T he strengths o very dilute solutions are commonly expressed in terms o parts per million (ppm) or parts per billion (ppb), that is, the number o parts o the agent per 1 million or 1 bil- lion parts o the whole. For example, we are all amiliar with f uoridated drinking water in which f uoride has been added at levels o between 1 to 4 parts per million (1:1,000,000 to 4:1,000,000) or the purpose o reducing dental caries.
We also are aware o and concerned with the presence o trace amounts o contami- nants in our drinking water and ood which can pose a risk to our health and sa ety. Many pharmacists serve on community committees and boards that address environmental issues. Although they may not re er to themselves as envir onmental phar macists, their backgrounds and interest in public health make them invaluable members o such bodies.
Pharmacists have a special leadership role in providing guidance in the sa e disposal o unused and/or expired medications.4,5 Federal regulations and guidelines have been estab- lished to address this issue.6,7
Example Calculations of Parts per Million and Parts per Billion
(1) Express 5 ppm of iron in water in percent strength and ratio strength.
5 ppm = 5 parts in 1,000,000 parts = 1:200,000, ratio strength, and
= 0.0005, percentage strength
(2) T he 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?
12.5 ppm = 12.5 g (drug) in 1,000,000 g ( eed) T hus,
1 000 000 12 5
5 200 0 065 , ,
.
, . g
g
g x g
x g
=
= = 65 mg
(3) T he drinking water in a community has detected lead in its drinking water at a level of 2.5 ppb. The EPA’s MCL is set at 15 ppb. Express the difference between these two values as a ratio strength.
15 ppb − 2.5 ppb = 12.5 ppb = 12.5:1,000,000,000 = 1:80,000,000
6 • P r nt s tr ngth, Ratio s tr ngth, and Oth r e xpr ion of c on ntration 101
PRa Ct ICE PROb l EmS Weight-in-Volume Calculations
1. CLO BEX lotion contains 0.05% w/v clobetasol propionate in 118 mL contain- ers. Calculate the content o drug, in milligrams.
2. Of oxacin ophthalmic solution 0.3%
D isp. 10 mL
H ow many milligrams o of oxacin are contained in each milliliter o the dispensed prescription?
3.8 D examethasone sodium phosphate 100 mg Sterile water or injection ad 100 mL
Calculate the percent strength o dexamethasone sodium phosphate in the prescription.
4. I 100 mL o a pharmaceutical preparation contains 20 mL o a 50% w/v solution o benzalkonium chloride, what is the percent strength o that agent in the solution?
5. A tissue plasminogen activator (T PA) ophthalmic solution is prepared to contain 25 mg/100 mL.
(a) Calculate the percent concentration o T PA in the solution.
(b) W hat volume o a solution containing T PA, 50 mg/50 mL, should be used to prepare each 100 mL o the ophthalmic solution?
6. H ow many milligrams o methylparaben are needed to prepare 8 luidounces o a solution containing 0.12% w/v o methylparaben?
7. A pharmacist emptied the contents o eight capsules, each containing 300 mg o clindamycin phosphate, into a liquid vehicle to prepare 60 mL o a suspension.
Calculate the percent strength o clindamycin phosphate in the preparation.
8. Ketorolac ophthalmic solution 0.5%
Disp. 5 mL
Sig: One drop q.i.d. prn allergic conjunctivitis
H ow many milligrams o the active constituent would be present in each drop o the ophthalmic solution i the dropper service delivers 20 drops per milliliter?
(a) 0.25 mg (b) 25 mg
(c) 0.025 mg (d) 1.25 mg
9. A ormula or an anti ungal shampoo contains 2% w/ v ketoconazole. H ow many grams o ketoconazole would be needed to prepare 240 mL o the shampoo?
10. T he biotechnology drug inter eron gamma-1b (ACT IMMU N E) contains 100 mcg/0.5 mL. Calculate the percent strength o the solution.
11. Filgrastim (N EUPO G EN ) pre illed syringes contain 480 mcg o active constituent in each 0.8 mL. T he equivalent concentration is:
(a) 0.6%
(b) 0.384 mg/mL (c) 0.06%
(d) 0.6 g/mL
102 Pharma euti al c al ulations
12. Levofloxacin (LEVAQ UIN ) injection contains 5 mg/mL of levofloxacin and 5%
of dextrose. H ow much of each would be delivered to a patient upon the admin- istration of a 100-mL injection?
