Pharmaceutical Calculations (2) Re-expressing simple mass/volume concentrations Phil Rowe Liverpool School of Pharmacy

Re-expressing concentrations - the plan of the next 3 presentations We will tackle the problem of re-expressing concentrations in three stages. These are shown on the next 3 slides:-

Pharmaceutical calculations 2 Molarity %(w/v) ppm Ratio Mass/volume Molarity %(w/v) ppm Ratio Current presentation ‘Pharmaceutical Calculations (2)’ deals only with inter-conversions within this category. i.e. one mass/volume into another.

Pharmaceutical calculations 3 Molarity %(w/v) ppm Ratio Mass/volume Molarity %(w/v) ppm Ratio The next presentation ‘Pharmaceutical Calculations (3)’ will deal with interconversions EITHER from mass/volume to another system OR from another system to mass/volume

Pharmaceutical calculations 4 Molarity %(w/v) ppm Ratio Mass/volume Molarity %(w/v) ppm Ratio Then ‘Pharmaceutical Calculations (4)’ will deal with inter-conversions from any system to any other, using mass/volume as an intermediate step where necessary.

Inter-converting concentrations expressed as mass/volume Tips

Tip (1) Take it easy – Do one step at a time. Example: You need to convert 25mg per 5ml to units of g/L. If you are very confident you could do it in a single step, changing both the volume and the mass units. However, at this stage, you are probably better tackling one thing at a time. It would be possible to change either the volume first and then the mass or vice versa. Either is OK. In the example calculation that follows, volume is tackled first.

Tip (1) Take it easy – Do one step at a time. Example: You need to convert 25mg per 5ml to units of g/L. First convert the volume to litres 25mg per 5ml = 5mg/ml = 5,000mg/L Then convert the mass to grams 5,000mg/L = 5g/L

Tip (2) When converting from one unit to another, jump one level at a time. Example: You need to convert 0.0025g/L to units of microgram/100ml. When tackling the mass units, don’t try to jump directly from g to micrograms; go via milligrams. Convert grams to micrograms via mg 0.0025g/L = 2.5mg/L = 2,500microgram/L Convert the volume to 100ml 2,500microgram/L = 250microgram/100ml

Tip (3) The “Increase/decrease both units” rule When a conversion involves either: Increasing both the mass and volume units by one level or Decreasing both the mass and volume units by one level there is no effective change of units and the number stays the same. 15mg/ml = 15g/L (mg goes up to g. ml goes up to L.) 200mg/L = 200microgram/ml (mg goes down to microgram. L goes down to ml.) 0.75ng/ml = 0.75microgram/L (ng goes up to microgram. ml goes up to L.)

Tip (4) Avoid intermediate calculations with excessively small or large numbers Example: A solution contains 1.5 microgram per 0.1ml. Re-express as g/L. You could proceed as below (But I wouldn’t recommend it!) Convert micrograms to grams via mg 1.5microgram/0.1ml = 0.0015mg/0.1ml = 0.0000015g/0.1ml Convert the volume to litres 0.0000015g/0.1ml = 0.000015g/ml = 0.015g/L Profusion of zeros makes arithmetic errors very likely!

Tip (4) Avoid intermediate calculations with excessively small or large numbers A better approach is: A solution contains 1.5 microgram per 0.1ml. Re-express as g/L. Convert 0.1ml to 1ml 1.5microgram/0.1ml = 15microgram/ml Convert microgram to mg 15microgram/ml = 0.015mg/ml Use the “increase/decrease both units” rule 0.015mg/ml = 0.015g/L

Examples of inter-converting mass/volume concentrations Question 1 (of 12) Re-express 0.75mg/100ml in units of microgram/100ml Answers are provided after all the questions.

Examples of inter-converting mass/volume concentrations Question 2 (of 12) Re-express 2.5mg per 5ml in units of mg/L Answers are provided after all the questions.

