1. Pharmaceutical Calculations (3)
Inter-converting mass/volume units with any other
Phil Rowe Liverpool School of Pharmacy

2. Inter-conversions
We need to be able to start with a concentration in one set of units and re-express it in another. e.g. re-express the concentration of a 0.1mM aspirin solution in terms of ppm.
This particular case would be difficult to perform as a direct calculation! However, such inter-conversions are achievable if we go via simple mass/vol units.
Continued on next slide …

3. Inter-conversions
Most of the 7 different methods for expressing concentration can be reasonably easily inter-converted, except %(v/v) and %(w/w).
Converting %(v/v) to mass/volume units would be a problem because the numerator (top of the fraction) would have to be converted from volume to mass units, thus involving the specific gravity of the liquid in question. This is much more complex and %(v/v) is excluded from this presentation.
Similarly, trying to convert %(w/w) to mass/volume units would mean changing the denominator from mass to volume units. %(w/w) is therefore also excluded from the rest of this discussion.

4. Inter-conversions Molarity %(w/v) Mass/volume ppm
The remaining 5 methods of expressing concentration can however all be inter-converted reasonably easily.
Molarity
%(w/v)
Mass/volume
ppm
Ratio e.g. 1 in 50,000
All of the outer units can readily be converted to units of mass/volume and vice versa.

5. Inter-conversions – The general idea
Proceed in two steps, using mass/vol as a ‘common currency’.
Convert initial units into mass/vol
Convert mass/vol to required final units
Molarity %(w/v) ppm Ratio
Mass/volume
Molarity %(w/v) ppm Ratio

6. The problem posed previously:
Inter-conversions
The problem posed previously:
Re-express the concentration of a 0.1mM aspirin solution in terms of ppm. (The RMM of aspirin is 180)
Stage 1: Convert 0.1mMolar to mass/vol
1mM = 180mg/L 0.1mM = 18mg/L
Stage 2: Convert mass/vol units to ppm
1mg/L = 1 ppm 18mg/L = 18ppm

7. Inter-conversions
In this presentation we will simply ensure that you can do either of the above steps separately.
Then in the next presentation, we will put it all together, so we can convert any units into any others.

8. (1) Converting between … Molarity and mass/volume
(a) Molarity
Mass/volume
e.g. convert 0.05M aspirin to mg/100ml. (RMM aspirin = 180)
1M = (RMM) g/L 1M = 180g/L 0.05M = 180 x 0.05g/L = 9g/L = 9,000mg/L = 900mg/100ml

9. (1) Converting between … Molarity and mass/volume
(b) Mass/volume
Molarity
e.g. convert aspirin (450mg/L) to mM. (RMM aspirin = 180)
(RMM) mg/L = 1mM 180mg/L = 1mM 1mg/L = 1/180mM 450mg/L = 450/180mM = 2.5mM

10. (1) Converting between … Molarity and mass/volume
Hint: When converting to or from a molar concentration always start by defining 1M (or 1mM etc).
If converting from a molarity, start with:- 1M = 180g/L or 1mM = 180mg/L etc
If converting to a molarity, start with:- 180g/L = 1M or 180mg/L = 1mM etc
(Above all assumes RMM = 180)

11. (1) Converting between … Molarity and mass/volume
Example questions
1) Re-express 25micromolar aspirin (RMM 180) in units of microgram/ml.
2) Re-express 0.72mg/100ml aspirin (RMM 180) in micromolar units

12. (1) Converting between … Molarity and mass/volume
Answer 1
Re-express 25micromolar aspirin (RMM 180) in units of microgram/ml.
1microM = 180microgram/L 25microM = 180 x 25microgram/L = 4,500microgram/L = 4.5microgram/ml

13. (1) Converting between … Molarity and mass/volume
Answer 2
Re-express 0.72mg/100ml aspirin (RMM 180) in micromolar units
Get rid of the awkward 100ml 0.72mg/100ml = 7.2mg/L
180mg/L = 1mM 1mg/L = 1/180mM 7.2mg/L = 7.2/180mM = 0.04mM = 40micromolar

14. (2) Converting between … %(w/v) and mass/volume
(a) %(w/v)
Mass/volume
e.g. convert 0.9%(w/v) NaCl to mg per 5ml.
0.9%(w/v) = 0.9g/100ml = 900mg/100ml = 9mg/ml = 45mg per 5ml

15. (2) Converting between … %(w/v) and mass/volume
(b) Mass/volume
%(w/v)
e.g. convert NaCl (9g/L) to %(w/v).
9g/L = 0.9g/100ml = 0.9%(w/v)

16. (2) Converting between … %(w/v) and mass/volume
Hint: When converting to a concentration expressed as %(w/v), the secret is to get everything into g and ml units and then adjust so that the value is x g/100ml. You then have the answer as a %.

