density, specific gravity and specific volume€¦ · whereas specific gravity, being a ratio of...

Pharm. Calc./Compounding

Sherif S. Ebada, Ph.D.

Contact information:Assoc. Prof. Dr. Sherif S. EbadaPharmaceutical Chemistry Dept.Office hours:

Tuesdays and Thuresdays: 10:00 am–12:00 pmE-mail: [email protected]

Lecture 2

1

Required Textbook

Howard C. Ansel and Shelly J. Stockton Pharmaceutical Calculations. 15th Ed. 2

1. Measure 5 × 0.2 mL 1.0 mL of the oil2. Dilute with 1.5 mL of alcohol

to make 2.5 mL of dilution3. Measure 1/5 of dilution, or 0.5 mL of dilution, which will

contain 0.2 mL of clove oil.

Density, specific gravity and specific volume

• Density (d) is mass per unit volume of a substance. It is usually expressed as grams per cubic centimeter (g/cc)( g/ml).

• Specific gravity (sp gr) is a ratio, expressed decimally, of the weight of a substance to the weight of an equal volume of a substance chosen as a standard, both substances at the same temperature or the temperature of each being known.

• Water for the specific gravities of liquids and solids; while standard for gases is hydrogen.

Example:Thus, if 10 mL of sulfuric acid weighs 18 g, and 10 mL of water, under similar conditions, weighs 10 g, the specific gravity of the acid is:

United States Pharmacopeia, the standard temperature for specific gravities is25⁰C, except for that of alcohol, which is 15.56⁰C by government regulation

Lighter

Heavier

Specific gravities may be expressed decimally to as many places as the accuracy of their determination warrants. In pharmaceutical work, this expression may be to two, three, or four decimal places. Because substances expand or contract at different rates when their temperatures change, accurate work necessitates allowing carefully for variations in the specific gravity of a substance. In the United States Pharmacopeia, the standard temperature for specific gravities is 25°C, except for that of alcohol, which is 15.56°C by government regulation.

The density of a substance is a concrete number (1.8 g/mL in the example), whereas specific gravity, being a ratio of like quantities, is an abstract number (1.8 in the example). Whereas density varies with the units of measure used, specific gravity has no dimension and is therefore a constant value for each substance (when measured under controlled conditions). Thus, whereas the density of water may be variously expressed as 1 g/mL, 1000 g/L, or 621⁄2 lb/cu ft, the specific gravity of water is always 1.

Example:

• If 54.96 mL of an oil weighs 52.78 g, what is the specific gravity of the oil?

If a pint of a certain liquid weighs 601 g, what is the specific gravity of the liquid?

A pycnometer is a special glass bottle used to determinespecific gravity. Pycnometers are generally available forlaboratory use in volumes ranging from 1 mL to 50 mL.Pycnometers have fitted glass stoppers with a capillaryopening to allow trapped air and excess fluid to escape.

Some pycnometers have thermometers affixed, becausetemperature is a factor in specific gravity determinations.

In using a pycnometer, it is first weighed empty and thenweighed again when filled to capacity with water. The weightof the water is calculated by difference. Since 1 g of waterequals 1 mL, the exact volume of the pycnometer becomesknown. Then, when any other liquid subsequently is placed inthe pycnometer, it is of equal volume to the water, and itsspecific gravity may be determined.

Examples of pycnometers used to determine the specific gravity of liquids. Shown are 1-mL and 25-mL sizes.

Calculating Weight, Knowing the Volume and Specific Gravity

What is the weight, in grams, of 2 fl. oz. of a liquid having a specific gravity of 1.118?

What is the volume, in milliliters, of 1 lb of methyl salicylate with a specific gravity of 1.185?

Pharmaceutical Applications

• To convert the weight of an ingredient or preparation tovolume or vice versa.

• To calculate the equivalent strength of a preparation on thebasis of either weight or volume.

• In automated pharmaceutical equipment used by pharmaciststo prepare total parenteral nutrition (TPN) admixtures.

• In urinalysis (Clinical Application).

• In these automated compounders, the purpose of the specific gravity ofthe large-volume liquids being mixed is to determine the weights ofcomponents (e.g., dextrose, amino acids, and water). The componentweights are automatically calculated, based on the specific gravity,volume, and percentage concentration of the solutions used (e.g., 70%dextrose injection) in the ad mixture. The automatic compounder thenuses the weight to make the correct mixture rather than the volume of thesolution being measured.

