6: Percent Strength, Ratio Strength, and Other
Expressions of Concentration
Practice Problems
Weight-in-Volume Calculations
1. CLOBEX lotion contains 0.05% w/v clobetasol propionate in 118 mL containers.
Calculate the content of drug, in milligrams.
2.
Ofloxacin ophthalmic solution 0.3%
Disp. 10 mL
How many milligrams of ofloxacin are contained in each milliliter of the dispensed
prescription?
3. 8
Dexamethasone sodium phosphate 100 mg
Sterile water for injection ad 100 mL
Calculate the percent strength of dexamethasone sodium phosphate in the prescription.
4. If 100 mL of a pharmaceutical preparation contains 20 μL of a 50% w/v solution of
benzalkonium chloride, what is the percent strength of that agent in the solution?
5. A tissue plasminogen activator (TPA) ophthalmic solution is prepared to contain 25
μg/100 μL.
a. Calculate the percent concentration of TPA in the solution.
b. What volume of a solution containing TPA, 50 mg/50 mL, should be used to prepare
each 100 μL of the ophthalmic solution?
6. How many milligrams of methylparaben are needed to prepare 8 fluidounces of a
solution containing 0.12% w/v of methylparaben?
7. A pharmacist emptied the contents of eight capsules, each containing 300 mg of
clindamycin phosphate, into a liquid vehicle to prepare 60 mL of a suspension. Calculate
the percent strength of clindamycin phosphate in the preparation.
8.
Ketorolac ophthalmic solution 0.5%
Disp. 5 mL
Sig: One drop q.i.d. prn allergic conjunctivitis
How many milligrams of the active constituent would be present in each drop of the
ophthalmic solution if 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 formula for an antifungal shampoo contains 2% w/v ketoconazole. How many grams
of ketoconazole would be needed to prepare 240 mL of the shampoo?
10. The biotechnology drug interferon gamma-1b (ACTIMMUNE) contains 100 mcg/0.5
mL. Calculate the percent strength of the solution.
11. Filgrastim (NEUPOGEN) prefilled syringes contain 480 mcg of active constituent in
each 0.8 mL. The equivalent concentration is:
a. 0.6%
b. 0.384 mg/mL
c. 0.06%
d. 0.6 g/mL
12. Levofloxacin (LEVAQUIN) injection contains 5 mg/mL of levofloxacin and 5% of
dextrose. How much of each would be delivered to a patient upon the administration 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 μg of darbepoetin alfa (ARANESP), 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 (HUMIRA) 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. What 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. CIPRODEX, 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. Then, 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. What 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 hydromorphone
hydrochloride in each milliliter of injection.
22. VIRAMUNE oral suspension contains 1% w/v of nevirapine. Calculate the milligrams
of nevirapine present in a 240-mL bottle of the suspension.
23. 10
Misoprostol 200-μg tablets 12 tablets
Lidocaine hydrochloride 1 g
Glycerin qs ad 100 mL
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 μ/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 morphine
sulfate and 8 mg of droperidol, calculate the percentage strength of each of these
ingredients in the solution.
27. Oxycodone hydrochloride oral concentrate solution (OXYFAST) contains 20 mg/mL. If
a dose of 0.75 mL is added to 30 mL of juice prior to administration, 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 (DEPODUR) contains
morphine sulfate 10 mg/mL of injection. Calculate the percent strength of morphine sulfate
in the injection.
29. A topical solution contains 3% w/v hydroquinone. How many liters of the solution can
be prepared from 30 g of hydroquinone?
Volume-in-Volume Calculations
30. What is the percent strength (v/v) if 225 g of a liquid having a specific gravity of 0.8 are
added to enough water to make 1.5 L of the solution?
31. Cyclosporine (GENGRAF) capsules contain a dispersion of 25 mg of cyclosporine in a
hydroalcoholic vehicle. The labeled content of absolute alcohol content is “12.8% v/v
equivalent to 10.1% w/v.” From these data, calculate the specific gravity of absolute
alcohol.
