Calculation of Mixtures from Stock Medications

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Chapter 13

Calculation of Mixtures from Stock Medications

Objectives

• Interpret labels for the weight/volume of solute in solvent

• Dilute stock medications to the required strength using strengths expressed as percentages, fractions, and ratios

• Calculate the weight/volume of active ingredient in a substance

• Using alligation, calculate the weight/volume of stock medications needed to prepare a desired compound

Key Words

Pretest

Interpret the following labels to show the weight/volume of solute in the solvent. In those instances in which the solvent is unknown, state as the drug “in the solvent.” Round answers to tenths. Show all calculations.

image 1 A label for isopropyl alcohol reads 70% isopropyl alcohol.

image 2 A label reads Zephiran chloride 0.2%.

image 3 A label reads sodium hypochlorite 10%.

image 4 A label reads epinephrine 2.25% nebulizer.

image 5 The label on isopropyl alcohol reads 1 : 2.

image 6 The label on a 25 mL saline vial shows a 1 : 25 solution.

image 7 A Burrow’s solution 100-mL label reads 1 : 7.5.

image 8 A physician orders 1 L of a 10% boric acid solution to be used for compresses.

image 9 A physician orders 65 mL of a 1 : 15 sodium hypochlorite solution to be used in the office.

10. An order is to supply 10 mL of a drug at 50 mg/mL. The stock supply is 2.5 g/10 mL.

11. A physician asks that 500 mL of a 10% solution of a medication be prepared. The stock supply of the solution is 75%.

image 12 A physician asks that 325 mL of a 1% sodium bicarbonate solution be prepared. The stock medication is 650 mg/tab.

image 13 A physician asks the pharmacy to prepare 1 L of a 1 : 2000 silver nitrate solution to be used for an irrigation solution. The stock solution is 1% silver nitrate solution.

image 14 Prepare 250 mL of a 0.02% benzalkonium chloride solution to be used for cleansing skin before surgery. Stock strength of the solute is 1%.

image 15 A physician desires 3 L of a 15% Neomycin solution to use for irrigation of a wound. The available Neomycin is found in 0.5 g tablets.

image 16 A physician wants a patient to receive epinephrine 4 mg. The available medication is 1 : 1000 injectable. The medication is to be added to 500 mL of D-5-W.

image 17 A physician orders calcium gluconate 0.5 g to be used to prepare 1 L IV fluids. The medication is available in a vial marked calcium gluconate 1 : 2000 injectable.

image 18 A medical office needs 0.25 L of a 10% Lysol solution for disinfecting the office.

image 19 A physician desires 100 mL of a 50% creosol solution to be prepared from a 1 : 2 creosol solution.

image 20 A stock bottle of sodium perborate 1 : 50 solution is available. The dentist asks that 200 mL of solution be prepared.

Introduction

Special populations such as geriatric or pediatric patients often require an adjustment of medication strength found in stock medications supplied by manufacturers. Stock solutions may also be stored in concentrated amounts, to save space and for economic reasons, for dilution later. Stock supplies are usually found in commonly used solution strengths. By diluting the stock medication, the amount of medication necessary may be placed in a volume that is more easily measured or in a volume that may meet the needs of the physician’s prescription or order. The pharmacy is responsible for preparing weaker solutions to meet physicians’ orders or to make the administration of the correct amount of medication more accurate.

Remember from previous chapters that a solution is made of the solute (the drug to be dissolved) and the solvent (the liquid in which the solute will be dissolved). First, the amount of solute in a solution must be understood before dilution may occur. Using a process of dilution called alligation, the medication strength may be changed to meet the required strength. Dilution means to make a strong concentration of medication weaker or to add more solvent to the solute. Alligation is the mathematical calculation that determines the necessary amount of two different concentrations required to prepare the desired concentration for the medication order.

