Concentration and dilution pharmaceutical calculations

Concentration and dilutionpharmaceutical calculation
Dr. rasha khalaf‫الصفحة‬1
‫االولى‬ ‫المرحلة‬
‫الثاني‬ ‫الكورس‬
Pharmaceutical calculation
Lecture one
Percentage and Ratio Strength
Concentration and dilution

Percentage and Ratio Strength
percent
 means “per 100.”
 represented as a percent (%)
 50% means 50 parts in 100
(used frequently for expressing the
concentration of active or inactive
materials in pharmaceutical
preparations.
Ratio Strength
 Like percentage,
another way of expressing
concentrations.
 5% means 5 parts per
100 or 5:100
((used in The concentrations
of weak solutions ex. 1:1000
For the purpose of calculation,
percents are changed to decimal fractions by dropping the percent sign (%) and
dividing the number by 100 (e.g. 12.5% =12.5/100= 0.125).
The decimal fraction can be changed back to percent by multiplying by 100 and
adding the percent sign (%).
strength ratio is simplified by making the first figure equal to
1;
thus 5:100 = 1:20
Express 0.02% as ratio strength
Express 1:4000 as a percentage
strength

Concentrations
(indicate the amount of active ingredient per total volume or weight of substance)
WEIGHT/VOLUME-1
 describes the concentration of a solid dissolved in a liquid.
 Suspension and IV solutions are an example of weight/volume concentration.
 They are expressed as % w/v, or x g/100 mL.
 An IV solution of D5%W (5% w/v) has 5 g/100 mL of dextrose.
Examples:
How many grams of dextrose are required to prepare 4000 mL of a 5% w/v
solution?

How many grams of potassium permanganate should be used in compounding
the following prescription?
Potassium Permanganate 0.02%
Purified Water ad 250 mL
Sig. as directed.
Note : To calculate the percentage weight-in-volume of a solution or liquid
preparation, given the weight of the solute or constituent and the volume of the
solution or liquid preparation, it should be remembered that the volume, in
milliliters, of the solution represents the weight, in grams, of the solution or
liquid preparation as if it were pure water.
Ex: What is the percentage strength (w/v) of a solution of urea, if 80 mL
contains 12 g?
EX; A prescription calls for 8 gram of a 50 % magnesium sulfate
solution. How many milliliters is needed?

WEIGHT/WEIGHT-2
 (true percentage or percentage by weight) indicates the number of parts by
weight of active ingredient contained in the total weight of the solution or
mixture considered as 100 parts by weight.
 They are expressed as % w/w, or x g/100 g.
 used to describe solid or semisolid products because they are
measured based on their mass or weight ex.Ointments, creams, gels, lotions
How many grams of phenol should be used to prepare 240 g of a 5%
(w/w) solution in water?
How many grams of a drug substance are required to make 120 mL of a
20% (w/w) solution having a specific gravity of 1.15?
How many grams of a drug substance should be added to 240 mL of
water to make a 4% (w/w) solution?

If 1000 mL of syrup with a specific gravity of 1.313 contains 850 g
of sucrose, what is its percentage strength (w/w)?
How many grams of benzocaine should be used in
compounding the following prescription?
Rx
Benzocaine 4%
Polyethylene Glycol ad 2 g
Make 24 suppositories. Sig. use one as directed
What weight of a 5% (w/w) solution can be prepared from 2 g of
active ingredient?

If 1500 g of a solution contains 75 g of a drug substance, what is
the percentage strength (w/w) of the solution?
If 5 g of boric acid is added to 100 mL of water, what is the
percentage strength (w/w) of the solution?

VOLUME / VOLUME-3
 Volume/volume concentration (% v/v) describes the
concentration of a liquid
dissolved in another liquid
 ex.
o Acetic acid is another liquid that is often diluted in
either water or saline
o Alcohol is yet another liquid dissolved into another liquid.
Example :
In preparing 250 mL of a certain lotion, a
pharmacist used 4 mL of liquefied phenol. What
was the percentage (v/v) of liquefied phenol in the
lotion?
What is the percentage strength v/v of a solution of
800 g of a liquid with a specific gravity of 0.8 in
enough water to make 4000 mL?

How many milliliters of liquefied phenol should be
used in compounding the following prescription?
Peppermint spirit contains 10% v/v of peppermint
oil. What volume of the spirit will contain 75 mL of
peppermint oil?