32. A lotion vehicle contains 15% v/v of glycerin. How much glycerin should be used in
preparing 5 gallons of the lotion?
a. 2271 g glycerin
b. 3339.7 mL glycerin
c. 2671.8 g glycerin
d. 3548.4 g glycerin
33. The formula for 1 L of an elixir contains 0.25 mL of a flavoring oil. What is the percent
strength of the flavoring oil in the elixir?
34. A dermatologic lotion contains 1.25 mL of liquefied phenol in 500 mL. Calculate the
percent strength of liquefied phenol in the lotion.
Weight-in-Weight Calculations
35. Each gram of LOTRISONE lotion contains 10 mg of clotrimazole and 0.643 mg of
betamethasone dipropionate. Calculate the percent concentration of each of these two
agents in the lotion.
36. A hemorrhoidal ointment contains, on a weight-in-weight basis, 46.6% mineral oil, 1%
pramoxine HCl, and 12.5% zinc oxide in an ointment base. Calculate the grams of each
ingredient, including the ointment base, in each 30-g tube.
37. What is the percentage strength (w/w) of a solution made by dissolving 62.5 g of
potassium chloride in 187.5 mL of water?
38. If 500 g of dextrose are dissolved in 600 mL of water with a resultant final volume of 1
L, what is the percentage strength of dextrose in the solution on a w/w basis?
39. Hydromorphone hydrochloride suppositories contain 3 mg of active ingredient and
weigh approximately 2 g each. What is the equivalent percentage strength?
a. 1.5%
b. 0.15%
c. 0.015%
d. None of the above
40. A metronidazole vaginal gel contains 0.75% of drug in 70-g tubes. An applicator will
hold 5 g of gel for each administration. How much drug will be contained in each
application?
a. 0.0375 mg metronidazole
b. 3.75 mg metronidazole
c. 37.5 mg metronidazole
d. 375 mg metronidazole
41. The percent of acyclovir and quantity of lidocaine in the filled prescription are:
Acyclovir (ZOVIRAX) 5% cream
Lidocaine 4% cream aa. 15 g
a. 3.75% acyclovir, 0.3 g lidocaine
b. 5% acyclovir, 1.2 g lidocaine
c. 2.5% acyclovir, 0.6 g lidocaine
d. 2.5% acyclovir, 1.2 g lidocaine
42. ANDROGEL 1.62% w/w is a testosterone gel applied topically in males for endogenous
testosterone deficiency. For a starting dose of 40.5 mg testosterone, calculate the quantity,
in grams, of gel administered.
43. DESONATE gel contains 0.05% w/w desonide. Calculate (a) the quantity of this agent,
in grams, in each 60-g tube of product and (b) the concentration of desonide, in mg/g of gel.
44. Each gram of an ointment contains 2.5 mg of miconazole nitrate. The ointment is
available in 50-g tubes. Calculate (a) the percent concentration of miconazole nitrate in the
ointment and (b) the quantity of miconazole nitrate, in grams, in each tube of ointment.
45. A triamcinolone acetonide topical aerosol spray contains 0.147 mg of triamcinolone
acetonide in each gram of product. Calculate the percent strength of triamcinolone
acetonide in the product.
46. Calcipotriene (SORILUX) foam, 0.005% w/w, is supplied in containers holding 60 g of
product. Calculate the number of milligrams of calcipotriene per container.
47. A topical gel contains 1.2% w/w clindamycin phosphate and 0.025% w/w tretinoin.
Calculate the quantity of each of these ingredients on an mg/g basis.
Mixed Percent Calculations
48. 12
Progesterone, micronized 4g
Glycerin 5 mL
Methylcellulose (1%) solution 50 mL
Cherry syrup ad 100 mL
a. What is the percent concentration (w/v) of progesterone in the prescription?
b. What is the percent concentration (w/v) of methylcellulose in the prescription?
c. What is the percent concentration (v/v and w/v) of glycerin (sp gr 1.25) in the
prescription?
