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

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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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image

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

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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

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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

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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

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5 g×x=0.5 g×100 mL

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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)

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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)

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image

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.

1. imageHow many grams of sucrose must be dissolved in 500 mL of water to make a 75% solution? ____________________

2. How many milliliters of 10% solution can be made from 750 g of a chemical? ____________________

3. imageA stock lotion contains 10% methyl salicylate.

4. If 15 mL of peppermint oil is in 500 mL of a solution, what is the percentage strength of the fluids? ____________________

5. imageEpinephrine is available in 5% solution.

6. A 20-mL vial of medication contains 50 mg/mL.

7. imageHow many grams of boric acid would be necessary to prepare 60 mL of a 5% solution? ____________________

8. imageOn hand is a 15% solution of sodium hypochlorite. The physician wants 1 L of a 0.15% solution.

9. imageA stock liter contains 50% sodium bicarbonate. A physician desires 2 L of 6% solution.

10. imageA physician desires 100 mL of a 15% iodine preparation. Ten mL of solution is to be added to 1 pt of water as a soak.

11. imageA physician orders a 2% vinegar solution as a douche. A patient asks how much vinegar should be put in each pint of water. (Round to the whole number.)

12. imageHow many milliliters of a 50% dextrose solution would be administered to a patient in hypoglycemia to provide 150 mg of dextrose? ____________________

13. imageHow many milliliters of sterile water should be added to 75 g of sucrose to make a 2.5% solution? ____________________

14. imageHow many grams of dextrose are necessary to prepare 3000 mL of a 10% solution? ____________________

15. image imageA prescription is written to prepare a mouthwash containing tetracycline 1 g, nystatin suspension 60 mL, Benadryl 60 mL and qs to 240 mL with dexamethasone.

16. imageA prescription is written to prepare a lotion using Aristocort Lotion 1% to be mixed with 60 mL of hand lotion to make a 0.5% lotion.

17. A dentist sends a prescription for a mouth swish for pain.

18. imageA physician orders a 30% solution of dextrose in 500 mL.

19. imageHow many grams of 100% zinc oxide would be necessary to prepare 4 oz of a 10% ointment?

20. imageA dermatologist writes a prescription for 0.25% menthol and 0.5% phenol in Vaseline to make 1 g of ointment.

Interpreting Solution Labels and Calculating Medication In Ratio Dosages

Weak solutions are often expressed in terms of ratio strength such as 1 : 10, which is merely another way to express percentage strength. The 1 : 10 ratio means that 1 part of solute is found in 10 parts of total solution, or 10 parts of solute are found in 100 parts of total solution, or a 10% compound. If the 1 : 10 ratio were a weight (solid) solute found in a volume (liquid) of solvent, 1 g of solute would be found in 10 mL of total solution. If both the solute and solvent were in liquid form, 1 mL of solute would be found in 10 mL of total solution. Finally, if both the solvent and solute are solid (weight), 1 g of solute would be found in 10 g of total compound. To calculate the ratio strengths in a solution or mixture, you may use the ratio and proportion method.

Tech Note

Remember that 1 mL of liquid is equal to 1 g of solid in weight.

Example 13-5

A medication with ratio strength of 1 : 500 has what percentage strength?

1 part:500 parts::x:100%

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500x=100

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image

x=0.2%

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Example 13-6

A medication contains 4 mg/mL of solution. What is the ratio strength of the solution?

Remember that the ratio strength is expressed in grams per 100 mL, so a conversion from milligrams to grams must first be calculated.

4 mg=0.004 g

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0.004 g:1 mL::1 g:x

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0.004 g×x=1 mL×1 g

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0.004x=1 mL

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x=250 mL

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Ratio strength=1:250

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Example 13-7

What ratio strength of a solution can be made by dissolving Benadryl 50 mg in a lotion to make 150 mL?

Again,change 50 mg to grams to get 0.05 g.

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0.05 g:150 mL::1 g:x mL

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0.05 g×x=150 mL×1 g

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image

0.05x=150

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x=3000 mL

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Ratio strength=1:3000

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Practice Problems B

Calculate the following problems for medications in ratio dosage. Round answers to hundredths unless otherwise indicated. Show all your calculations.