17. (2) Converting between … %(w/v) and mass/volume
Example questions
1) Re-express 5.5%(w/v) sodium chloride in units of mg/ml
2) Re-express 0.045g per 5ml sodium chloride in units of %(w/v).

18. (2) Converting between … %(w/v) and mass/volume
Answer 1
Re-express 5.5%(w/v) sodium chloride in units of mg/ml
5.5% = 5.5g/100ml = 55g/L = 55mg/ml

19. (2) Converting between … %(w/v) and mass/volume
Answer 2
Re-express 0.045g per 5ml sodium chloride in units of %(w/v).
0.045g per 5ml = 0.9g/100ml = 0.9%(w/v)

20. (3) Converting between … ppm and mass/volume
(a) ppm
Mass/volume
e.g. convert fluoride (5ppm) to mg/100ml.
1ppm = 1mg/L 5ppm = 5mg/L = 0.5mg/100ml

21. (3) Converting between … ppm and mass/volume
(b) Mass/volume
ppm
e.g. convert fluoride (800 microgram/L) to ppm.
1mg/L = 1ppm 800mg/L = 800ppm 800 microgram/L = 0.8ppm

22. (2) Converting between … ppm and mass/volume
Hint: When converting to a concentration expressed as ppm, the secret is to get everything into mg and Litre units and then adjust so that the value is x mg/L. You then have the answer as ppm.

23. (3) Converting between … ppm and mass/volume
Example questions
1) Re-express 35microgram/100ml fluoride in units of ppm
2) Re-express 2.5ppm fluoride in units of microgram/ml

24. (3) Converting between … ppm and mass/volume
Answer 1
Re-express 35microgram/100ml fluoride in units of ppm
35microgram/100ml = 350microgram/L = 0.35mg/L = 0.35ppm

25. (3) Converting between … ppm and mass/volume
Answer 2
Re-express 2.5ppm fluoride in units of microgram/ml
2.5ppm = 2.5mg/L = 2.5microgram/ml

26. (4) Converting between … Ratio and mass/volume
(a) Ratio
Mass/volume
e.g. convert adrenaline (1 in 200,000) to microgram/ml.
1 in 200,000 = 1g/200,000ml = 1mg/200ml = 5mg/L = 5microgram/ml

27. (4) Converting between … Ratio and mass/volume
(b) Mass/volume
Ratio
e.g. convert adrenaline (500 microgram/100ml) to a ratio
500microgram/100ml = 1mg/200ml = 1g/200,000ml = 1 in 200,000

28. (4) Converting between … Ratio and mass/volume
Hint: When converting to a concentration expressed as a ratio, the secret is to get everything into gram and ml units and then adjust so that the value is 1g/ x ml. You then have the answer as a ratio.

29. (4) Converting between … Ratio and mass/volume
Example questions
1) Re-express adrenaline (5mg/L) as a ratio.
2) Re-express adrenaline (1 in 200,000) in units of mg/100ml.

30. (4) Converting between … Ratio and mass/volume
Answer 1
Re-express adrenaline (5mg/L) as a ratio.
5mg/L = 5g/1,000L = 5g/1,000,000ml = 1g/200,000ml = 1 in 200,000

31. (4) Converting between … Ratio and mass/volume
Answer 2
Re-express adrenaline (1 in 200,000) in units of mg/100ml.
1 in 200,000 = 1g/200,00ml = 1mg/200ml = 0.5mg/100ml

32. What you should be able to do
Re-express a concentration quoted in any of the following units:- - molarity - %(w/v) - ppm - ratio in units of mass/volume
Vice versa