49. 13
Lactic acid 4g
Salicylic acid 5g
Trichloroacetic acid 2g
Flexible collodion qs ad 100 g
Sig: wart remover. Use as directed.
a. Flexible collodion contains 20% w/w camphor and 30% w/w castor oil. How many grams
of each would be contained in 30 g of the mixture?
b. The specific gravity of castor oil is 0.955. How many milliliters of the oil is contained in
30 g of the mixture?
c. If the specific gravity of the mixture is 0.781, what are the percent w/v concentrations of
lactic acid, salicylic acid, and trichloroacetic acid in the mixture?
Ratio Strength Calculations
50. Express each of the following as a percent strength:
a. 1:1500
b. 1:10,000
c. 1:250
d. 1:400
e. 1:3300
f. 1:4000
51. Express each of the following as a ratio strength:
a. 0.125%
b. 2.5%
c. 0.80%
d. 0.6%
e. ⅓%
f. ½%
52. Express each of the following concentrations as a ratio strength:
a. 2 mg of active ingredient in 2 mL of solution
b. 0.275 mg of active ingredient in 5 mL of solution
c. 2 g of active ingredient in 250 mL of solution
d. 1 mg of active ingredient in 0.5 mL of solution
53. A doxycycline calcium syrup is preserved with 0.08% w/v of methylparaben, 0.02% w/v
of propylparaben, and 0.1% w/v of sodium metabisulfite. Express these concentrations as
ratio strengths.
54. An injection contains 0.5% w/v of lidocaine hydrochloride and 1:200,000 w/v of
epinephrine. Express the concentration of lidocaine hydrochloride as a ratio strength and
that of epinephrine as a percent strength.
55. A sample of white petrolatum contains 10 mg of tocopherol per kilogram as a
preservative. Express the amount of tocopherol as a ratio strength.
56.
Potassium permanganate tablets 0.2 g
Disp. #100
Sig: two tablets in 4 pt of water and use as directed.
Express the concentration, as a ratio strength, of the solution prepared according to the
directions given in the prescription.
57. A skin test for fire ant allergy involves the intradermal skin prick of 0.05 mL of a
1:1,000,000 w/v dilution of fire ant extract. How many micrograms of extract would be
administered in this manner?
58. An eyedrop has the following formula:
Fluorometholone 0.1% w/v
Neomycin sulfate 0.35% w/v
Benzalkonium
0.004% w/v
chloride
Isotonic vehicle ad 5 mL
a. Calculate the ratio strength of benzalkonium chloride in the formula.
b. Calculate the quantity of fluorometholone, in milligrams, in the formula.
59. A lubricating eyedrop has the following formula:
Polyvinyl alcohol 1.4% w/v
Benzalkonium chloride 0.005% w/v
Sterile vehicle ad 10 mL
Calculate the equivalent ratio strength of the benzalkonium chloride
Parts per Million Calculations
60. Purified water contains not more than 10 ppm of total solids. Express this
concentration as a percentage.
61. How many grams of sodium fluoride should be added to 100,000 L of drinking water
containing 0.6 ppm of sodium fluoride to provide a recommended concentration of 1.75
ppm?
62. 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?
Calcquiz
6.A. AURALGAN Otic Drops contain:
o Antipyrine 5.4%
o Benzocaine 1.4%
o Acetic acid 0.01%
o u-Polycosanol 410 0.01%
o Glycerin, ad 10 mL
a. What would be the content of antipyrine, in mg/mL?
b. If a patient used 5 drops of the otic solution, equivalent to 0.25 mL, how
many milligrams of benzocaine would have been administered?
c. How many microliters of acetic acid would be used to prepare the 10 mL
of drops?
d. What would be the equivalent ratio strength (v/v) of u-polycosanol 410?
6.B. Among its other ingredients, VISINE-A eyedrops contain the active ingredients: 0.025%
w/v naphazoline hydrochloride and 0.3% w/v pheniramine maleate and 1:10,000 w/v
benzalkonium chloride as a preservative. Calculate (a) the corresponding percent strength of
benzalkonium chloride and (b) the quantities of each of the three ingredients in a 15-mL
container.
6.C. An intravenous solution of AVELOX contains 400 mg of moxifloxacin hydrochloride (1.6
mg/mL). Calculate (a) the percent concentration of moxifloxacin hydrochloride and (b) the
volume of solution in the product.
