Pharmaceutical Calculations (4)

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Pharmaceutical Calculations (4)
General inter-conversions
Phil Rowe Liverpool School of Pharmacy
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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
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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.
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Six examples worked out for you
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(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
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(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)
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(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
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(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 12,000
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(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
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(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
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Now some for you to try
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Examples of general conversions
Question 1 Re-express 0.0007(w/v) cyanocobalamin
in units of ppm
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Examples of general conversions
Question 2 Re-express adrenaline (1 in 200,000)
in micromolar units (RMM adrenaline 183.2)
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Examples of general conversions
Question 3 Re-express 42micromolar fluoride as
ppm. (RMM fluoride 19)
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Examples of general conversions
Question 4 Re-express buprenorphine (1 in 4,000)
as a (w/v)
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Examples of general conversions
Question 5 Re-express 20ppm lead as a ratio.
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Examples of general conversions
Question 6 Re-express 2mM strychnine
hydrochloride (RMM 406.9) as a (w/v)
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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.
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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
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Examples of general conversions
Answer 3 Re-express 42micromolar fluoride as ppm.
(RMM fluoride 19) Stage 1 Convert to
mass/volume1micromolar 19microgram/L42micromol
ar 19 x 42microgram/L
798microgram/L Stage 2 Convert to ppm798
microgram/L 0.8mg/L
0.8ppm
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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)
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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.
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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)
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What you should be able to do

• Inter-convert concentrations quoted in any of
  the following units- - mass/volume -
  molarity - (w/v) - ppm - ratio