1. imagePrepare 500 mL of a 1 : 200 vinegar solution to be used as a douche.

2. imagePrepare 1000 mL of a 1 : 25,000 silver nitrate solution to be used by a urologist.

3. How many milligrams of a drug are in 1.5 mL of a 1 : 5000 solution? ____________________

4. How many milligrams of a drug are found in 1500 mL of a 1 : 750 solution? ____________________

5. How many grams of NaCl would be necessary to make 500 mL of a 1 : 5000 solution? ____________________

6. How many fluid ounces of water should be added to 4 mL of a 1 : 4 concentration to make a 1 : 6 concentration? ____________________

7. If a medication is available in 1 : 500 concentration, how many milliliters would be necessary to provide 750 mg? ____________________

8. imageA boric acid solution is 1 : 10 strength. How many milliliters of 1 : 10 boric acid solution would be necessary to prepare 100 mL of a 5% solution? ____________________

9. An order is written for 1500 mL of a 1 : 10 antiseptic solution. The stock solution is 1 : 5.

10. imageEpinephrine is available in a 1 : 10,000 solution for the treatment of asthma.

11. imageA physician orders a 4% solution of potassium permanganate.

12. imageTylenol with codeine elixir is 25% codeine.

13. A physician orders 1 L solution of sodium chloride 1 : 200.

14. A physician orders a 10% dextrose solution.

15. imageA dentist desires an antiseptic mouthwash of sodium bicarbonate 1 : 40.

16. imageA floor order is received for epinephrine 0.5 mg to be administered IM stat. The supply of epinephrine is 1 : 1000 solution in a 1-mL vial.

17. imageA physician orders Prostigmin 0.4 mg IM stat. The available medication is Prostigmin 1 : 2000 in a 1-ml vial.

18. imageA physician desires a solution of 500 mL of isopropyl alcohol 30%. The available alcohol is isopropyl alcohol 7 : 10.

19. imageA physician orders desoximetasone cream 0.25% 5 g to be used for a patient with allergic dermatitis. The available medication is desoximetasone cream 1 : 2.

20. imageA physician asks that 0.4 g of potassium permanganate be dissolved to prepare a finished pint of solution. (Round to hundredths.)

Calculating The Dilution of Stock Solutions

Diluting stock solutions may be necessary to prepare a solution ordered by the physician. The ability to prepare these solutions from stock medication is also a way in controlling the numbers of medications that are kept in stock. Stock medications are generally more potent or concentrated than the usual desired solution for prescriptions; therefore this medication must be diluted or compounded to a weaker strength. Using stock solutions that are purer and stronger forms of the drug, larger volumes of medications may be prepared from small medication quantities, and space in the pharmacy is saved. Stock solutions have the strength written on the label, and a diluent is added to prepare the compound as ordered. When diluting compounds, the amount of active ingredient or solute remains the same and the solvent amount is increased, reducing the percentage or dilution of the stock solution. Remember from earlier in this chapter that the solvent and solute may be in solid forms, as well as liquid.

Two rules are important in simplifying this process:

Tech Note

Remember that when calculating these problems, as with all math calculations for medication administration, you must use the parts or units in the equivalent measurement system.

Two formulas are available for diluting medications. Either may be used, so the choice depends on what is most comfortable for the person doing the calculation.

Example 13-8

A physician orders 1 L of 10% boric acid solution to be prepared from 40% boric acid solution.

FORMULA 1

Amount of stocksolution necessary=Amount of solution prescribed×Strength prescribedStrength of stock solution

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Step1 —x(Amount of stock)solution necessary=1000mL(amount of solution desired)×10%(strength desired)40%(Strength of stock solution))

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x=1000 mL×10%40%

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image

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x=250 mL of boric acid solution

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Step 2—To complete this calculation, take the amount of solute (250 mL) and subtract it from the final amount of the solution (1000 mL).

