 20% zinc oxide ointment?
7. How many grams of white petrolatum should be mixed with
250 g of 5% and 750 g of 15% zinc oxide ointments to prepare a
10% ointment?
8. How many milliliters each of a 2% w/v solution and a 7% w/v
solution should be used in preparing 1 gallon of 3.5 % w/v
solution?
PRACTICE PROBLEMS
9. What percentage of alcohol in a mixture containing 1500 of
witch hazel (14% alcohol), 2000 mL glycerin, and 5000 mL of
50% alcohol?
10. Four equal amounts of belladonna extract, containing 1.15%,
1.3%, 1.35%and 1.2% of alkaloids, respectively, were mixed.
What was the percentage strength w/w of the mixture?
PRACTICE PROBLEMS