Dilutions
Stock solutions are generally concentrated solutions or solids
that are used to prepare smaller concentration
expressed as ratio strengths or percentage w/v or w/w (1:400
w/v), (50% w/v).
Dilution of these concentrated solutions or solids creates a
smaller concentration in a higher volume that will allow for
easier, more accurate measurement of a desired dose.
The amount of medication (or solute) in the solution did not
change, only the volume of the liquid (diluent).
A solution that has a concentration 50% (50 g/100 mL) and has
the volume doubled now has a concentration of 25% (25 g/100
mL).
A cream with a percent strength of 18% (18 g/100 g) and a weight
of 20 g that is combined with an additional 20 g of cream base
would now have a percent strength of 9% (9 g/100 g).
Ex :-How many milliliters of 1:500 w/v solution is needed to
make 3 L of a 1:2000 w/v solution?
750 mL of the concentrated solution is added to 2250 mL of the diluent to obtain 3 L total volume with a concentration
of 1:2000.

Diluting liquids changes the concentration of that liquid. Since
three of the four components are already known, the
concentration of the new solution can be determined by:
 using the proportion rule.
 by using the following formula:
Q1 (quantity 1) x C1 (concentration 1) = Q2 (quantity 2) x C2 (concentration 2)
Ex : What is the new concentration (% strength) of a
dextrose 70% 500 mL solution diluted to 2000 mL?
Q1 xC1 = Q2 x C2
500 mL x 70% = 2000 mL x x%
3500 = 2000x
17.5%= x
Ex :How many milliliters of 3% gentamicin solution can be
made from 60 mL of 10% gentamicin?
Q1 x C1 = Q2 x C2
60 mL x 10% = x mL x 3%
600 = 3x
x = 200 mL
ex: From stock solution 0.9% Nacl prepare 100 ml 0.45 % solution
V1 x C1 = V2 x C2
V1 x 0.9 % = 100 ml x 0.45 %
V1 = 100 * 0.45/ 0.9 = 50 ml
[take 50 ml 0.9% and complete by water to 100 ml which result 0.45% (half normal saline)].

Ex : from solution 0.9 % Nacl prepare100 ml 0.18% solution.
ALLIGATIONS
Alligations is a method used to
 calculate the percent strength when combining multiple strengths
of the same ingredient.
 when the volume of each of two different strengths of the same
ingredient must be determined in order to make a new strength..
to determine the new percent strength. There are two different
ways to do this calculation
The first method uses the total volumes of the solutions and the
total grams of the ingredient in the solutions, and then, using the
proportion rule, the new percent strength is determined.

Ex :Mix to gether 100 mL of 50% dextrose with 250 mL of 40%
dextrose and 450 mL of 70% dextrose. What is the new percent
strength?
The second method uses the percent strengths converted into
decimals and then multiplied by their respective volumes. This
new volume then is divided by the
original volume and the answer is multiplied by 100 to obtain a
percent strength.
Ex: Mix together 100 mL of 50% dextrose with 250 mL of 40%
dextrose and 450 mL of 70% dextrose. What is the new
percent strength?
50% = 0.5 × 100 mL = 50 mL
40% = 0.4 × 250 mL = 100 mL
70% = 0.7 × 450 mL = 315 mL
Totals: 800 mL 465 mL
465 mL ÷ 800 mL = 0.58125 × 100 = 58.125% = 58%

Alligations alternate
is the method used to determine the volume necessary
for each ingredient combined (i.e., same ingredient, different
percent strength) to produce a new percent strength. This new
percent strength must be in-between the two being combined.
It resembles a tic-tac-toe board and provides a great visual for
calculating. The answers obtained will be the ratio in which the
ingredients should be combined. The ratio should always be
simplified to it smallest form.
Ex :A patient needs 70% dextrose and the pharmacy carries 95%
and 30% strengths.
What proportion is needed to make the 70% solution?

(higher %) 95 - (desired %) 70 = 25, which represents the parts
needed of lower %
(desired %) 70 - (lower %) 30 = 40, which represents the parts
needed of higher %
The ratio of 40:25 can be simplified to 8:5. This means, for every
eight parts of
95%, five parts of 30% will be used.
Ex :Mix 70% and 30% dextrose to obtain 1000 mL of a 40%
concentration
1 part + 3 part = 4 parts total, 1000 mL/4 parts = 250 mL/part
1 part 70% = 250 mL × 1 = 250 mL
3 parts 30% = 250 mL × 3 = 750 mL/1000 mL
Ex : Mix 50% and 5% dextrose to obtain 100 mL of a 10%
concentration

Concentration and dilution pharmaceutical calculations

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