• In normal adults, the specific gravity of urine is usually within the range of1.010 and 1.025 with a normal fluid intake (this range may vary with thereference source).

• Specific gravity is an indicator of both the concentration of particles in theurine and a patient’s degree of hydration.

• A higher-than-normal specific gravity indicates that the urine isconcentrated. This may be due to the presence of excess waste productsor electrolytes in the urine, the presence of glucose (glucosuria) or protein(proteinuria), excessive water loss, decreased fluid intake, or other factors.

• A low specific gravity indicates that the urine is dilute, which may be aresult of diabetes insipidus, renal disease (by virtue of the kidney’sreduced ability to concentrate urine).

• Specific volume, in pharmaceutical practice, is an abstractnumber representing the ratio, expressed decimally, of thevolume of a substance to the volume of an equal weight ofanother substance taken as a standard, both having the sametemperature

• Specific volume tells us how much greater (or smaller) involume a mass is than the same weight of water.

If 25 g of glycerin measures 20 mL and 25 g of water measures 25 mL underthe same conditions, the specific volume of the glycerin is:

Calculate the specific volume of a syrup, 91.0 mL of which weighs 107.16 g.

• Because specific gravity and specific volume are reciprocals, a substance that is heavier than water will have a higher specific gravity and a lower specific volume.

• What is the specific volume of phosphoric acid having a specific gravity of 1.71?

• 1 • 1.71 = 0.585, answer

Using Specific Gravity to Determine Weight / Volume Costs

(1) What is the cost of 1000 mL of glycerin, specific gravity 1.25, bought at $5.43

per pound?

1000 mL of water weighs 1000 g

Weight of 1000 mL of glycerin = 1000 g × 1.25 = 1250 g

1 lb = 454 g

(2) What is the cost of 1 pint of chloroform, specific gravity 1.475, bought at

$25.25 per pound?

1 pint = 473 mL

473 mL of water weighs 473 g

Weight of 473 mL of chloroform = 473 g × 1.475 = 697.7 g

1 lb = 454 g

A pharmacist received the following prescription:

The pharmacist has no clindamycin phosphate powder but does have clindamycin phosphate sterile solution, 150 mg/mL, in vials. From the label, the pharmacist learns that the solution is aqueous.(a) How many milliliters of the clindamycin phosphate sterile solution should thepharmacist use in filling the prescription?(b) How many milliliters of 95% v/v of alcohol are required?(c) How many milliliters of water should be added to make 120 mL?

b) If the pharmacist had had clindamycinphosphate powder with which to fill theprescription, 1.8 g would have been used,and that quantity would have taken up anegligible volume on solution in the 52% v/valcohol. Thus, the interpretation of theprescription is that the120 mL (not 120 mL -12 mL) of 52%v/valcohol should be used.

(c) Due to contraction when alcohol and water are mixed, the volume of water cannot be determined by subtracting 65.68 mL from 120 mL; thus, a sufficient volume of water is used (q.s.) to make 120 mL, answer.

Percentage, Ratio Strength, and Other Expressions of Concentration

Objectives

• Define the expressions percent weight-in-volume, percent volume-in-volume, percent weight-in-weight, ratio strength

• Convert percent strength to ratio strengthand vice versa

• Apply percent strength and ratio strength to pharmaceutical calculations

PercentageThe term percent, or the symbol %, when used without qualification means:

• for solutions or suspensions of solids in liquids, percent weight-in-volume;

• for solutions of liquids in liquids, percent volume-in-volume;

• for mixtures of solids or semisolids, percent weight-in-weight; and

• for solutions of gases in liquids, percent weight-in-volume.

Percentage Preparations

• Percent weight-in-volume (w/v)– Number of grams of solute in 100 mL solution

– % w/v

• Percent volume-in-volume (v/v)– Number of mL of a solute in 100 mL solution

– % v/v

• Percent weight-in-weight (w/w)– Number of grams of a solute in 100 gm solution

– % w/w

Important notes

• When to use which term

– w/v – solutions, suspensions of solids in liquids

– v/v – liquids in liquids

– w/w – mixtures of solids (creams)

• *Overall idea of this section*

– Solution = Solute + Solvent

• How many grams of potassium permanganate should be used in compounding the following prescription?