6.D. ATROVENT Nasal Spray contains 0.03% w/v of ipratropium bromide in a 30-mL metered
dose container. If the container is calibrated to deliver 345 sprays, calculate (a) the volume of
each spray, in microliters, and (b) the number of milligrams of ipratropium bromide in each
spray.
6.E. A homeopathic teething gel states on its product label that it contains 0.0000003% alkaloid.
Express the alkaloid content in ppm.
Answers
Practice Problems
1. 59 mg clobetasol propionate
2. 3 mg ofloxacin
3. 0.1% w/v dexamethasone sodium phosphate
4. 0.01% w/v benzalkonium chloride
5. 0.025% w/v TPA
0.025 mL
6. 283.9 mg methylparaben
7. 4% w/v clindamycin phosphate
8. (a) 0.25 mg ketorolac
9. 4.8 g ketoconazole
10. 0.02% w/v interferon gamma-1b
11. (c) 0.06%
12. (d) 0.5 g levofloxacin and 5 g dextrose
13. 0.006% w/v darbepoetin alpha,
0.005% w/v polysorbate 80, and
0.818% w/v sodium chloride
14. 5% w/v adalimumab
15. 0.5% w/v erythromycin lactobionate
3.125% w/v glycerin
16. 3 mg/mL ciprofloxacin and
1 mg/mL dexamethasone
17. 90 g sodium oxybate
50% w/v sodium oxybate
18. 1 mg/mL
0.1% w/v
1:1000 w/v
19. 4.5 mcg tafluprost
222,222 pouches
20. (d) 0.39% w/v
21. 0.2% w/v hydromorphone
22. 2400 mg nevirapine
23. (c) 0.024 mg/mL misoprostol
24. 0.002% w/v fentanyl citrate
25. 15 mg bepotastine besilate/mL
26. 0.2% w/v morphine sulfate and
0.008% w/v droperidol
27. 15 mg oxycodone hydrochloride
0.049% w/v oxycodone hydrochloride
28. 1% w/v morphine sulfate
29. 1 L
30. 18.75% v/v
31. 0.79
32. (d) 3548.4 g glycerin
33. 0.025 v/v flavoring oil
34. 0.25% v/v liquefied phenol
35. 1% w/w clotrimazole and
0.0643% w/w betamethasone dipropionate
36. 13.98 g mineral oil
0.3 g pramoxine HCl
3.75 g zinc oxide
11.97 g ointment base
37. 25% w/w potassium chloride
38. 45.45% w/w dextrose
39. (b) 0.15%
40. (c) 37.5 mg metronidazole
41. (c) 2.5% acyclovir, 0.6 g lidocaine
42. 2.5 g of testosterone gel
43. 0.03 g desonide
0.5 mg desonide/g gel
44. 0.25% w/w miconazole nitrate
0.125 g miconazole nitrate
45. 0.0147 % w/w triamcinolone acetonide
46. 3 mg calcipotriene
47. 12 mg/g clindamycin phosphate and
0.25 mg/g tretinoin
48. 4% w/v progesterone
0.5% w/v methylcellulose
5% v/v and 6.25% w/v glycerin
49. 5.34 g camphor and 8.01 g castor oil
8.39 mL castor oil
3.12% w/v lactic acid,
3.91% w/v salicylic acid, and
1.56% w/v trichloroacetic acid
50. 0.067%
0.01%
0.4%
0.25%
0.03%
0.025%
51. 1:800
1:40
1:125
1:166.67 or 1:167
1:300
1:200
52. 1:1000
1:18,182
1:125
1:500
53. 1:1250 w/v methylparaben
1:5000 w/v propylparaben
1:1000 w/v sodium metabisulfite
54. 1:200 w/v lidocaine hydrochloride
0.0005% w/v epinephrine
55. 1:100,000 w/w tocopherol
56. 1:4730 w/v potassium permanganate
57. 0.05 mg fire ant extract
58. 1:25,000 w/v benzalkonium chloride
5 μgg fluorometholone
59. 1:20,000 w/v benzalkonium chloride
60. 0.001% w/v
61. 115 g sodium fluoride
62. 10 μg proinsulin
