1. If a child’s dose (5 mL) of a cough syrup contains 10 mg of dextromethorphan hydrobromide, what mass of drug is contained in 240 mL?
240 mL/5 mL = x mg/10 mg
x = 240*10/5 = 480 mg
2. How many milligrams of dextromethorphan base (molecular weight = 271.4) are equivalent to 10 mg of dextromethorphan hydrobromide (molecular weight = 352.3)?
x mg /10 mg = 271.4/352.3
x = 10*271.4/352.3
= 7.7 mg
3. A vancomycin solution containing 1000 mg of vancomycin hydrochloride diluted to 250 mL with D5W is to be infused at a constant rate with a continuous-drip intravenous infusion set that delivers 25 drops/mL. What flow rate (drops per minute) should be used to infuse all 250 mL of the vancomycin hydrochloride solution in 2 hrs?
250 mL/2 hrs *1 hr/60 mins *25 drops/1 mL = 52 drops/min
4. What is the percentage strength v/v of the tolu balsam tincture in the syrup preparation? By proportion, we can solve the problem in one step.
50 mL tolu balsam tincture/x mL tolu balsam tincture = 1000 mL syrup/100 mL syrup ; x = 5%
5. What is the concentration, in percent w/v, of a solution containing 2 mEq of potassium chloride per milliliter?
Calculations involving milliequivalents are easily solved if the practitioner follows a predefined procedure to determine the milliequivalent weight. This involves three steps.
1. Find the molecular weight (mol wt).
Atomic wt K = 39
Atomic wt Cl = 35.5
39 + 35.5 = 74.5 g = mol wt of KCl
2. Calculate the equivalent weight (Eq wt) of KCl.
Eq wt = mol wt/valence = 74.5/1 = 74.5 g
3. Determine the milliequivalent weight, which is 1/1000 of the equivalent weight.
mEq wt = 74.5 g/1000 = 0.745 g or 74.5 m
Now that we know the milliequivalent weight, we can calculate by dimensional analysis and proportion the concentration in percentage in a fourth step.
4. 0.0745 g/mEq *2 mEq = 0.149 g of drug
0.149 g drug/1 mL = x g drug/100 mL ;
x =14.9 g/100 mL = 14.9%
6. How many grams of drug substance should be used to prepare 240 g of a 5% w/w solution in water?
The first step in any percentage w/w problem is to attempt identification of the total mass of the mixture. In this problem, the total mass is, obviously, provided (240 g).
b. The problem can be easily solved through dimensional analysis.
240 g mixture *5.0 g drug/100 g drug = 12 g
7. How many milliliters of a 1:50 stock solution of ephedrine sulfate should be used in compounding the following prescription?
Rx
rose water, a.d. 30 mL
0.25 g/100 mL*30 mL = 0.075 g drug required
x = 3.75 mL of stock solution required for prescription
8. How much drug should be added to 30 mL of water to make a 10% w/w solution?
The volume of water that is displaced by the drug is unknown, so the final volume is unknown. Likewise, even though the mass of solvent is known (30 mL*1 g/mL = 30 g), it is not known how much drug is needed, so the total mass is unknown. The water represents 100% - 10% = 90% of the total mixture. Then, by proportion, the mass of drug to be used can be identified.
30 g of mixture (water)/ x g of mixture (drug) = 90%/ 10%;
x = 3.33 g of drug required to make a solution
The common error that many students make in solving problems of this type is to assume that 30 g is the total mass of the mixture. Solving the problem with that assumption gives the following incorrect answer.
x g drug/10 g drug = 30 g mixture/100 g mixture; x = 3 g of drug (incorrect answer)
9. If 30 milliliters (mL) represent 1⁄6 of the volume of a prescription, how many milliliters will represent 1⁄4 of the volume?
1⁄6 = 0.167 and 1⁄4 = 0.25
0.167 (volume)/0.25 (volume) = 30 (mL)/x (mL)
x = 44.91 or 45 mL.
10. If 10 pints of a 5% solution are diluted to 40 pints, what is the percentage strength of the dilution?
10 (pints)/40 (pints) = x (%)/5 (%)/
x = 10*5/40 %
= 1.25%
11. Calculate the smallest quantity of a substance that can be weighed on the balance with the desired precision.
The equation used:
100%*Sensitivity Requirement (mg)/Acceptable Error (%) = Smallest Quantity (mg)
12. Using a graduated cylinder, a pharmacist measured 30 milliliters of a liquid. On subsequent examination, using a narrow-gauge burette, it was determined that the pharmacist had actually measured 32 milliliters. What was the percentage of error in the original measurement?
13. When the maximum potential error is 4 milligrams in a total of 100 milligrams, what is the percentage of error?
4 mg*100%/100 mg = 4%,
14. What is the percent compliance rate if a patient received a 30-day supply of medicine and returned in 45 days for a refill?
% Compliance rate = 30 days/45 days*100% = 66.6%
15. If 54.96 mL of an oil weighs 52.78 g, what is the specific gravity of the oil?
54.96 mL of water weighs 54.96 g
Specific gravity of oil = 52.78 (g)/54.96 (g) = 0.9603
16. A glass plummet weighs 12.64 g in air, 8.57 g when immersed in water, and 9.12 g when immersed in an oil. Calculate the specific gravity of the oil.
12.64 g - 9.12 g = 3.52 g of displaced oil
12.64 g - 8.57 g = 4.07 g of displaced water
Specific gravity of oil 3.52 (g)/4.07 (g) = 0.865
17. What is the volume, in milliliters, of 492 g of nitric acid with a specific gravity of 1.40?
492 g of water measure 492 mL
492 mL/1.40 = 351 mL
18. What is the percentage strength (w/v) of a solution of urea, if 80 mL contains 12 g?
80 mL of water weighs 80 g
80 (g)/12 (g) = 100 (%)/x (%)
x = 15%
19. Express 14000 as a percentage strength.
4000 (parts)/1 (part) =100 (%)/x (%)
x = 0.025%, a
20. A certain injectable contains 2 mg of a drug per milliliter of solution. What is the ratio strength (w/v) of the solution?
2 mg = 0.002 g
0.002 (g)/1 (g) = 1 (mL)/x (mL)
x = 500 mL
Ratio strength = 1:500
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