Pharmaceutical Calculations (2)

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Pharmaceutical Calculations (2)
Re-expressing simple mass/volume concentrations
Phil Rowe Liverpool School of Pharmacy
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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-
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Pharmaceutical calculations 2
Mass/volume
Molarity(w/v)ppmRatio
Molarity(w/v)ppmRatio
Current presentation Pharmaceutical Calculations
(2) deals only with inter-conversions within
this category. i.e. one mass/volume into
another.
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Pharmaceutical calculations 3
Mass/volume
Molarity(w/v)ppmRatio
Molarity(w/v)ppmRatio
The next presentation Pharmaceutical
Calculations (3) will deal with interconversions
EITHER from mass/volume to another system OR from
another system to mass/volume
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Pharmaceutical calculations 4
Mass/volume
Molarity(w/v)ppmRatio
Molarity(w/v)ppmRatio
Then Pharmaceutical Calculations (4) will deal
with inter-conversions from any system to any
other, using mass/volume as an intermediate step
where necessary.
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Inter-converting concentrations expressed as
mass/volume
Tips
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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.
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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
litres25mg per 5ml 5mg/ml
5,000mg/L Then convert the mass to
grams5,000mg/L 5g/L
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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, dont 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
100ml2,500microgram/L 250microgram/100ml
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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.)

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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 wouldnt recommend it!) Convert
micrograms to grams via mg 1.5microgram/0.1ml
0.0015mg/0.1ml
0.0000015g/0.1ml Convert the
volume to litres0.0000015g/0.1ml 0.000015g/ml
0.015g/L
Profusion of zeros makes arithmetic errors very
likely!
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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
mg15microgram/ml 0.015mg/ml Use the
increase/decrease both units rule0.015mg/ml
0.015g/L
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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
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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
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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
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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
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Examples of inter-converting mass/volume
concentrations
Answer 5 Re-express 40mg per 5ml in units of
g/L 40mg per 5ml 8mg/mlUse Increase/decrease
both units rule8mg/ml 8g/L
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Examples of inter-converting mass/volume
concentrations
Answer 6 Re-express 35mg/L in units of g/L Only
mass units change35mg/L 0.035g/L
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Examples of inter-converting mass/volume
concentrations
Answer 7 Re-express 50mg/ml in units of g/L Use
Increase/decrease both units rule50mg/ml
50g/L
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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
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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
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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 ng7,500pg/ml 7.5ng/ml
0.0075microgram/ml
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Examples of inter-converting mass/volume
concentrations
Answer 11 Re-express 60microgram per 5ml in units
of mg per 5ml Only mass units change60microgram
per 5ml 0.06mg per 5ml
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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
microgram0.004mg/ml 4microgram/ml
4,000ng/ml
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What you should be able to do

• Re-express a concentration quoted in units of
  mass/volume in any other units of mass/volume