1000 mL (total amount of solution ordered) − 250 mL of boric acid solution (amount of solute necessary) = 750 mL (Amount of solvent necessary to prepare the amount of fluid to the physician’s order)

FORMULA 2

SV(Stock volume)×S%(Stock percentage)=DV(Desired volume)×D%(Desired percentage)

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Step1 —x(SV)×40%=1000 mL×10%

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40%×x=10%×1000 mL

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40x=10,000 mL

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x=10,000 mL÷40(or 1000 mL÷4 after cancelling zeros)

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x=250 mL of boric acid

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Step 2—To complete this calculation, you must take the amount of solute (250 mL) and subtract this from the final amount of the solution (1000 mL).

1000mL(Total amount of solution necessary)−250 mL(Amount of solute necessary)=750 mL(Amount of solvent necessary to prepare the amount of fluid to the)physician’s order

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Practice Problems C

Calculate the following problems using either formula described earlier. Round to tenths as appropriate and to other decimal places as indicated. Show your calculations.

1. imagePrepare 1 L of Lysol 3% from a stock solution of Lysol 10%.

2. imagePrepare 500 mL 5% creosol solution from a stock solution of creosol 1 : 10.

3. imageHow many milliliters of sterile water are necessary to prepare 8 oz of 40% solution of isopropyl alcohol from a 70% stock solution? ____________________

4. imagePrepare 1.5 L of creosol 1 : 200 from a 2% stock solution.

5. imagePrepare 1 oz of a 0.002% solution of Merthiolate from a 1% stock solution. (Round to hundredths.)

6. imageA physician orders glycerin solution 15% 250 mL to be used as an enema. The available stock solution is glycerin 25%.

7. imageA physician orders 1 pint of 7.5% dextrose in water. The stock solution of dextrose is 50%.

8. imageHow many milliliters of 20% Zephiran chloride are necessary to prepare 8 ounces of a 7.5% solution?

9. imageA physician desires 1.5 L of potassium chloride 15% from a stock solution that is 20% potassium chloride.

10. imageA medical office needs 3 L of a 1 : 10 solution of hypochlorous acid. The stock solution is Clorox 25%.

11. imageA physician desires 8 oz of Betadine solution 2%. The stock solution is Betadine 10%.

12. imagePrepare 3 L of hydrogen peroxide 1 : 40. The stock solution is hydrogen peroxide 5%.

13. imagePrepare 600 mL of a 2.5% solution from a 10% hydrogen peroxide solution.

14. imagePrepare 4 L of a 1 : 50 solution of potassium permanganate from a 5% potassium permanganate stock solution.

15. image imagePrepare 10 mL of 0.01% adrenaline solution for injection from a 2% adrenaline ampule. (Round to hundredths.)

16. imageA physician desires 500 mL of 2% calcium chloride solution to be given IV. The stock solution is calcium chloride 10%.

17. How many fluid ounces of a 6% solution can be made from 30 mL of a 36% solution?

18. imageA stock solution of 1 : 50 of mercuric chloride is available to prepare 250 mL of 0.02% solution. How many milliliters of stock solution are necessary? ____________________

19. Prepare 500 mL of 10% disinfectant from a 50% stock solution.

20. imageA physician orders 1 pint of 10% ethyl alcohol. The stock solution is 100 mL of 95% ethyl alcohol.

Calculating Medication Dilutions Using Alligation

Alligation is a mathematical method of solving calculations involving the mixing of solutions or compounds possessing different percentage strengths. Alligation alternate is a method of calculating the number of parts of two components of a given strength that are mixed to prepare a mixture of the desired strength. A final proportional calculation permits the translation of relative parts found by alligation to the desired specific amount.

image Tech Alert

Alligation indicates the parts of two given stock medications needed to prepare the desired compound strength.

image Tech Alert

Preparation of diluted compounds from stock medications to meet a prescription ordered compounds is actually accomplished in two distinct steps. The first calculation is to find the parts of each stock medication needed for the compound (Steps 1-7 below). The second calculation is to find the volume/weight of each stock medication needed to prepare the ordered strength (Step 8 below).