(a) 5 g levofloxacin and 5 g dextrose (b) 50 mg levofloxacin and 5 g dextrose
(c) 500 mg levofloxacin and 500 mg dextrose (d) 0.5 g levofloxacin and 5 g dextrose
13. An injection contains, in each milliliter, 60 mg of darbepoetin alfa (ARAN ESP), 0.05 mg of polysorbate 80, and 8.18 mg of sodium chloride. Calculate the percent of each in the injection.
14. An injection of adalimumab (H U MIRA) contains 40 mg/0.8 mL. Calculate the percent concentration of the injection.
15.9 Erythromycin lactobionate 500 mg Dexamethasone sodium phosphate 100 mg
Glycerin 2.5 mL
Sterile water for injection ad 100 mL M. ft. ophthalmic solution
(a) W hat is the percent strength of erythromycin lactobionate in the prescription?
(b) If glycerin has a specific gravity of 1.25, what is its percent concentration in the prescription?
16. CIPRO DEX, an otic suspension, contains 0.3% w/v ciprofloxacin and 0.1% w/v dexamethasone in 7.5-mL drop containers. Calculate the quantities of each agent based on mg/mL.
17. A 180-mL bottle of an oral solution contains sodium oxybate, 0.5 g/mL.
Calculate (a) the quantity of sodium oxybate, in grams, in the bottle and (b) the percent strength of sodium oxybate in the solution.
18. In the preparation of an intravenous infusion, a vial containing 115 mg of drug is diluted to 5 mL with sodium chloride for injection. T hen, the contents of the vial are added to 110 mL of an infusion solution. Calculate the drug strength of the final infusion in (a) mg/mL, (b) percent strength, and (c) ratio strength.
19. An ophthalmic solution contains tafluprost, 0.0015% w/v, available in 0.3 mL pouches for single use. Calculate (a) the quantity of tafluprost, in micrograms, in each pouch and (b) the number of single-dose pouches that the manufacturer may prepare from each 1 g of drug.
20. A pharmacist adds 10 mL of a 20% w/v solution of a drug to 500 mL of D5W for parenteral infusion. W hat is the percentage strength of the drug in the infusion solution?
(a) 2% v/v (b) 2% w/v
(c) 1.96% w/v (d) 0.39% w/v
21. Calculate the percentage strength of an injection that contains 2 mg of hydro- morphone hydrochloride in each milliliter of injection.
22. VIRAMU N E oral suspension contains 1% w/v of nevirapine. Calculate the mil- ligrams of nevirapine present in a 240-mL bottle of the suspension.
23.10 Misoprostol 200-mg tablets 12 tablets Lidocaine hydrochloride 1 g
Glycerin qs ad 100 mL
6 • P r nt s tr ngth, Ratio s tr ngth, and Oth r e xpr ion of c on ntration 103 Calculate the strength of misoprostol in the prescription.
(a) 2.4% w/v misoprostol (b) 0.0002% w/v misoprostol
(c) 0.024 mg/mL misoprostol (d) 2.4 mcg/mL misoprostol
24.11 Fentanyl citrate 20 mg/mL Bupivacaine hydrochloride 0.125%
Sodium chloride (0.9%) injection ad 100 mL
Calculate the percentage concentration of fentanyl citrate in the prescription.
25. Bepotastine besilate (BEPREVE) ophthalmic solution contains 1.5% w/v of the therapeutic agent. Express this concentration in mg/mL.
26. If 100 mL of a solution for patient-controlled anesthesia contains 200 mg of mor- phine sulfate and 8 mg of droperidol, calculate the percentage strength of each of these ingredients in the solution.
27. O xycodone hydrochloride oral concentrate solution (O XYFAST ) contains 20 mg/mL. If a dose of 0.75 mL is added to 30 mL of juice prior to administra- tion, calculate (a) the milligrams of oxycodone hydrochloride administered and (b) the percent concentration of oxycodone hydrochloride in the drink.
28. A morphine sulfate extended-release liposome injection (D EPOD UR) contains morphine sulfate 10 mg/mL of injection. Calculate the percent strength of mor- phine sulfate in the injection.
29. A topical solution contains 3% w/v hydroquinone. H ow many liters of the solu- tion can be prepared from 30 g of hydroquinone?