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Pharmaceutical Calculations (4)

Pharmaceutical Calculations (4). General inter-conversions. Phil Rowe Liverpool School of Pharmacy. General inter-conversions. In the previous presentation, we restricted ourselves to inter-conversions that were either from mass/volume to another unit or vice versa.

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Pharmaceutical Calculations (4)

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  1. Pharmaceutical Calculations (4) General inter-conversions Phil Rowe Liverpool School of Pharmacy

  2. General inter-conversions In the previous presentation, we restricted ourselves to inter-conversions that were either from mass/volume to another unit or vice versa. We now allow for any inter-conversion. Where necessary these will be via mass/volume. Mass/volume Molarity%(w/v)ppmRatio Molarity%(w/v)ppmRatio

  3. Look out for obvious short-cuts The method of converting via mass/volume provides a sure-fire method that always produces the answer. However, there are some cases where there is an obvious short-cut. If you are confident that a short-cut will work, then by all means use it. In the examples that follow, a donkey symbol indicates those cases where a short-cut would be better.

  4. Six examples worked out for you …

  5. (1) Converting from …%(w/v) to molarity e.g. Re-express 0.9%(w/v) aspirin in units of molarity (RMM aspirin = 180) Stage 1: Convert to mass/volume0.9% = 0.9g/100ml = 9g/L Stage 2: Convert to molarity180g/L = 1M1g/L = 1/180M9g/L = 9/180M = 0.05M

  6. (2) Converting from …ppm to %(w/v) e.g. Re-express 20ppm fluoride in units of %(w/v) When converting ppm to %, there is always an easy short-cut, as one is parts per million and the other is effectively parts per hundred. The conversion can be done by simply dividing by 10,000. Thus 20ppm = 20/10,000 = 0.002% Stage 1: Convert to mass/volume20ppm = 20mg/L = 0.02g/L Stage 2: Convert to %(w/v)0.02g/L = 0.002g/100ml = 0.002%(w/v)

  7. (3) Converting from …Ratio to ppm e.g. Re-express 1 in 200,000 adrenaline in units of ppm In this case there is also an obvious short-cut. Multiply both sides by 5 to give 5 in 1,000,000 and so 5ppm Stage 1: Convert to mass/volume1 in 200,000 = 1g/200,000ml = 1g/200L Stage 2: Convert to ppm1g/200L = 1,000mg/200L = 5mg/L = 5ppm

  8. (4) Converting from …Molarity to ratio e.g. Re-express 2.78mM aspirin as a ratio (RMM aspirin = 180) Stage 1: Convert to mass/volume1mM = 180mg/L2.78mM = 2.78 x 180mg/L = 500mg/L Stage 2: Convert to a ratio500mg/L = 0.5g/L = 1g/2L = 1g/2,000ml = 1:2,000

  9. (5) Converting from …ppm to molarity e.g. Re-express 1.5ppm fluoride in micromolar units (RMM fluoride = 19) Stage 1: Convert to mass/volume1.5ppm = 1.5mg/L Stage 2: Convert to micromolar19mg/L = 1mM1mg/L = 1/19mM1.5mg/L = 1.5/19mM = 0.079mM = 79micromolar

  10. (6) Converting from …%(w/v) to a ratio e.g. Re-express 0.2%(w/v) lidocaine as a ratio Stage 1: Convert to mass/volume0.2% = 0.2g/100ml Stage 2: Convert to a ratio0.2g/100ml = 1g/500ml = 1 in 500

  11. Now some for you to try …

  12. Examples of general conversions Question 1 Re-express 0.0007%(w/v) cyanocobalamin in units of ppm

  13. Examples of general conversions Question 2 Re-express adrenaline (1 in 200,000) in micromolar units (RMM adrenaline 183.2)

  14. Examples of general conversions Question 3 Re-express 42micromolar fluoride as ppm. (RMM fluoride = 19)

  15. Examples of general conversions Question 4 Re-express buprenorphine (1 in 4,000) as a %(w/v)

  16. Examples of general conversions Question 5 Re-express 20ppm lead as a ratio.

  17. Examples of general conversions Question 6 Re-express 2mM strychnine hydrochloride (RMM 406.9) as a %(w/v)

  18. Examples of general conversions Answer 1 Re-express 0.0007%(w/v) cyanocobalamin in units of ppm Short-cut is available:% is parts per 100 and ppm is parts per 1,000,000. Conversion is simply x 10,000. 0.0007% = 0.0007 x 10,000 = 7ppm Conversion via mass/vol (mg/L) will yield same result, but slower.

  19. Examples of general conversions Answer 2 Re-express adrenaline (1 in 200,000) in micromolar units (RMM adrenaline 183.2) Stage 1: Convert to mass/volume1 in 200,000 = 1g/200,000ml = 1g/200L = 5mg/L Stage 2: Convert to micromolar units183.2mg/L = 1mM1mg/L = 1/183.2mM5mg/L = 5/183.2mM = 0.0273mM = 27.3 micromolar

  20. Examples of general conversions Answer 3 Re-express 42micromolar fluoride as ppm. (RMM fluoride = 19) Stage 1: Convert to mass/volume1micromolar = 19microgram/L42micromolar = 19 x 42microgram/L = 798microgram/L Stage 2: Convert to ppm798 microgram/L ≈ 0.8mg/L = 0.8ppm

  21. Examples of general conversions Answer 4 Re-express buprenorphine (1 in 4,000) as a %(w/v) Stage 1: Convert to mass/volume1 in 4,000 = 1g/4,000ml = 0.25g/1,000ml Stage 2: Convert to %(w/v)0.25g/1,000ml = 0.025g/100ml = 0.025%(w/v)

  22. Examples of general conversions Answer 5 Re-express 20ppm lead as a ratio. There is a short-cut available. Divide both sides by 20:- 20 parts per million = 1 part per 50,000 = 1 in 50,000 Conversion via mass/vol (mg/L) will yield same result, but slower.

  23. Examples of general conversions Answer 6 Re-express 2mM strychnine hydrochloride (RMM 406.9) as a %(w/v) Stage 1: Convert to mass/volume1mM = 406.9mg/L2mM = 406.9 x 2mg/L = 814mg/L = 0.814g/L Stage 2: Convert to %(w/v)0.814g/L = 0.0814g/100ml ≈ 0.081%(w/v)

  24. What you should be able to do • Inter-convert concentrations quoted in any of the following units:-- mass/volume- molarity- %(w/v)- ppm- ratio

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