The final strength of the mixture must lie somewhere between the strengths of the component parts. This means that the prepared mixture must be stronger than its weakest part and weaker than the strongest component. Therefore the strength of the prepared mixture is “weighted” by the relative amounts of the components involved. If the mixture contains more of the weaker component, the prepared mixture will lie closer to the weaker component. If the mixture contains more of the stronger component, the mixture will be closer to that side of the equation.

To begin alligation alternate, think of preparing a box for playing tic-tac-toe to allow the numbers to be placed in the four corners and in the center box.

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Step 1—Prepare the graph.

Step 2—Place the strength to be calculated in the center box.

Step 3—Place the highest percentage concentration in the left upper corner.

Step 4—Place the lowest percentage concentration in the lower left corner.

Step 5—Subtract the center square from the left upper square and place in the lower right square to reveal the parts of the lowest percentage concentration to be used in the new mixture.

Step 6—Subtract the lower left square from the center box and place in the upper right corner to reveal the parts of the highest percentage concentration to be used in the new mixture.

Step 7—Add the calculated parts together to find the total parts of the two ingredients in the compound.

Step 8—When the total quantity of the mixture is included in the prescription, then the parts of the mixture are placed into two ratio and proportion equations to calculate the exact amount of each ingredient to use. The total number of calculated parts is placed in the first ratio with the total amount of compound. The second ratio set in the proportion is the calculated number of parts of the stock ingredients to the unknown total compound amount. This step must be calculated for each part of the compound.

Example 13-9

Prepare 1 L solution of 70% alcohol from 50% alcohol and 95% alcohol.

Step 1—Draw the graph for calculating alligation.

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Step 2—Place the strength to be calculated in the center box.

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Step 3—Place the highest percentage concentration in the left upper corner.

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Step 4—Place the lowest percentage concentration in the lower left corner.

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Step 5—Subtract the center square from the left upper square and place in the lower right square to reveal the parts of the lowest percentage concentration to be used in the new mixture.

image Tech Alert

Notice that the answers are now in parts, not unit values.

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Step 6—Subtract the lower left square from the center box and place in the upper right corner to reveal the parts of the highest percentage concentration to be used in the new mixture.

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Step 7—Add the parts of the concentration to find the total parts in the compound.

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To prepare this solution, mix 20 parts of 95% alcohol with 25 parts of 50% alcohol.

Remember, this is a proportional amount that must be used to find the exact part amounts when the total weight or volume of the compound is indicated.

The total number of compound parts as calculated using the alligation graph is 45 parts in 1000 mL (1 L) of solution.

First, calculate the number of milliliters of 95% alcohol (stock solution).

45 parts:1000 mL::20 parts:x

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45 parts×x=20 parts×1000 mL

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45x=20,000mL

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x=444.4 mL of95% alcoholor444mLof95% alcohol

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Second, calculate the total number of milliliters of 50% alcohol (stock solution).

45 parts:1000 mL::25 parts:x

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45 parts×x=1000 mL×25 parts

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45x=25,000 mL

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x=555.6mLof50%alcoholor556mLor50%alcohol

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Now check your calculations:

444mLof95% alcohol+556 mLof50%alcohol=1000 mLof70%alcohol

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Therefore the calculations are correct.

Tech Note

Always check your calculations to be sure the total volume/weight of the calculated compound equals the desired prescription weight/volume.

Diluting Stock Medications Using Strengths In Percentage, Fractions, and Ratios

Alligation medial is a method of calculation that may be used to define the weighted average percentage strength of a mixture of two or more substances with known quantities and strengths. When two or more solutes must be added to one compound, this method allows rapid calculation. The percentage strength must be expressed as a whole number for each component. The quantities must be expressed in common measurements such as same weight or same volume indicators. If a percentage of the solvent is not provided, in most cases it may be considered to be 0%.

Alligation medial, another means of checking for accuracy, involves multiplying the percentage as a decimal by the total number of milliliters in the preparation to obtain the total number of grams in the compound. Then multiply the components by the same formula and add the total grams together to check for calculation accuracy.