Interpreting Solution Labels and Calculating Solutions In Percentages

A solution is a mixture of two or more substances with a percentage of weight/volume being greater than the other. These substances are present as a gas/liquid, liquid/liquid, or solid/liquid. The solution may be prepared by mixing two liquids, as in mixing chocolate syrup with milk to make chocolate milk; mixing a gas with a liquid, as in adding carbon dioxide to water to prepare carbonated water for a fountain soda; or mixing a solid with a liquid, such as adding water to powdered instant tea. The material with the highest percentage of weight/volume to be mixed in the solid or gas form is considered a solute, whereas the substance with the lower percentage of weight/volume is a solvent. But what if both substances are liquids? In this case the liquid in the smaller amount is considered the solute or concentrate, and the greater amount of liquid is considered the solvent or the diluent. When the solute is shown as part of the solvent, the resultant solution may be expressed as a ratio strength or percentage strength.

As a review of previous chapters, percentage means that there are so many parts per 100. So 25% is 25 parts of solute in 100 parts of total solution or the parts of the percentage represent 1 g of solute in 100 mL of solvent. Percentages may be expressed as weight in weight (w/w) showing the number of grams of a solute in 100 g of total solvent. Percent of weight in volume (w/v) is the number of grams of solute in 100 mL of solvent. Finally, percentage may be expressed as volume in volume (v/v) or the number of milliliters of solute in 100 mL of total solvent. Weight in weight is found with semi solid or solid preparations, whereas weight in volume and volume in volume are found with liquid preparations.

With percentage preparations, the easiest method for calculation is the ratio and proportion method. If a review of the ratio and proportion method is necessary, see Chapter 2.

Calculating Weight-in-Weight Solutions

With weight-in-weight percentage calculations, the solutes and solvents will be expressed in weights such as grams, milligrams, grains, pounds, and other weights. Therefore the percentage will measure the total weight of one substance in the total weight of the final compound. With the solute being a solid weight and the solvent being a solid or semi-solid weight, the final product will be either a solid or a semi-solid preparation such as powder, cream, or ointment. Remember that the units used in the equation for ratio and proportion must be in the same measurements such as grams and milligrams.

Example 13-1

imageA physician asks that you prepare 100 grams of 2.5% hydrocortisone cream from available hydrocortisone cream 10%.

What is the weight of hydrocortisone in stock medication?

The label interpretation of 10% is 10 g in 100 g of stock medication.

What is the weight of hydrocortisone in each 100 g of base to complete this order? ____________________

The desired weight of hydrocortisone in the order is 2.5 grams.

What weight of the 10% stock medication is needed to prepare the 2.5% cream?

< ?xml:namespace prefix = "mml" />2.5g:x=10g:100 g base

image
image

10 gx=2.5 g×100 g

image
image

10x=250 g

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x=25010or25g of10%hydrocortisone to prepare a 2.5%hydrocortisone cream

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How many grams of hydrocortisone are needed to prepare 5 g of the 2.5% cream?

2.5 g:100g base::x:5 g ofbase

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100x=12.5 g

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x=12.5100or 0.125g of hydrocortisone per 5g ofcream

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Calculating Weight-in-Volume Solutions

Calculations for weight-in-volume percentages will show a strength or weight such as grams, milligrams, and other weights of medication in a volume such as liters, milliliters, drams, pints, or other liquid measures of solvent. A weight-in-volume is similar to a weight-in-weight because in a 1% solution, 1 g of solute is found in 100 mL of the solvent if the solvent has the same specific gravity of water. Again, the ratio and proportion method is preferred for calculating these solutions. With weight-in-volume, the numerator or solute is measured in grams, whereas the denominator or solvent is measured in milliliters.

Tech Note

Remember that 1 g of water is equivalent to 1 mL of water, or 1 mL of water weighs 1 g.

image Tech Alert

Be sure the solute and solvent are found in the same ratio and proportion positions.

Example 13-2

imageHow many milliliters of a 10% boric acid solution can be made from 20 g of boric acid?