How many grams of aminobenzoic acid should be used in preparing 8 fluidounces of a 5% solution in 70% alcohol?

If ibuprofen tablets are permitted to contain not less than 90% and not more than 110% of thev labeled amount of ibuprofen, what would be the permissible range in content of the drug, expressed in milligrams, for ibuprofen tablets labeled 200 mg each?

A pharmacist receives the following prescription but does not have hydrocortisonepowder on hand. However, the pharmacist does have an injection containing 100 mgof hydrocortisone per milliliter of injection. A search of the literature indicates thatthe injection has a specific gravity of 1.5.

Rx, Hydrocortisone 1.5%Cold Cream qs 30 g

(a)How many grams of hydrocortisone are needed to fill the prescription?(b) How many milliliters of the hydrocortisone injection would provide thecorrect amount of hydrocortisone?(c) How many grams of cold cream are required?

• How many milliliters of liquefied phenol should be used in compounding the following prescription?

How many milligrams of hydrocortisone should be used in compounding the following prescription?

How many grams of benzocaine should be used in compounding the following prescription?

Parts per Million (PPM) and Parts per Billion (PPB)

The strengths of very dilute solutions are commonly expressed in terms of parts per million (ppm) or parts per billion (ppb), i.e., the number of parts of the agent per 1 million or 1 billion parts of the whole.

Express 5 ppm of iron in water in percentage strength and ratio strength.

The concentration of a drug additive in an animal feed is 12.5 ppm. How many milligrams of the drug should be used in preparing 5.2 kg of feed?

Ratio Strength

• Another way of expressing the percentage strength of a solution

• Example: Express 5% as a ratio strength

– 5 parts per 100, or 5:100

– Commonly we express ratio strength as 1:x

– So 5:100 would be expressed 1:20

• General form: 1 part of solute per x parts of solution

Chapter 6 Problem 7

• If a pharmacist dissolved the contents of eight capsules, each containing 300 mg of clindamycin phosphate, into a sufficient amount of an astringent liquid base to prepare 60 mL of topical solution, what would be the percentage strength (w/v) of clindamycin phosphate in the prescription?

Chapter 6 Problem 29

• A topical solution contains 3% w/v hydroquinone. How many liters of the solution can be prepared from 30 g of hydroquinone?


• If 500 g of dextrose are dissolved in 600 mL of water with a resultant final volume of 1 liter, what is the percentage strength of dextrose in the solution on a w/w basis?


• A sample of white petrolatum contains 10 mg of tocopherol per kilogram as a preservative. Express the amount of tocopherol as a ratio strength.


• In acute hypersensitivity reactions, 0.5 mL of a 1:1000 (w/v) solution of epinephrine may be administered subcutaneously or intramuscularly. Calculate the milligrams of epinephrine given.


• If a commercially available insulin preparation contains 1 ppm of proinsulin, how many micrograms of proinsulin would be contained in a 10-mL vial of insulin?

Calculating quantities from a master formula

Quantities provided by the master formula have to be scaled up or down, depending on the quantity of the product required. Using proportion or a multiplying factor.

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When a combination of wt and vol. is used without indicating the exact final volume or

weight of the preparation: An excess quantity is normally calculated for and the required

amount measured.

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Calculations involving parts:

The no. of parts is added up and the quantity of each ingredient calculated by proportion or multiplying factor to provide the correct amount.

Calculations involving parts:

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Calculations involving percentages

Conventions which apply when dealing with formulae which include percentages:•A solid in a formula where the final quantity is stated as a weight is calculated as weight in weight (w/w).•A solid in a formula where the final quantity is stated as avolume is calculated as weight in volume (w/v).•A liquid in a formula where the final quantity is stated as a volume is calculated as volume in volume (v/v).•A liquid in a formula where the final quantity is stated as a weight is calculated as weight in weight (w/w).•A gas in a solution is always calculated as w/w, unless specified otherwise. FormaldehydeSolution BP is a solution of 34-38% w/w formaldehyde in water.


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some situations where the standard conventions do not apply:

Syrup BP is a liquid solution of sucrose and water. If the normal conventionapplied it would be w/v, However, in the BP formula the concentration ofsucrose is quoted as w/w.

Syrup BP is: Sucrose 66.7% w/w,Water to 100%

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density, specific gravity and specific volume€¦ · whereas specific gravity, being a ratio of...

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