Examples of inter-converting mass/volume concentrations Question 3 (of 12) Re-express 655mg/L in units of microgram/ml Answers are provided after all the questions.

Examples of inter-converting mass/volume concentrations Question 4 (of 12) Re-express 800mg/L in units of g/100ml Answers are provided after all the questions.

Examples of inter-converting mass/volume concentrations Question 5 (of 12) Re-express 40mg per 5ml in units of g/L Answers are provided after all the questions.

Examples of inter-converting mass/volume concentrations Question 6 (of 12) Re-express 35mg/L in units of g/L Answers are provided after all the questions.

Examples of inter-converting mass/volume concentrations Question 7 (of 12) Re-express 50mg/ml in units of g/L Answers are provided after all the questions.

Examples of inter-converting mass/volume concentrations Question 8 (of 12) Re-express 150microgram/ml in units of mg per 5ml Answers are provided after all the questions.

Examples of inter-converting mass/volume concentrations Question 9 (of 12) Re-express 0.035g/100ml in units of mg/L Answers are provided after all the questions.

Examples of inter-converting mass/volume concentrations Question 10 (of 12) Re-express 7,500pg/ml in units of microgram/ml Answers are provided after all the questions.

Examples of inter-converting mass/volume concentrations Question 11 (of 12) Re-express 60microgram per 5ml in units of mg per 5ml Answers are provided after all the questions.

Examples of inter-converting mass/volume concentrations Question 12 (of 12) Re-express 0.004mg/ml in units of ng/ml Answers are provided after all the questions.

Examples of inter-converting mass/volume concentrations Answer 1 Re-express 0.75mg/100ml in units of microgram/100ml [Only mass units change] 0.75mg/100ml = 750microgram/100ml

Examples of inter-converting mass/volume concentrations Answer 2 Re-express 2.5mg per 5ml in units of mg/L 2.5mg per 5ml = 5mg/10ml = 500mg/L

Examples of inter-converting mass/volume concentrations Answer 3 Re-express 655mg/L in units of microgram/ml [Use “Increase/decrease both units” rule] 655mg/L = 655microgram/ml

Examples of inter-converting mass/volume concentrations Answer 4 Re-express 800mg/L in units of g/100ml 800mg/L = 0.8g/L = 0.08g/100ml

Examples of inter-converting mass/volume concentrations Answer 5 Re-express 40mg per 5ml in units of g/L 40mg per 5ml = 8mg/ml [Use “Increase/decrease both units” rule] 8mg/ml = 8g/L

Examples of inter-converting mass/volume concentrations Answer 6 Re-express 35mg/L in units of g/L [Only mass units change] 35mg/L = 0.035g/L

Examples of inter-converting mass/volume concentrations Answer 7 Re-express 50mg/ml in units of g/L [Use “Increase/decrease both units” rule] 50mg/ml = 50g/L

Examples of inter-converting mass/volume concentrations Answer 8 Re-express 150microgram/ml in units of mg per 5ml 150microgram/ml = 0.15mg/ml = 0.75mg per 5ml

Examples of inter-converting mass/volume concentrations Answer 9 Re-express 0.035g/100ml in units of mg/L 0.035g/100ml = 35mg/100ml = 350mg/L

Examples of inter-converting mass/volume concentrations Answer 10 Re-express 7,500pg/ml in units of microgram/ml [Mass units change two levels - go via ng] 7,500pg/ml = 7.5ng/ml = 0.0075microgram/ml

Examples of inter-converting mass/volume concentrations Answer 11 Re-express 60microgram per 5ml in units of mg per 5ml [Only mass units change] 60microgram per 5ml = 0.06mg per 5ml

Examples of inter-converting mass/volume concentrations Answer 12 Re-express 0.004mg/ml in units of ng/ml [Mass units change two levels - go via microgram] 0.004mg/ml = 4microgram/ml = 4,000ng/ml

What you should be able to do Re-express a concentration quoted in units of mass/volume in any other units of mass/volume