Example 13-10

Following is the calculation of the previous solution using alligation medial to prove the calculation was made correctly.

Amount desired(milliliters,etc.)×Percent(in a decimal)=Grams

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Prepare 1 L solution of 70% alcohol from 50% alcohol and 95% alcohol

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This calculation shows that the calculations using alligation alternate are correct.

Practice Problems D

Complete these problems using alligation and calculation of the necessary amounts of each component to prepare the amount of compound ordered. Round to tenths unless otherwise indicated. Verify calculations for accuracy using alligation medial. Indicate the calculation of weight/volume of the solute/solvent on each line by indicating the solute/solvent with the answer, such as ____________________ of (15%). Show your work.

1. imageOn hand is a 6% solution of sodium hypochlorite and a 15% solution of sodium hypochlorite. Prepare 500 mL of a 10% solution of sodium hypochlorite.

2. imageAvailable are two ointment strengths containing 5% boric acid and 20% boric acid. Prepare 1 g of a 12.5% ointment.

3. A physician orders 20 g of a 15% tannic acid ointment. Available are two tannic acid ointments in 12% and 25%.

4. imagePrepare 500 mL of 15% potassium chloride solution using 20% potassium chloride and 5% potassium chloride solution.

5. imagePrepare 500 mL of 0.9% sodium chloride solution from a 10% sodium chloride solution.

6. imagePrepare 750 mL of 3% sodium bicarbonate solution from a 15% solution and 1% solution.

7. Prepare 200 mL of 10% dextrose solution using 5% dextrose solution and 50% dextrose solution.

8. imagePrepare 3 L of 3% Lysol solution using 1.5% Lysol and 5% Lysol solutions.

9. A physician desires 50 g of a 7.5% ointment. The available ointments are 2.5% and 15%.

10. imagePrepare 2 L of 40% alcohol from 10% alcohol and 55% alcohol.

11. imagePrepare 500 mL of 4% potassium permanganate solution using 1 : 10 potassium permanganate solution and 1 : 50 potassium permanganate solution.

12. Prepare 250 mL of 8% dextrose solution. The available dextrose solutions are D-5-W and D-10-W.

13. A physician orders 50 mL dextrose 7.5% to be administered IV stat. The available dextrose is D-5-W and dextrose 50% solution.

14. imagePrepare 200 mL of 5% potassium chloride. The available potassium chloride is 20%.

15. Prepare 50 mL of 1.8% sodium chloride solution. The available sodium chloride solutions are 0.9% and 5%. (Round answers to hundredths.)

16. imagePrepare 2.5 g of hydrocortisone ointment 7.6%. The available hydrocortisone ointments are in strengths of 2.5% and 10%.

17. imageA physician orders 1.5 L of a 12% Burrow’s solution. The available Burrow’s solutions are 5% and 25%.

18. Prepare 75 mL 9% solution of dextrose in water. The available medications are D-5-W and dextrose 25% solution.

19. imageA patient needs epinephrine for an acute asthma attack. The physician orders 100 mL of epinephrine 4%. The available epinephrine is 1 : 10 and 1 : 100.

20. imageA physician orders 8 oz of 3% lidocaine solution. The available lidocaine is 1% and 4%.

Review

Stock supplies are often used to prepare compounds that are less concentrated in weight/volume than the stock medications. Stock supplies are often found in commonly used strengths. To obtain the correct amount of medication for the physician’s order or for administering a dose of medication more accurately, the stock medication may need dilution. The processes of dilution or alligation may be used for these purposes. Dilution is the adding of more solvent to the solute to prepare the weaker solution. This can be accomplished using ratio and proportion. If the medication is in two different concentrations, alligation is the method for preparing the medication. However, if the “weighted average” percentage strength is necessary for mixture of two or more substances with a known quantity and concentration, alligation medial may be used for the calculation. As the pharmacy technician, you must know how to calculate the strength and must also know the correct method for calculation on the basis of the information given.

Posttest

Before taking the Posttest, retake the Pretest to check your understanding of the materials presented in this chapter.

