Reducing & Enlarging Formulas . Lecturer: dr. Asmaa abdelaziz Faculty of pharamcay Ibn hayan University 1

Reducing & Enlarging Formulas . Factor (F) = Amount Desired . Amount of Formula 2

I. Formulas that specify amount of ingredients Ex 1:From the following formula, calculate the quantity of each ingredient required to make 240 ml of Calamine lotion? Factor (F) = Amount desired Amount of formula F = 240 / 1000 = 0.24 The amount of each ingredient in the original formula is multiplied by 0.24 Rx.   Calamine 80 g. Zinc oxide Glycerin 20 ml. Bentonite Magma 250 ml. Lime water, to make 1000 ml. 3

Example 2 Rx. Phenobarbital 4 g. Orange oil 0.75 ml. Amaranth solution   Phenobarbital 4 g. Orange oil 0.75 ml. Amaranth solution 10 ml. Alcohol 150 ml. Glycerin 450 ml. Syrup Purified water, to make 1000 ml. Calculate the quantity of each ingredient needed to make 150 ml? Factor (F) = Amount desired Amount of formula F = 150 / 1000 = 0.15 The amount of each ingredient in the original formula is multiplied by 0.15 4

Percentage Preparations 1.Percent weight-in- volume (w/v):expresses the number of grams of constituent in 100 ml solution or liquid preparation[ Solids, liquids or gases in liquids] 2-Percent volume-in-volume(v/v:) expresses the number of milliliters of a constituent in 100mL of solution or liquid preparation. [Liquids in liquids] 3-Percent weight-in-weight (w/w):expresses the number of grams of a constituent in 100 g. of solution or liquid preparation. [Mixture of solids] 5

Cont.Percentage Preparations 4-Milligram percent (mg%): expresses the number of mg of a substance in 100 ml of solution or liquid preparation. 5-Part per million (ppm): is an expression used for very dilute solutions, e.g. ,the limit of arsenic present in zinc oxide. is 65 ppm ( 6 ppm = 0.0006 %) 6

Examples:  example.1: How many grams of dextrose are required to prepare 4000ml of 5% solution? 5 g.→ = 100 ml. x → = 4000 ml. x = 4000 x 5 / 100 = 200 g. 7

examples Example 2 How many grams of Aminobenzoic acid should be used in preparing 240 ml of a 5% solution in 70% alcohol?    5 g. →100 ml   x→ 240 ml x = 240 x 5 / 100 = 12 g. 8

Ratio strength When a ratio strength (e.g., 1 :1000) is used to designate a concentration, it is to be interpreted as follows: 1-For solid in. liquid: 1 g. of a solute in 1000 ml. of solution or liquid preparation   2-For liquid in liquid: 1 mI. of a constituent in 1000 ml. of solution or liquid preparation 3-For solid in solid: 1g. of a constituent. in 1000 g. of the mixture. 9

Examples: [ 1 ] Express 0.02 % as a ratio strength? 0.02 →100   1 part → x parts x = 1 x 100/ 0.02 = 5000 parts Ratio = 1 : 5000    10

Example 2 [ 2 ] Express 1 : 4000 as a percentage strength?   1 part → 4000 parts = x → 100 x % = 1 x 100 /4000 = 0.025 %

examples [3] How many grams of Potassium permanganate should be used in preparing 500 ml of 1:2500 solution? 1 part → 2500 parts x → 100 X = 100/2500 = 0.04% 0.04 → 100 ml → 500 ml = 500 x 0.04 / 100 = 0.2 g

Dilution and Concentration : Diluent: A substance that is added to a pharmaceutical product to reduce the strength of the product. A diluent most often has no drug substance in it, sterile water and petrolatum for example.

Cont. Dilution and Concentration : Stock solutions: Strong solutions from which weaker ones are made

Relationship Between Strength and Quantity 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. (The volume increases the strength decreases).  

Problem Solving Q1 (C1) = Q2 (C2) Q1: quantity of solution/ mixture (1) C1 : conc. of solution/ mixture (1) Q2: quantity of solution/ mixture (2) C2: conc. Of solution/ mixture (2)  

Dilutions and Concentrations of Liquids Ex: If 500 mL of a 15% (v/v) solution of methyl salicylate in alcohol are diluted to 1500 mL, what will be the percentage strength (v/v)? Q1 (C1) = Q2 (C2)  500 mL (15 %) = (1500 mL) (X %)  X = (500 x 15) / 1500  X = 5% (answer)  

Example: If 50 mL of a 1:20 (w/v) solution of aluminum acetate are diluted to 1000 mL, what is the ratio strength (w/v)? 1 part → 20 parts → 100 = 100/20 = 5% Use same formula • Q1 (C1) = Q2 (C2) • (50 mL) (5 %) = 1000 mL (X %) • X% = (50 x5) /1000 • X = 0.25% = 0.25 / 100 • = 1:400 (answer)

Determine Amount of Solution of a Desired Strength Example: How many grams of 10% (w/w) ammonia solution can be made from 1800 g of 28% (w/w) strong ammonia solution? Use the same formula Q1 (C1) = Q2 (C2) •  (1800 g)(28 %) = (X g) (10%) •  X = (1800 x 28) /10 •  X = 5040 g (answer)

Cont. Determine Amount of Solution of a Desired Strength Example: How many milliliters of a 1:5000 (w/v) solution of phenylmercuric acetate can be made from 125 mL of a 0.2% solution? 1:5000 = 0.02% Use the same formula Q1 (C1) = Q2 (C2) •  (125 mL) (0.2 %) =(X mL) (0.02 %) •  X = 1250 mL (answer)   

example How many milliliters of a 1:400 (w/v) stock solution should be used to make 4 liters of a 1:2000 (w/v) solution? 4 liters = 4000 mL 1:400 = 0.25% 1:2000 = 0.05% Use the same formula Q1 (C1) = Q2 (C2) X mL (0.25 %) = 4000 mL (0.05%) X = 800 mL (answer)

example How many millilitres of a 1:400 (w/v) stock solution should be used in preparing 1 gallon of a 1:2000 (w/v) solution? 1 gallon = 3785 mL 1:400 = 0.25% 1:2000 = 0.05% Q1 (C1) = Q2 (C2) •  X (0.25%) = (3785 mL)(0.05%) •  X = 757 mL (answer)

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