10 g:100 mL::20 g:x

image

10x=100 mL×20(Notice that the grams have been canceled.)

image

10x=2000

image

x=200 mL

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Calculate Volume-in-Volume Solutions

Again using ratio and proportion, the amount of liquid solute in liquid solvent can be calculated. The percentage indicates the weight of solute in the solvent in a volume measurement.

Tech Note

Remember that all the measurements in the equation must be in the same units, such as milliliters, liters, pints, and cups. In this calculation you may have milliliters : milliliters, liters : liters, pints : pints, and the like, but each side of the proportion must be in the same measurement system, such as Dose in weight available : Dose of base form :: Dose in weight desired : x.

Example 13-3

A physician orders 15 mL of a 10 mcg/mL dilution of a drug for a child. The stock medication is 40 mcg/mL.

How many micrograms of the drug will be needed to prepare the order?

10 mcg:1 mL::x:15 mL

image

x = 10 × 15 mcg or 150 mcg of the medication is necessary

How many milliliters of the stock medication are necessary?

40mcg:1mL::150 mcg:x

image

40x=150 mL

image

x=15040or154(Notice that the zeros are canceled.)

image

x=3.75 mL of stock solution are necessary

image

How many milliliters of diluent are necessary?

15 mL Total volume of solution−3.75 mL volume of stock solution=11.25 mL volume of diluent necessary

image

Calculate the Amount of Drug and Solvent

In some cases the calculation of the quantity of the pure drug, either liquid or solid, must be determined to prepare a solution of a certain strength. The amount of solvent is the amount of diluent added to the solute to make the required volume of the necessary solution. The final volume of solution will contain the amount of stock medication required for the physician’s order.

The following formula will allow the calculation of these solutions:

StrengthofsolutionavailableDesiredornewvolumeofsolutionAmount or volume of soluteTotal volume of solution= Amount of desired or new soluteVolume of desired solution

image

The first step is to write the percentage strength as a ratio and then write the desired solution as a ratio. Then solve for x.

Example 13-4

image imageA physician desires a 1% lidocaine preparation in hand lotion for itching. How many grams of lidocaine would be necessary to prepare 50 mL of this solution?

First interpret that 1% is 1 g/100 mL.

StrengthofsolutionDesiredamountofsolution1g(Amount of solute)100 mL(Total volume of solution)=x(Amount of desired solute)50mL(Volume of desired solution)1g100 mL=x50 mL

image

100 mL×x=50 mL×1 g

image
image

100x=50 g

image

x=50 g÷100

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x=0.5 g of lidocaine is necessary to prepare this solution

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If the medication available is lidocaine 5%, what volume of lidocaine is necessary for this order?

5 g:100 mL::0.5 g:x

image

5 g×x=0.5 g×100 mL

image
image

5x=50 mL

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x=10 mL

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To calculate volume of solvent in volume of solution, use the following:

Volume of solvent=Volume of finished solution−Volume ofsolute

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What is the amount of hand lotion that should be used to prepare this solution?

Volume of solvent=50 mL(finished solution)−10 mL(Volume of solute)

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Amount of solvent(hand lotion)=50 mL−10 mLor40 mL

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Reducing and Enlarging Ordered Preparations

When a volume of a known solution requires reducing or enlarging to meet a physician’s order, the original strength of the preparation may be used for the calculation of the new volume or weight of the preparation. For example, using the above calculations in Example 13-4, if the physician desires 100 mL, the answer can be figured using ratio and proportion.

10 mL(solute):50 mL(prepared medication)::x:100 mL(prepared medication)

image
image

50x=1000 mL(solute)

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x=20 mL of solute is needed to prepare 100 mL of ordered medication

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40 mL(solvent):50mL(prepared medication)::x:100 mL(prepared medication)

image
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50 mL(solvent)x=4000

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x=80 mL of solvent to prepare 100 mL of ordered medication

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The volume of solute to solvent for 100 mL of ordered medication would be 20 mL solute to 80 mL of solvent.

Practice Problems A

Calculate the following problems. Round all answers to tenths. Show all your calculations.

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