Calculate the following problems using the appropriate method for each. As previously, show all of your work. Round to tenths, unless otherwise indicated.

image 1 How many grams of dextrose must be dissolved in sterile water to prepare 100 mL of a 60% solution? ____________________

image 2 If 15 mg of amoxicillin is added to 100 mL of sterile water, what is the percentage strength of the total volume of prepared medication? (Round to thousandths.) ____________________

image 3 A physician orders 5 mL of epinephrine 1% added to 45 mL of sterile water to prepare 50 mL of solution.

image 4 A lotion of 5% methyl salicylate is to be prepared for a patient with allergic dermatitis.

image 5 A lotion of 250 mL of 3% calamine lotion is to be prepared from a 7.5% calamine lotion.

image 6 A stock pint of sodium bicarbonate contains 60% solution. The physician prescribes 1.5 L of 15% sodium bicarbonate solution.

image 7 Prepare 250 mL of a 1 : 500 silver nitrate solution.

 8. A liquid stock is available in a 1 : 350 concentration. You are asked to prepare a pint of 1 : 500 solution.

image 9 A boric acid solution of 1 : 5 is available as a stock solution. A physician asks that you prepare 10 oz of 15% solution.

image 10 A physician orders 250 mL 0.05% epinephrine solution. The available epinephrine is 1 : 500 in 10 mL vials.

image 11 Prepare 500 mL of creosol 1 : 150 from a stock solution of creosol solution 2.5%.

12. A physician orders 250 mL of 15% dextrose in water. The stock solution is 50% dextrose in 10-mL ampules.

image 13 A physician orders 6 oz of glycerin solution 7.5% to be used as a retention enema. The available stock glycerin solution is 25%.

image 14 Prepare 250 mL of a 3% hydrogen peroxide solution from a 12% hydrogen peroxide solution.

image 15 Prepare a 2.5% solution from a 1-pt stock hydrogen peroxide 15% solution.

image 16 On hand is a 5% sodium hypochlorite solution and a 20% sodium hypochlorite solution. Prepare 1 L sodium hypochlorite 12% solution. Check your calculations by alligation medial.

17. Prepare 500 mL of a 12.5% dextrose solution. Available is D-5-W and dextrose 50%. Check your calculations by alligation medial.

image 18 Prepare 2.5 L of 6% Lysol solution using 5% Lysol and 8% Lysol. Check your calculations using alligation medial.

image 19 Prepare 750 mL of 0.75% sodium chloride solution from 0.9% NaCl and 0.45% NaCl solutions. Verify your calculations using alligation medial.

image 20 Prepare 2 L of 12.5% KCl solution using 20% KCl and 10% KCl. Verify the calculations using alligation medial.

Review of Rules

Interpreting Solution Labels

Calculating Medication Dilutions Using Alligation

Step 1—Prepare the graph.

Step 2—Place the strength to be calculated in the center box.

Step 3—Place the highest percentage concentration in the upper left corner.

Step 4—Place the lowest percentage concentration in the lower left corner.

Step 5—Subtract the center square from the upper left square and place in the lower right square to reveal the parts of the lowest percentage concentration to be used in the new mixture. Notice that the answers are now in parts and not in unit values.

Step 6—Subtract the lower left square from the center box and place in the upper right corner to reveal the parts of the highest percentage concentration to be used in the new mixture.

Step 7—Add the calculated parts together to find the total parts of the two ingredients in the compound.

Step 8—When the total quantity of the mixture is included in the prescription, the parts of the mixture are placed into ratio and proportion to calculate the exact amount of each compound to use. The total number of parts is placed in ratio with the total amount of compound. The second ratio is the calculated number of parts to the unknown. This formula must be calculated for each part of the mixture.

Related posts:

Conversion of Clinical Measurements of Numbers, Time, and Temperature Assessment of Mathematical Calculation Skills Needed for Pharmacy Technicians Reconstitution of Powders or Crystals into Liquid Medications Interpretation of Medication Labels and Orders Interpreting Physicians’ Orders for Dosages Calculation of Medications for Special Populations Based on Body Weight and Patient Age