pharmaceutical calculations (3)

Pharmaceutical Calculations (3)Inter-converting

mass/volume units with any other

Phil Rowe Liverpool School of Pharmacy

Inter-conversionsWe 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 …

Inter-conversionsMost 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.

Inter-conversions

Mass/volume

Molarity %(w/v)

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.

The remaining 5 methods of expressing concentration can however all be inter-converted reasonably easily.

Inter-conversions – The general idea

Proceed in two steps, using mass/vol as a ‘common currency’.

1) Convert initial units into mass/vol

2) Convert mass/vol to required final units

Molarity%(w/v)ppmRatio

Mass/volume Molarity%(w/v)ppmRatio

Inter-conversionsThe 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/L0.1mM = 18mg/L

Stage 2: Convert mass/vol units to ppm

1mg/L = 1 ppm18mg/L = 18ppm

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.

(1) Converting between … Molarity and mass/volume

(a) Molarity Mass/volume

1M = (RMM) g/L1M = 180g/L0.05M = 180 x 0.05g/L = 9g/L = 9,000mg/L = 900mg/100ml

e.g. convert 0.05M aspirin to mg/100ml. (RMM aspirin = 180)

(1) Converting between … Molarity and mass/volume

(b) Mass/volume Molarity

(RMM) mg/L = 1mM180mg/L = 1mM1mg/L = 1/180mM450mg/L = 450/180mM = 2.5mM

e.g. convert aspirin (450mg/L) to mM. (RMM aspirin = 180)

(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 or1mM = 180mg/L etc

• If converting to a molarity, start with:-180g/L = 1M or180mg/L = 1mM etc

(Above all assumes RMM = 180)

(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

(1) Converting between … Molarity and mass/volume

Answer 1

Re-express 25micromolar aspirin (RMM 180) in units of microgram/ml.

1microM = 180microgram/L25microM = 180 x 25microgram/L = 4,500microgram/L = 4.5microgram/ml

(1) Converting between … Molarity and mass/volume

Answer 2

Re-express 0.72mg/100ml aspirin (RMM 180) in micromolar unitsGet rid of the awkward 100ml0.72mg/100ml = 7.2mg/L

180mg/L = 1mM1mg/L = 1/180mM7.2mg/L = 7.2/180mM = 0.04mM = 40micromolar

(2) Converting between … %(w/v) and mass/volume

(a) %(w/v) Mass/volume

0.9%(w/v) = 0.9g/100ml = 900mg/100ml = 9mg/ml = 45mg per 5ml

e.g. convert 0.9%(w/v) NaCl to mg per 5ml.

(2) Converting between … %(w/v) and mass/volume

(b) Mass/volume %(w/v)

9g/L = 0.9g/100ml = 0.9%(w/v)

e.g. convert NaCl (9g/L) to %(w/v).

(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 %.

(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).

(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

(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)

(3) Converting between … ppm and mass/volume

(a) ppm Mass/volume

1ppm = 1mg/L5ppm = 5mg/L = 0.5mg/100ml

e.g. convert fluoride (5ppm) to mg/100ml.

(3) Converting between … ppm and mass/volume(b) Mass/volume ppm

1mg/L = 1ppm800mg/L = 800ppm800 microgram/L = 0.8ppm

e.g. convert fluoride (800 microgram/L) to ppm.

(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.

(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

(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

(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

(4) Converting between … Ratio and mass/volume

(a) Ratio Mass/volume

1 in 200,000 = 1g/200,000ml = 1mg/200ml = 5mg/L = 5microgram/ml

e.g. convert adrenaline (1 in 200,000) to microgram/ml.

(4) Converting between … Ratio and mass/volume

(b) Mass/volume Ratio

500microgram/100ml = 1mg/200ml = 1g/200,000ml = 1 in 200,000

e.g. convert adrenaline (500 microgram/100ml) to a ratio

(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.

(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.

(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

(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

What you should be able to do

• Re-express a concentration quoted in any of the following units:- - molarity - %(w/v) - ppm - ratioin units of mass/volume

• Vice versa