Pharmaceutical Calculations: Percentage, Ratio Strength, and Other Expressions of Concentration
Danielle DelVillano, Pharm.D.
Define the expressions percent weight-in-volume, percent volume-in-volume, percent weight-in-weight, ratio strengthConvert percent strength to ratio strength and vice versaApply percent strength and ratio strength to pharmaceutical calculations
Definition: rate per hundredExpressed as:50/10050%0.50Example: express 12.5% as an equivalent decimal fraction12.5/100, or 0.125
Percent weight-in-volume (w/v)Number of grams of solute in 100mLsolution%w/vPercent volume-in-volume (v/v)Number ofmLof a solute in 100mLsolution%w/vPercent weight-in-weight (w/w)Number of grams of a solute in 100mLsolution%w/w
When to use which termw/v– solutions, suspensions of solids in liquidsv/v– liquids in liquidsw/w– mixtures of solids (creams)*Overall idea of this section*Solution = Solute + Solvent
Number of grams of solute in 100mLsolutionFor a 3% solution…3gof solute in 100mLsolution
Problem 1 (w/v)
How many grams of dextrose are required to prepare 4000mLof a 5% solution?(5% solution = 5gof dextrose in 100mL)5g=xg100mL4000mLx= 200g
Problem 2 (w/v)
What is the percentage strength of a solution of urea, if 80mLcontains 12g?(% strength =xgin 100mL)12g=xg80mL100mLx= 15%
Number ofmLof solute in 100mLsolutionFor a 5% solution…5mLof solute in 100mLsolution
Problem 3 (v/v)
How manymLofliquifiedphenol should be used in compounding of the following prescription?Liquifiedphenol 2.5%Calamine lotion ad 240mL2.5mL=xmLx= 6mL100mL240mL
Problem 4 (v/v)
What is the percentage strength (v/v) of a solution of 800gof a liquid with a specific gravity of 0.800 in enough water to make 4000mL?800gwater = 800mLwater1000mL=xmL4000mL1000mL800mL/ 0.800 = 1000mLsolutex= 25 %
Number ofgof solute in 100gsolutionFor a 8% solution…8gof solute in 100gsolution*Important to note*Unlikew/v, the weight of the solute is INCLUDED in the weight of the solution for these problems
Problem 5 (w/w)
How should you prepare 100mLof a 2% (w/w) solution of a drug substance in a solvent having a specific gravity of 1.25?100mLsolvent * 1.25 = 125gsolvent100% solution – 2% solute = 98% solvent2%=xg98% 125gMix 2.25gdrug with 125gx= 2.25gof solvent
Problem 6 (w/w)
If 5gof boric acid is added to 100mLof water, what is the percentage strength (w/w) of the solution?100mLwater = 100gwater100gwater (solvent) + 5gboric acid (solute) =105gsolution5g=xx= 4.76%105g100mL
Another way of expressing the percentage strength of a solutionExample: Express 5% as a ratio strength5 parts per 100, or 5:100Commonly we express ratio strength as 1:xSo 5:100 would be expressed 1:20General form: 1 part of solute perxparts of solution
Converting between the Strength Expressions
Express 0.02% as a ratio strength0.02=1 partx= 5000100xparts Answer: 1:5000Express 1:4000 as a percentage strength1 part=xx= 0.025%4000 parts 100
Problem 7 (ratio)
A certaininjectablecontains 2 mg of drug per milliliter of solution. What is the ratio strength (w/v) of the solution?2 mg = 0.002g0.002g=1gx= 500mL1mLxmLAnswer: 1:500
Problem 8 (ratio)
How many milligrams of hexachlorophene should be used in compounding the following prescription?Hexochlorophane1:400Hydrophillicointment ad 10g1g=xgx= 0.025g= 25 mg400g10g
Parts Per Million (PPM) and Parts Per Billion (PPB)
Strengths of very dilute solutionsExample: 1-4 PPMflouridein drinking water1 PPM – 4 PPM1:1000000 – 4:1000000
Problem 9 (PPM)
The concentration of a drug additive in an animal feed is 12.5ppm. How many milligrams of the drug should be used in preparing 5.2 kg of feed?12.5 PPM = 12.5:100000012.5g=xgx= 0.065g= 65 mg1000000g5200g
Ansel, H. C. (2009)PhamaceuticalCalculations(13th Ed.).Philadelphia:LippincottWilliams & Wilkins, andWoltersKluwerPublishers
Chapter 6 Problem 7
If a pharmacist dissolved the contents of eight capsules, each containing 300 mg ofclindamycinphosphate, into a sufficient amount of an astringent liquid base to prepare 60mLof topical solution, what would be the percentage strength (w/v) ofclindamycinphosphate in theprescription?
Chapter 6 Problem 29
A topical solution contains 3%w/vhydroquinone. How many liters of the solution can be prepared from 30gofhydroquinone?
Chapter 6 Problem 30
What is the percentage strength (v/v) if 225gof a liquid having a specific gravity of 0.8 is added to enough water to make 1.5 liters of the solution?
Chapter 6 Problem 38
If 500gof dextrose are dissolved in 600mLof water with a resultant final volume of 1 liter, what is the percentage strength of dextrose in the solution on aw/wbasis?
Chapter 6 Problem 57
A sample of white petrolatum contains 10mg oftocopherolper kilogram as apreservative. Express the amount oftocopherolas a ratio strength.
Chapter 6 Problem 65
In acute hypersensitivity reactions, 0.5mLof a1:1000(w/v) solution ofepinephrinemay be administeredsubcutaneouslyor intramuscularly. Calculate the milligrams of epinephrine given.
Chapter 6 Problem 70
If a commercially available insulinpreparationcontains 1ppmofproinsulin, how many micrograms ofproinsulinwould be contained in a 10-mL vial of insulin?